Seismological constraints on the down-dip shape of normal faults

Seismological constraints on the down-dip shape of normal faults Summary We present a seismological technique for determining the down-dip shape of seismogenic normal faults. Synthetic models of non-planar source geometries reveal the important signals in teleseismic P and SH waveforms that are diagnostic of down-dip curvature. In particular, along-strike SH waveforms are the most sensitive to variations in source geometry, and have significantly more complex and larger-amplitude waveforms for curved source geometries than planar ones. We present the results of our forward-modelling technique for 13 earthquakes. Most continental normal-faulting earthquakes that rupture through the full seismogenic layer are planar and have dips of 30°–60°. There is evidence for faults with a listric shape from some of the earthquakes occurring in two regions; Tibet and East Africa. These ruptures occurred on antithetic faults, or minor faults within the hanging walls of the rifts affected, which may suggest a reason for the down-dip curvature. For these earthquakes, the change in dip across the seismogenic part of the fault plane is ≤30°. Body waves, Earthquake source observations, Dynamics and mechanics of faulting 1 INTRODUCTION It is not known whether major earthquake-generating normal faults are dominantly planar, or whether the dip of the fault changes with depth so that they have significant curvature. Seismic reflection profiles and geological exposures commonly reveal both listric and planar normal faults in sedimentary units. There is ongoing debate regarding whether faults with steep surface dips flatten into subhorizontal detachment horizons around the depth of the brittle-ductile transition (e.g. Velasco et al. 2010). High-resolution bathymetric studies have revealed in great detail the corrugated, domed footwalls exposed in oceanic core complexes, but the geometrical evolution of these structures, and whether or not they slip in earthquakes, remains enigmatic (Escartín et al. 2008; MacLeod et al. 2009; Smith et al. 2014). The loss in resolution of geodetic techniques (e.g. GPS and InSAR) at depth, together with the non-uniqueness involved in inverting surface measurements for fault geometry and slip, means that it is difficult, using geodetic techniques, to determine the down-dip shape of seismogenic faults, particularly at the depths at which earthquakes nucleate. In this paper, we present a seismological technique for constraining the down-dip curvature of active normal faults. The advantage of using seismology is that it sheds light on the shape of the seismogenic part of the fault at the time it was active, and the technique is only sensitive to the parts of the fault that are important in generating earthquakes. The wider implications of this work lie in several areas. First, normal fault curvature controls the geometry of basins and affects mechanisms of crustal thinning. For example, curved faults bounding regions which deform internally can accommodate significantly more extension than a series of planar faults bounding rigid crustal blocks (Jackson & McKenzie 1983; Jackson & White 1989). Second, the processes that initiate, drive, impede and finally stop earthquake ruptures are intrinsically linked to the physical attributes of faults (e.g. Sibson 1985; Scholz 1998), therefore knowledge of the shape of faults is important in investigations of fault rheology and mechanics. Third, the down-dip shape of normal faults has implications for assessing earthquake hazard, from the perspective of the location of energy release and the down-dip width of fault available to rupture. First, we discuss our approach and model set-up, and how our method differs from that of Braunmiller & Nábělek (1996), on whose work we build. We then present a synthetic example to highlight the features of teleseismic waveforms that are indicative of the presence or absence of down-dip curvature. Finally, we describe the application of our method to a catalogue of continental and oceanic normal-faulting events, and present the results of the modelling along with a discussion of the constraints on the down-dip shape of the fault for each earthquake. Though we focus on normal faults, our technique is equally applicable to thrust earthquakes. 2 DATA AND FAULT MODELS If an earthquake occurs on a fault plane with down-dip curvature, as the rupture proceeds through time and advances across the fault surface, different portions of the fault, which have different dips, will contribute to the signal recorded at a seismometer. If the rupture is of sufficient duration then the moment contributions from different parts of the fault plane, which contain information about the source geometry, are separate enough in time to be detected in seismic waveforms. We exploit this complexity in the waveforms in this study. We define down-dip fault curvature as the difference in dip between the upper and lower portions of the fault. A listric geometry, that is, decreasing dip with increasing depth, is defined as having negative curvature; a convex-up surface has positive curvature; and a plane has zero curvature. A curved surface can be approximated by a series of connected planes with different dips. For simplicity, and building upon the work of Braunmiller & Nábělek (1996), we model earthquakes using three subsources (Fig. 1). In this model, the rupture surface is approximated by three planes (tri-planar), and the subsources are offset in time and space, to represent the progress of the rupture through different parts of the fault. Figure 1. View largeDownload slide Setup of tri-planar model geometry. Left: Initial planar model. For real earthquakes, the moment obtained for the point-source centroid (red dot) parameters is used to estimate the dimensions of a planar rupture patch of dimensions L × L. Right: We use three-subsource models to simulate curvature: the planar rupture is broken into three rectangular patches, of dimensions L × $$\frac{L}{3}$$, and a subsource centroid (numbered orange dots) is located at the centre of each. The relative timing of each subsource is determined by the size of the estimated rupture plane and a rupture velocity of 2.5 km s−1. The length of the source time function (STF) for each subsource (orange triangles labelled with numbered orange dot) is constrained so that the overall duration of the three-subsource event is the same as the length of the source time function obtained for the point-source inversion (red triangle). Figure 1. View largeDownload slide Setup of tri-planar model geometry. Left: Initial planar model. For real earthquakes, the moment obtained for the point-source centroid (red dot) parameters is used to estimate the dimensions of a planar rupture patch of dimensions L × L. Right: We use three-subsource models to simulate curvature: the planar rupture is broken into three rectangular patches, of dimensions L × $$\frac{L}{3}$$, and a subsource centroid (numbered orange dots) is located at the centre of each. The relative timing of each subsource is determined by the size of the estimated rupture plane and a rupture velocity of 2.5 km s−1. The length of the source time function (STF) for each subsource (orange triangles labelled with numbered orange dot) is constrained so that the overall duration of the three-subsource event is the same as the length of the source time function obtained for the point-source inversion (red triangle). Our study is restricted to events with magnitudes >Mw 5.5, below which we commonly do not see clear waveforms in broadband seismograms, and <Mw 6.5, above which the waveform complexity resulting from the rupture of multiple fault segments results in trade-offs with the fault geometry. Unlike field-based, InSAR or seismic reflection studies, our resolution is not limited by the depth extent of the rupture, or by geographic considerations (such as site access, errors due to topographic or meteorological effects, or whether the epicentre is on land or under the oceans). The seismological technique we present is a forward-modelling method, based on the comparison of recorded waveforms with synthetic waveforms for tri-planar faults with planar and curved geometries. To construct the geometry of the three subsources for the tri-planar models, we estimate the dimensions of the rupture plane using the seismic moment of the centroid solution and fault scaling laws (as described below). For real earthquakes, we invert for these centroid parameters using P- and SH-waveform inversions, using the MT5 programme of Zwick et al. (1994) and McCaffrey et al. (1991) (discussed further below). For the synthetic earthquake, discussed in the next section, the value of the moment (and other source parameters) is chosen to be representative of the real earthquakes that we investigate. We refer to this initial centroid solution, on which the tri-planar models are based, as the planar model or single-plane solution. We estimate the dimensions of a square fault plane using the seismic moment and a displacement-to-length ratio of 5 × 10−5 (Scholz 1982). This rupture plane is broken into three rectangular patches of length, L, and down-dip width, $$\frac{L}{3}$$ (Fig. 1). The centroids of the respective subsources are positioned at the centre of each subplane, and each subsource has a moment of $$\frac{M_0}{3}$$. The relative positions and depths of the three subsources are recalculated for each degree of fault curvature that we model, while enforcing that the combined parameters of the three-source models average to the centroid solution, and that the structural contiguity of the fault model is maintained. As we prescribe each subsource with the same moment, the moment-averaged source parameters are also the same as the centroid solution. These steps ensure that our models are of physically plausible fault ruptures that are consistent with the overall centroid parameters of the events. All subsources have strike and rake fixed to that of the centroid solution. The dip of the middle subsource is fixed to that of the centroid solution. To simulate down-dip curvature, the dips of the upper and lower subsources are varied in tandem, such that the average dip of the tri-planar model is the same as for the single-plane solution. The degree of curvature is the difference in dip between the upper and lower subsources (−80° is very listric, +80° is very convex-up). Dips are altered in 5° increments, resulting in models at 10° intervals of curvature, up to a maximum degree of curvature where the dip of the upper or lower subsource approaches vertical or horizontal. Rupture of a curved surface is simulated by setting a time delay between subsources. We assume rupture nucleates at depth (initiating with the deepest subsource, S1) and propagates upwards. We show in Appendix B in the Supporting Information the effects of rupture propagating from the surface downwards. The time delay between subsources is calculated using the model geometry and assuming a rupture velocity, vr, of 2.5 km s−1. Each subsource has the same source time function, defined by a single triangular element, the duration of which is set so that the overall duration of the tri-planar event matches that of the centroid solution. We carried out synthetic tests (Appendix B in the Supporting Information) that show that variations in the timing of moment-release (due to our choice of rupture velocity and source time function parameters) have only a minor effect on the waveforms compared to changes in the down-dip geometry, and that our assumptions therefore do not affect our ability to resolve down-dip curvature. 2.1 Previous work Braunmiller & Nábělek (1996) also used teleseismic body waveform data to examine the fault geometries in 6 normal-faulting earthquakes in Greece and western Turkey. They used three-subsource models to produce synthetic waveforms for rupture on faults with down-dip curvature, and found that SH wave shapes and polarities were strongly affected by down-dip curvature when observed at teleseismic stations lying approximately along-strike of the event. We build on their work to produce a new set of synthetic waveforms and present a technique for both identifying and constraining down-dip curvature from teleseismic data. We replicated the synthetic study of Braunmiller & Nábělek (1996) using the MT5 programme of Zwick et al. (1994) (which is detailed in Appendix A in the Supporting Information), and our method reproduces the differences in amplitude and polarity in the initial parts of P and SH waveforms between a planar rupture model and a curved fault plane (with 40° listric curvature) that they observed. We improve upon the study of Braunmiller & Nábělek (1996) by investigating the effects of the choice of model rupture velocity, source duration and propagation direction, which we describe in Appendix B in the Supporting Information. Different to Braunmiller and Nábělek, we also include the important and high-amplitude depth-phases (i.e. near-source surface reflections) in our synthetic waveforms, and we prescribe the subsource parameters such that our curved fault models are consistent with the centroid solution obtained through body waveform inversion. 3 SYNTHETICS We examine the effect on P and SH waveforms of changes in the down-dip geometry of a synthetic Mw 5.9 normal-faulting event, by computing synthetic seismograms for a suite of tri-planar models covering a −80° to +80° range of curvatures (Fig. 2), using the MT5 algorithm of McCaffrey et al. (1991) and Zwick et al. (1994). The synthetic stations were chosen to represent the typical epicentral distance ranges of teleseismic data used in body waveform inversions, and the magnitude of the synthetic earthquake was chosen to be similar to the real events discussed later. Figs 3 and 4 compare the synthetic SH and P waveforms for a planar fault model, with those for curved fault models at ±10°, 20°, 40°, 60° and 80° curvature. We investigate how waveform amplitude and complexity is affected by fault geometry and station location, and discuss the implications of our results for examining real data. Figure 2. View largeDownload slide Geometry of synthetic Mw 5.9 normal-faulting event and curvature models. Left: Red dot marks the point-source location (centroid) of the synthetic earthquake at a centroid depth, zc, on a cross-section perpendicular to the event strike. The source parameters are shown above and the P and SH focal spheres are to the left. The point-source event is envisaged to occur on a planar fault surface with the same parameters as the source centroid (which we later refer to as the planar model, or single-plane solution). The centroid sits at the centre of this fault plane (black line). Right: Tri-planar models are generated by splitting the single-plane solution into three equal-sized rectangles, the dips of which are varied in order to simulate curvature. The cross-sections are perpendicular to strike and show the down-dip geometry of the tri-planar models in grey, relative to the single-plane solution centroid depth (dashed red line). Rupture of a tri-planar fault model is simulated using three point sources (subsources) with $$\frac{1}{3}$$ the moment of the single-plane solution, which are offset in space and time from each other. In the model rupture propagates from the bottom up, so the first subsource (1) is the deepest, the last (3) the shallowest. The location of each subsource centroid (orange dot) is at the centre of each of the three rectangular planes. Each cross-section is labelled with the amount of model down-dip curvature (difference in dip between the upper and lower planes) on the top right. On the bottom left, each cross-section has a P focal sphere showing the nodal planes of subsource 1 (solid), 2 (dashed) and 3 (dotted). Figure 2. View largeDownload slide Geometry of synthetic Mw 5.9 normal-faulting event and curvature models. Left: Red dot marks the point-source location (centroid) of the synthetic earthquake at a centroid depth, zc, on a cross-section perpendicular to the event strike. The source parameters are shown above and the P and SH focal spheres are to the left. The point-source event is envisaged to occur on a planar fault surface with the same parameters as the source centroid (which we later refer to as the planar model, or single-plane solution). The centroid sits at the centre of this fault plane (black line). Right: Tri-planar models are generated by splitting the single-plane solution into three equal-sized rectangles, the dips of which are varied in order to simulate curvature. The cross-sections are perpendicular to strike and show the down-dip geometry of the tri-planar models in grey, relative to the single-plane solution centroid depth (dashed red line). Rupture of a tri-planar fault model is simulated using three point sources (subsources) with $$\frac{1}{3}$$ the moment of the single-plane solution, which are offset in space and time from each other. In the model rupture propagates from the bottom up, so the first subsource (1) is the deepest, the last (3) the shallowest. The location of each subsource centroid (orange dot) is at the centre of each of the three rectangular planes. Each cross-section is labelled with the amount of model down-dip curvature (difference in dip between the upper and lower planes) on the top right. On the bottom left, each cross-section has a P focal sphere showing the nodal planes of subsource 1 (solid), 2 (dashed) and 3 (dotted). Figure 3. View largeDownload slide Synthetic SH waveforms generated for a Mw 5.9 normal-faulting earthquake, with a strike, average dip and rake of 000°/45°/270°. SH waveforms were generated at the synthetic stations shown here, at an epicentral distance of 55°, which is typical of the epicentral distance ranges of teleseismic data used in body waveform inversions. The station position (intersection of the ray path with the lower hemisphere projection of the focal sphere) is shown with a solid black dot on the SH focal sphere. Synthetic waveforms are plotted around the SH focal sphere (which shows the nodal surfaces for an event with 0° down-dip curvature) at the approximate station azimuth, and labelled with the alphanumeric station name (bold) and azimuth. Synthetic SH waveforms, generated from tri-planar models, are shown for events with ±10°, 20°, 40°, 60° and 80° curvature in blue. Solid blue lines are for negative curvature (listric), dotted blue for positive curvature (convex up). Model curvature increases radially outwards, that is, the inner ring shows waveforms for models with 10° curvature, the outer 80°. Synthetics for curved models (blue) are plotted on top of a synthetic single-plane, 1-source centroid model (black) with 0° curvature. Figure 3. View largeDownload slide Synthetic SH waveforms generated for a Mw 5.9 normal-faulting earthquake, with a strike, average dip and rake of 000°/45°/270°. SH waveforms were generated at the synthetic stations shown here, at an epicentral distance of 55°, which is typical of the epicentral distance ranges of teleseismic data used in body waveform inversions. The station position (intersection of the ray path with the lower hemisphere projection of the focal sphere) is shown with a solid black dot on the SH focal sphere. Synthetic waveforms are plotted around the SH focal sphere (which shows the nodal surfaces for an event with 0° down-dip curvature) at the approximate station azimuth, and labelled with the alphanumeric station name (bold) and azimuth. Synthetic SH waveforms, generated from tri-planar models, are shown for events with ±10°, 20°, 40°, 60° and 80° curvature in blue. Solid blue lines are for negative curvature (listric), dotted blue for positive curvature (convex up). Model curvature increases radially outwards, that is, the inner ring shows waveforms for models with 10° curvature, the outer 80°. Synthetics for curved models (blue) are plotted on top of a synthetic single-plane, 1-source centroid model (black) with 0° curvature. Figure 4. View largeDownload slide Synthetic P waveforms generated for a Mw 5.9 normal-faulting earthquake, with a strike, average dip and rake of 000°/45°/270°. Key as for Fig. 3, but curved model synthetics are in red and the P focal sphere is shown, with compressional quadrants shaded in grey. The P stations are at an epicentral distance of 60°, and the station position (intersection of the ray path with the lower hemisphere projection of the P focal sphere) is shown with a solid black dot. Figure 4. View largeDownload slide Synthetic P waveforms generated for a Mw 5.9 normal-faulting earthquake, with a strike, average dip and rake of 000°/45°/270°. Key as for Fig. 3, but curved model synthetics are in red and the P focal sphere is shown, with compressional quadrants shaded in grey. The P stations are at an epicentral distance of 60°, and the station position (intersection of the ray path with the lower hemisphere projection of the P focal sphere) is shown with a solid black dot. 3.1 Synthetic waveforms The synthetic seismograms at stations within ∼30° of fault strike have significantly more complex SH waveforms for all curved fault models than for the planar case, even those with only ±10° curvature (Fig. 3). The SH waveforms at these stations also have much higher amplitudes for curved models, and along-strike nodal stations (stations S1 and S13) show waveforms whereas none are present for the planar model. These effects are more pronounced for models with greater curvature. At stations with azimuths at high angle to strike, SH waveforms for curved models are not as complex, and have similar amplitudes to (and are harder to distinguish by eye from) those for the planar fault model. However, for models with high curvature, the dip of the lowermost plane (subsource S1) may be high or low enough that the nodal plane for this subsource lies on the opposite side of where these stations plot on the focal sphere, that is, the station projects to a different quadrant of the SH focal sphere. In this case the SH waveform shows a small amplitude peak with the opposite sign to that of the waveform for the planar model (Fig. 5). At nodal stations perpendicular to strike (stations S6 and S20), there is no SH arrival in any model. These features arise because the SH nodal planes cut through the centre of the focal sphere, passing through parts of the focal sphere that are sampled by seismometers at teleseismic distances. Changes in dip within the source rotate the SH focal sphere such that the nodal planes sweep across the region in the lower hemisphere projection covered by the take-off angles of teleseismic waves. This effect makes SH waveforms highly sensitive to changes in down-dip curvature. Small changes in curvature therefore have a large effect on the SH waveforms at stations within ∼30° of fault strike. Therefore, to detect down-dip curvature in real earthquakes it is essential to include SH data from stations in the along-strike directions. This finding is consistent with the observations made by Braunmiller & Nábělek (1996). Figure 5. View largeDownload slide The effect of a high degree of model curvature on synthetic waveforms. This figure illustrates that stations at azimuths >30° from strike may also be sensitive to down-dip curvature. Left: Model fault geometry and P and SH focal spheres for synthetic single-source planar Mw 5.9 event, as for Fig. 2. Example synthetic waveforms for stations P7 and S9 are shown to the right of the appropriate focal sphere. For both the P and SH focal spheres, quadrants with positive waveform arrivals are shaded grey, and the appropriate station ray path intersection is marked with a black dot. Station labels are as for Figs 3 and 4. Right: Tri-planar models with 60° down-dip curvature, as for Fig. 2. The synthetic P (red) and SH (blue) waveforms for stations P7 and S9 are shown to the right; solid line for negative curvature, dotted for positive. The synthetic waveforms are the signal resulting from the summed contribution of the radiated energy from all three subsources, however we show the P and SH focal spheres for only the first (deepest) subsource, S1, which affects the initial part of the waveform. The quadrants with positive arrivals from S1 are shaded and the intersection of the ray path for station P7 and S9 on the focal sphere is shown with a black dot. The dip of S1 affects the position of the nodal surfaces relative to the station position, and the resultant polarity of the initial part of the waveform. Figure 5. View largeDownload slide The effect of a high degree of model curvature on synthetic waveforms. This figure illustrates that stations at azimuths >30° from strike may also be sensitive to down-dip curvature. Left: Model fault geometry and P and SH focal spheres for synthetic single-source planar Mw 5.9 event, as for Fig. 2. Example synthetic waveforms for stations P7 and S9 are shown to the right of the appropriate focal sphere. For both the P and SH focal spheres, quadrants with positive waveform arrivals are shaded grey, and the appropriate station ray path intersection is marked with a black dot. Station labels are as for Figs 3 and 4. Right: Tri-planar models with 60° down-dip curvature, as for Fig. 2. The synthetic P (red) and SH (blue) waveforms for stations P7 and S9 are shown to the right; solid line for negative curvature, dotted for positive. The synthetic waveforms are the signal resulting from the summed contribution of the radiated energy from all three subsources, however we show the P and SH focal spheres for only the first (deepest) subsource, S1, which affects the initial part of the waveform. The quadrants with positive arrivals from S1 are shaded and the intersection of the ray path for station P7 and S9 on the focal sphere is shown with a black dot. The dip of S1 affects the position of the nodal surfaces relative to the station position, and the resultant polarity of the initial part of the waveform. The shape of synthetic P waveforms is much less sensitive to station azimuth and degree of curvature (Fig. 4), because the P-wave nodal planes of normal-faulting earthquakes cut through parts of the focal sphere that are distant from the take-off angles of seismic waves received at stations at teleseismic distances. There are small changes in the width and location of peaks in the waveform, however the main effect is on the amplitude of the waveform, particularly at stations that lie perpendicular to strike. Considering the true (E-dipping) nodal plane that represents our synthetic normal fault, for positive curvature models (convex), stations that lie in the down-dip (East) direction have smaller amplitude and more complex P waveforms than stations in the up-dip (West) direction. The opposite is true for negative curvature (listric) models. This effect is stronger for models with greater curvature, as the dip of one subsource is steep and the projection of the relevant nodal plane passes close to stations in the focal sphere, resulting in less energy being received and smaller amplitudes being recorded at those stations (Fig. 5). 3.2 Implications for modelling real events If seismogenic faults have only small degrees of down-dip curvature, the diagnostic signals (SH waveform complexity and/or initial low-amplitude peaks with the wrong polarity) will only be detectable at stations lying at positions at or very close to along-strike. Identifying the shapes of the waveforms correctly requires picking the precise onset times for P and SH arrivals. Stations that lie near an SH nodal surface receive a lower energy signal and show lower amplitude SH arrivals in seismograms than stations lying elsewhere in the SH focal sphere. Along-strike broadband data must be examined carefully for clear arrivals that can be distinguished from the background noise. Picking the wrong SH arrival time would skew any attempt to resolve down-dip curvature. For this reason we pick the waveform arrivals by hand, and when modelling real earthquakes we include data from as many along-strike stations as possible, so that one wrong or uncertain SH arrival pick will not adversely distort the results. 4 APPLICATION TO REAL EARTHQUAKES We present a seismological, forward-modelling technique for determining the down-dip geometry of earthquake-generating dip-slip faults, based upon the synthetic models described above. We have applied this method to a catalogue of continental and oceanic events and present the results of the modelling in the next section. 4.1 Event selection We performed body-waveform inversions for a catalogue of normal-faulting events (Table 1), from a wide range of extensional environments. We then selected suitable earthquakes on which to apply our seismological technique for determining down-dip curvature. Events were chosen based on (1) magnitude, (2) source time function, and (3) station signal-to-noise ratio and distribution. Events need to be large enough (≥Mw 5.5) that the seismic contributions from different parts of the rupture plane are distinct and separate in space and time; and small enough (≤Mw 6.5) that the approximation of the earthquakes as a point source (centroid), on which the initial waveform inversion is based, is still valid. Factors such as changes in the rupture propagation direction, uneven moment release, or earthquake doublets, have a large effect on the resultant waveforms recorded at teleseismic distances. This level of complexity leads to multiple trade-offs with down-dip fault geometry. Therefore we select events that are one-segment ruptures, with relatively simple source time functions. In order to perform the modelling effectively there must be a good azimuthal distribution of stations at teleseismic distances, a high density of stations at close to along-strike azimuths, and seismograms with clear arrivals and a high signal-to-noise ratio. Table 1. Events used in this study. Event  Best-fit centroid parameters      Name  Region  Lat  Long  yymmdd  hh:mm:ss  Mw  M0  Strike  Dip  Rake  Depth      (°)  (°)        (N m)  (°)  (°)  (°)  (km)  L’Aquila  Italy  42.370  13.319  090406  01:32:42  6.2  2.60 × 1018  134  46  261  4.6  Colfiorito  Italy  43.079  12.781  970926  09:40:27  5.8  6.67 × 1017  123  40  270  5.4  Aegion  Greece  38.440  22.307  950615  00:15:50  6.2  2.34 × 1018  290  27  305  11.6  Grevena  Greece  40.143  21.717  950513  08:47:14  6.4  4.39 × 1018  245  39  271  11.2  Simav  Turkey  39.128  29.070  110519  20:15:25  5.8  7.02 × 1017  116  37  274  9.5                7.02 × 1017  291  53  269  9.5  Palu  Indonesia  −1.085  119.878  090302  00:03:41  5.6  2.82 × 1017  313  39  273  7.4                2.82 × 1017  128  51  265  7.4  MAR  Mid-Atlantic  26.552  −44.629  070301  23:11:52  5.9  7.84 × 1017  204  50  289  7    Ridge            7.84 × 1017  024  42  293  7  Gakkel  Arctic Sea  84.913  99.618  050306  05:21:40  6.2  2.95 × 1018  133  44  264  9.4  Ridge              2.95 × 1018  315  48  267  9.4  Zhongba 1  Tibet  30.681  83.650  040711  23:08:44  6.2  2.23 × 1018  163  40  268  10.5  Zhongba 2  Tibet  30.481  83.657  050407  20:04:40  6.2  2.26 × 1018  165  44  266  7.8  Karonga 1  Malawi  −10.158  33.825  091206  17:36:37  5.7  4.44 × 1017  164  38  270  4.2  Karonga 2  Malawi  −9.983  33.819  091208  03:08:57  5.8  5.77 × 1017  146  44  248  5.4  Karonga 3  Malawi  −10.019  33.831  091219  23:19:17  5.9  8.25 × 1017  158  43  262  5.3  Event  Best-fit centroid parameters      Name  Region  Lat  Long  yymmdd  hh:mm:ss  Mw  M0  Strike  Dip  Rake  Depth      (°)  (°)        (N m)  (°)  (°)  (°)  (km)  L’Aquila  Italy  42.370  13.319  090406  01:32:42  6.2  2.60 × 1018  134  46  261  4.6  Colfiorito  Italy  43.079  12.781  970926  09:40:27  5.8  6.67 × 1017  123  40  270  5.4  Aegion  Greece  38.440  22.307  950615  00:15:50  6.2  2.34 × 1018  290  27  305  11.6  Grevena  Greece  40.143  21.717  950513  08:47:14  6.4  4.39 × 1018  245  39  271  11.2  Simav  Turkey  39.128  29.070  110519  20:15:25  5.8  7.02 × 1017  116  37  274  9.5                7.02 × 1017  291  53  269  9.5  Palu  Indonesia  −1.085  119.878  090302  00:03:41  5.6  2.82 × 1017  313  39  273  7.4                2.82 × 1017  128  51  265  7.4  MAR  Mid-Atlantic  26.552  −44.629  070301  23:11:52  5.9  7.84 × 1017  204  50  289  7    Ridge            7.84 × 1017  024  42  293  7  Gakkel  Arctic Sea  84.913  99.618  050306  05:21:40  6.2  2.95 × 1018  133  44  264  9.4  Ridge              2.95 × 1018  315  48  267  9.4  Zhongba 1  Tibet  30.681  83.650  040711  23:08:44  6.2  2.23 × 1018  163  40  268  10.5  Zhongba 2  Tibet  30.481  83.657  050407  20:04:40  6.2  2.26 × 1018  165  44  266  7.8  Karonga 1  Malawi  −10.158  33.825  091206  17:36:37  5.7  4.44 × 1017  164  38  270  4.2  Karonga 2  Malawi  −9.983  33.819  091208  03:08:57  5.8  5.77 × 1017  146  44  248  5.4  Karonga 3  Malawi  −10.019  33.831  091219  23:19:17  5.9  8.25 × 1017  158  43  262  5.3  Hypocentre locations and times were retrieved from the ISC; location data for events occurring prior to 2009 is from the EHB bulletin. The centroid parameters were obtained through body waveform inversion in this study. If the true fault plane is not known, parameters for both nodal planes are shown. View Large 4.2 Procedure The main stages of the method are as follows: Perform a body waveform inversion to obtain point-source centroid focal parameters, moment and source time function for the chosen event. Use centroid solution to estimate source dimensions and set up geometry of tri-planar models. Generate synthetic waveforms for tri-planar models with a range of down-dip curvatures. Compare model synthetics with observed seismograms to constrain down-dip curvature. 4.2.1 Body waveform inversion procedure Teleseismic data was downloaded using the IRIS (Incorporated Research Institutions for Seismology) Wilber III system and P and SH arrivals were manually picked on broadband seismograms. A full list of stations we used, along with their network codes, is found in Appendix C in the Supporting Information. We used data from all networks with suitable records, and restrict the station epicentral distance range to 30°–90° and 30°–80° for P and SH data respectively. This ensures that the P and S signals are not affected by arrivals of waves that have diffracted, reflected or travelled through the core, and that they have not been affected by shallow lithospheric phases (e.g. Moho head waves). The broadband seismograms are first deconvolved from their instrumental response, and then reconvolved with the response of a long-period (15–100 s) World-Wide Standardized Seismograph Network (WWSSN) instrument. This procedure means that earthquakes of magnitudes Mw 5.0–6.5 can be modelled as a finite-duration rupture at a point source (centroid). We then used the MT5 programme of Zwick et al. (1994), based on the algorithm of McCaffrey & Abers (1988) and McCaffrey et al. (1991), to jointly invert P and SH waveforms for earthquake source parameters (strike, dip, rake, centroid depth, moment and source time function). Given an initial model (taken from the GCMT catalogue) and our arrival time picks, we generate synthetic P and SH waveforms and solve iteratively for the source parameters that give a minimum misfit between the observed waveform and synthetics within the inversion window. The inversion window starts at the picked arrival time and the length is set for P and SH data so that it includes only the body waveforms and their depth phases, and no additional phases. P, pP and sP phases are modelled on vertical component seismograms and S and sS phases on transverse component seismograms. Synthetics are computed based on the source parameters and calculated take-off angles (with amplitudes corrected for geometrical spreading and attenuation). We solve for the strike, dip and rake of the source (which dominantly affect the shape of the waveforms), and the centroid depth and source time function (which chiefly control the length and amplitude of the waveforms). The source is constrained to be purely double-couple. A full description of this procedure can be found in Taymaz et al. (1991) and Nábělek (1984), and similar waveform inversion techniques are used extensively in the literature (Bergman & Solomon 1985; Braunmiller & Nábělek 1996; Craig et al. 2011; Sloan et al. 2011). This technique refines the accuracy of source parameter estimates made by routine catalogues such as the GCMT, particularly for the centroid depth. The degree to which each focal parameter can be resolved is determined by fixing a parameter, for example, depth, at a series of values away from the best fit, and re-inverting for all other parameters. The fit of the synthetic to the observed seismograms is then compared at successive values of the fixed parameter to determine the range over which a reasonable fit has been found. Typical errors are ±4 km for depth, ±10° for strike, ±5° for dip and ±10° for rake (Molnar & Lyon-Caen 1989; Taymaz et al. 1991; Craig et al. 2014). We used a simple crustal velocity model consisting of a half-space of Vp = 6.5 km s−1, Vs = 3.7 km s−1, ρ = 2800 kg m−3. Discrepancies between the model velocity structure and the actual (unknown) velocity profile at the location of each earthquake (e.g. due to shallow, low-velocity sedimentary layers above the source) affect the estimated centroid depth, but not the geometry of the nodal planes (e.g. Bergman & Solomon 1985; Nelson et al. 1987; Taymaz et al. 1990; Middleton & Copley 2013). The lack of sensitivity of the orientation of the focal planes to the velocity model results from the constraint that the source be comprised of double-couple subsources, and the simultaneous inversion of P and SH waves at all stations (Fredrich et al. 1988). 4.2.2 Constraining down-dip geometry Having obtained a centroid solution for the earthquakes we study, we use the same procedure as that for the synthetic event (described above) to set up tri-planar models with down-dip curvature (Fig. 1). The MT5 programme (Zwick et al. 1994) is used to generate synthetic P and SH waveforms for the curved tri-planar models at all stations used in the initial inversion. As a first indicator of down-dip curvature in the source, we look for complex SH waveform shapes with higher than expected amplitudes at stations within 30° of the along-strike azimuth. We then attempt to put constraints on the down-dip geometry by determining the range of down-dip curvature models that produce an acceptable fit to all the waveform data. For each SH station (including those >30° from strike) and for every tri-planar curvature model, synthetic waveforms are compared to the observed seismogram, and the synthetic from the planar solution, in order to determine whether the synthetics produced with a curved fault plane yield a better fit to the observed data, and over what range of curvature there is an acceptable fit to the waveforms. We calculate the variance of the residuals between the recorded signals and the synthetic waveforms within the inversion window, and plot graphs of variance against curvature for SH-waveforms recorded at stations within 30° of strike. The important observations are how the misfit varies as a function of curvature for each station. The waveforms are visually inspected to check for features that may skew the plots or produce a misleading variance, such as synthetics that fit most of the waveform but have the wrong first motion (which would give a low variance of the residuals, despite having the wrong first motion), or the presence of noise in some seismograms (which may result in a high variance, even if the synthetic broadly fits the observed waveform). In order to constrain the down-dip curvature of an event, we examine the visual fit of synthetics together with the graphs of variance against curvature. If down-dip curvature is present, we expect to see a consistent agreement across the SH stations, with improved fits at curved models; though we expect the stations >30° from strike to be much less sensitive. Finally, to determine a preferred model, and to avoid biases due to uneven azimuthal distribution of stations or biases in favour of fitting SH-waveforms at the expense of P-waveforms, we examine the fit of the curved models as a whole, to all P- and SH-waveforms. Looking for common features among multiple stations is diagnostic of source, rather than receiver, effects. 5 RESULTS We present the results of body-waveform inversions (Table 1) and the constraints on the down-dip geometry (Table 2) of 13 events. We begin by presenting the source parameters and modelling results for a well-studied event, the 2009 L’Aquila earthquake. There are multiple independent geophysical inversion and aftershock studies for this event, against which we compare the results of our seismological technique, and test that the method is robust. We then describe the constraints on the down-dip geometry for the additional events that we studied; seven in the main text and five others in Appendix D in the Supporting Information. Table 2. Results from down-dip curvature modelling. Plain grey bars delimit range of down-dip curvature investigated for each event. Grey boxes indicate the extent to which down-dip geometry can be constrained—they show cross-sections of the model geometries that produce synthetics with an acceptable fit to recorded broadband seismograms. The red line marks the modelled centroid depth with respect to the model fault plane. Red dots mark the centroids for the events that show no resolvable evidence for down-dip curvature; orange dots mark the subsource centroids for our preferred tri-planar fault model for events where there is evidence for down-dip curvature. If the true fault plane (FP) is not known, modelling results for both nodal planes are shown (NP1 and NP2).     View Large We first detail the events with no evidence of down-dip curvature and describe to what extent the down-dip geometry can be constrained. We then describe the results for two groups of earthquakes (the Karonga sequence, East Africa, and the Zhongba earthquakes, Tibet) for which there is evidence of down-dip curvature in some events, and present the solution for our preferred model. For every event, the full solution of the initial body-waveform inversion (planar) and the solution for our preferred model geometry (if different) is in Appendix E in the Supporting Information, modelling of auxiliary planes (if the true fault plane is not known) is presented in in Appendix F in the Supporting Information, and synthetic P- and SH-waveforms for all models and stations are presented in Appendix G in the Supporting Information. 5.1 Test case: the 2009 April 6 L’Aquila earthquake, Italy The 2009 April 6 Mw 6.2 L’Aquila earthquake ruptured part of an NW–SE-trending fault system (Fig. 6) running through the central Apennines. Body-waveform seismology (e.g. Walters et al. 2009; Pondrelli et al. 2010; Scognamiglio et al. 2010; Herrmann et al. 2011), InSAR (e.g. Atzori et al. 2009; Walters et al. 2009), GPS (Anzidei et al. 2009; Cheloni et al. 2010; Serpelloni et al. 2011), GPS and strong motion (Cirella et al. 2009) and aftershock location (Chiarabba et al. 2009; Chiaraluce et al. 2011; Valoroso et al. 2013) studies agree on the first order source parameters (normal motion with a small component of right-lateral slip on a fault striking 127°–144°, dipping 45°–56° to the southwest), which are consistent with the those presented in this study (Fig. 7a). Geologic mapping and analysis of coseismic surface ruptures (EMERGEO Working Group 2009; Falcucci et al. 2009; Boncio et al. 2010; Bonini et al. 2014), up-dip surface projections of fault plane solutions and analysis of the ground displacements measured by InSAR and GPS (Atzori et al. 2009; Walters et al. 2009) demonstrate that the main shock ruptured the Paganica Fault. There is some disagreement on whether coseismic slip only occurred up-dip of the 8–10 km hypocentre (Herrmann et al. 2011; D’Agostino et al. 2012) or whether there was also a deeper slip patch between 9–14 km (Cirella et al. 2009; Cheloni et al. 2010), however most of the slip was shallower than the hypocentre. Our modelled centroid depth of 5 km, and the depth extent of model fault geometries (1–10 km) are consistent with the estimates of the extent of the fault plane in the source parameter studies mentioned above (1–15 km depth). Figure 6. View largeDownload slide Map of the Abruzzo Region, central Apennines, Italy (a) Regional map. The perimeter of box B is shown in dark grey. (b) Topography of the 2009 April 6 L’Aquila earthquake epicentral region. The focal mechanism obtained in this study is shown offset from the EHB location. Settlements (black squares) and major features are named. Known and active faults are in black, after Roberts & Michetti (2004); Chiarabba et al. (2009); EMERGEO Working Group (2009). The surface trace of the main-shock fault, the Paganica Fault (Pf), is marked in red. Part of the Campotosto Fault (Cf) was activated by an aftershock. Figure 6. View largeDownload slide Map of the Abruzzo Region, central Apennines, Italy (a) Regional map. The perimeter of box B is shown in dark grey. (b) Topography of the 2009 April 6 L’Aquila earthquake epicentral region. The focal mechanism obtained in this study is shown offset from the EHB location. Settlements (black squares) and major features are named. Known and active faults are in black, after Roberts & Michetti (2004); Chiarabba et al. (2009); EMERGEO Working Group (2009). The surface trace of the main-shock fault, the Paganica Fault (Pf), is marked in red. Part of the Campotosto Fault (Cf) was activated by an aftershock. Figure 7. View largeDownload slide Down-dip curvature modelling results for the 2009 April 6 L’Aquila earthquake.Figure overleaf. (a) Event location map, focal mechanism and distribution of stations. Centroid parameters obtained through body waveform inversion (planar solution) are shown above the map; the focal mechanism is plotted at the location of the epicentre. Stations used in the inversion are named. (b) Plots of variance against curvature for SH-stations within 30° of strike. Variance was calculated for the residuals between synthetic and recorded SH-waveforms, within the inversion window used to obtain the initial centroid solution, for each station and tri-planar model. (c) Down-dip curvature modelling results and synthetics for select stations. Cross-sections through model fault geometry are shown above. The range of curvature constrained by the data is highlighted in black, the best-fit model geometry in blue. Synthetic waveforms calculated for three-subsource models for select stations are plotted below (red for P-, blue for SH-waveforms), on top of the recorded waveform (black). For the 0°-curvature model, the synthetic from the point-source planar solution (grey) is plotted on top of the recorded waveform. The station positions are shown on the relevant focal sphere. Figure 7. View largeDownload slide Down-dip curvature modelling results for the 2009 April 6 L’Aquila earthquake.Figure overleaf. (a) Event location map, focal mechanism and distribution of stations. Centroid parameters obtained through body waveform inversion (planar solution) are shown above the map; the focal mechanism is plotted at the location of the epicentre. Stations used in the inversion are named. (b) Plots of variance against curvature for SH-stations within 30° of strike. Variance was calculated for the residuals between synthetic and recorded SH-waveforms, within the inversion window used to obtain the initial centroid solution, for each station and tri-planar model. (c) Down-dip curvature modelling results and synthetics for select stations. Cross-sections through model fault geometry are shown above. The range of curvature constrained by the data is highlighted in black, the best-fit model geometry in blue. Synthetic waveforms calculated for three-subsource models for select stations are plotted below (red for P-, blue for SH-waveforms), on top of the recorded waveform (black). For the 0°-curvature model, the synthetic from the point-source planar solution (grey) is plotted on top of the recorded waveform. The station positions are shown on the relevant focal sphere. Of eight stations within 30° of strike, six have SH-synthetics with a good fit to the observed data for the planar solution (e.g. RAYN, WCI; Fig. 7c). Models with >10° of curvature produce synthetic SH-waveforms for which the overall waveform shape and/or peak amplitudes and polarities are significantly different to the observed waveforms at these stations, that is, the recorded data precludes fault geometries of ≥20° of curvature for this event. Recorded waveforms at the other two stations in this azimuth range (MSEY and DWPF) are not fit well by the planar solution synthetics (most likely due to station noise of unknown origin); varying the down-dip geometry does not yield a better fit. Synthetics generated from some curved models yield fits that are equally good or better than the planar case for individual stations (e.g. WCI +30°; Fig. 7c). However, as all the stations record the same event, it is important to find a model that is consistent with the recorded P and SH waveforms at the majority of stations, rather than a model that yields excellent fits at only some of the along-strike SH stations. There is no consistent trend among the stations as a whole favouring either positive or negative curvature, and minor improvements in fit at individual stations are likely due to fitting noise. This feature is demonstrated by the differing minimum-variance model for each of the SH-stations within 30° of strike (Fig. 7b). The average variance of the residuals for these stations is lowest for a model with 0° curvature (i.e. planar). SH-stations at azimuths >30° from strike have wider ranges of down-dip curvature over which the model produces synthetics with an acceptable fit to the recorded data (e.g. TIXI; Fig. 7c); those that lie roughly perpendicular to strike are insensitive to changes in model geometry (e.g. HIA). Increasing the down-dip curvature produces only small amplitude changes in synthetic P-waveforms at most stations (e.g. TSUM), but large changes in stations with high take-off angles and that lie near a P nodal plane (e.g. KBS, ARU). For these stations, models with >20° curvature produce synthetic P-waveforms with larger amplitudes compared to the other stations (and compared to the planar model). We do not observe this azimuthal variation in the recorded P-waveform data. Taken as a whole, all these observations combined mean that we infer that the L’Aquila earthquake ruptured a planar fault. If there is a change in dip in the down-dip direction, it is not more than ±10°. Chiarabba et al. (2009), Chiaraluce et al. (2011) and Valoroso et al. (2013) relocated large catalogues of foreshocks and aftershocks associated with the L’Aquila main shock. All three studies showed tight clustering of the relocated events along a plane dipping ∼50° to the southwest. Their close spatial alignment argues for the Paganica Fault having a planar down-dip geometry, consistent with the results of our analysis of teleseismic body waveforms and down-dip curvature modelling. The corroboration of our result by other geophysical methods demonstrates the robustness of the technique. Based on modelling of regional broadband waveforms and extensive finite-fault models of velocity and accelerometer data, Herrmann et al. (2011) concluded that the major moment release in the L’Aquila earthquake occurred up-dip of and, 4–7 s after, the rupture initiation at the hypocentre. Cirella et al. (2009) jointly invert strong motion and GPS data and find that slip propagated up-dip with a velocity of 2.2–2.8 km s−1. These independent analyses further support our model assumptions; an upwards-propagating rupture, and the choice of a 2.5 km s−1 rupture velocity. 5.2 Planar ruptures Our analysis shows that the majority of normal-faulting earthquakes that are large enough to rupture through the seismogenic layer occur on planar faults. These events showed no strong evidence for down-dip curvature, had dips between 30°–60°, and could be constrained to be planar to within ±20°. We describe in detail below the 1997 September 26 Colfiorito earthquake, Italy, and the 1995 May 13 Grevena earthquake, northern Greece. A full description of our results for the additional planar ruptures (1995 June 15 Aegion earthquake, Greece; 2011 May 19 Simav earthquake, Turkey; 2009 March 2 Palu earthquake, Indonesia; 2007 March 1 earthquake, Mid-Atlantic Ridge; 2005 March 6 earthquake, Gakkel Ridge, Arctic Sea) is presented in Appendix D in the Supporting Information. 5.2.1 The 1997 September 26 Colfiorito earthquake, Italy The 1997 September 26 Colfiorito earthquake was largest of six 5 < Mw <6 events that struck the Abruzzo region (Fig. 8) of central Italy during September–October 1997, known as the Umbria-Marche sequence (Chiaraluce 2003). Our modelled centroid dip (40°) agrees well with that obtained by other authors through waveform inversion (Ekström et al. 1998; Morelli et al. 2000), the alignment of relocated aftershocks (Amato et al. 1998; Deschamps et al. 2000; Chiaraluce 2003) and various geodetic analyses (Hunstad et al. 1999; Stramondo et al. 1999; Salvi et al. 2000; De Martini et al. 2003). We obtain a centroid depth of 5 km, consistent with the 4–5.5 km depth of maximum slip obtained by Lundgren & Stramondo (2002) through joint inversion of GPS and InSAR data, and infer the depth extent of faulting to extend between >1 km to <8 km. This depth distribution is supported by observations that very little slip reached the surface (Cinti et al. 1999; Cello et al. 2000; Basili & Meghraoui 2001), aftershock hypocentres delineate a cut-off in seismicity beneath 8–9 km depth (Deschamps et al. 2000; Chiaraluce 2003), and forward-modelling of coseismic displacements on a fault plane with a similar depth extent adequately reproduces measured GPS and InSAR surface displacements (Hunstad et al. 1999; Salvi et al. 2000). Figure 8. View largeDownload slide Map of the Umbria-Marche Region, central Apennines, Italy.(a) Regional map. The perimeter of box B is shown in grey. (b) Topography of the 1997 September 26 Colfiorito earthquake epicentral region, overlaid with a simplified fault map (after Chiaraluce 2003). Settlements (black squares) and major features are named. Pre-exisiting, inactive thrusts are in grey, SW-dipping normal faults in black, and the trace of the major NE-dipping, Alto-Tiberino normal fault (ATF) is bold. The focal mechanism obtained in this study is shown offset from the EHB location. Figure 8. View largeDownload slide Map of the Umbria-Marche Region, central Apennines, Italy.(a) Regional map. The perimeter of box B is shown in grey. (b) Topography of the 1997 September 26 Colfiorito earthquake epicentral region, overlaid with a simplified fault map (after Chiaraluce 2003). Settlements (black squares) and major features are named. Pre-exisiting, inactive thrusts are in grey, SW-dipping normal faults in black, and the trace of the major NE-dipping, Alto-Tiberino normal fault (ATF) is bold. The focal mechanism obtained in this study is shown offset from the EHB location. Our planar solution yields synthetics with moderately good fits to the shape and amplitude of SH-waveforms recorded at all stations within 30° of strike (Fig. 9c). Models with ≥20° of curvature produce complex synthetic SH-waveforms that do not fit the observed data at these 6 stations, particularly for stations lying SE of the event (e.g. MSEY; Figs 9a and c). The average variance of SH-stations within 30° of strike is lowest for models with 0° to +10° curvature (Fig. 9b). For stations >30° from strike, the SH-waveforms are less sensitive to changes in the down-dip geometry (e.g. ALE; Fig. 9c), and individual stations have a wider range of curvatures over which the model generates a synthetic that fits the recorded waveform equally well. In general, increasing down-dip curvature has only a small effect on the amplitude of P-waveforms (e.g. FURI, FFC; Fig. 9c). Stations with high take-off angles and that lie near a P nodal plane (e.g. KBS, ARU; Fig. 9c) exclude geometries with ≥30° of curvature; for these geometries the initial dip is high or low enough that the P-synthetic produced at these stations may have the wrong initial polarity and/or a substantially different amplitude compared to P-synthetics for other stations and the observed data. There is no evidence to suspect down-dip curvature for this event. The data allows for a maximum of ±10° curvature; outside of this range the fit of synthetics at key stations deteriorates. We therefore infer that the Colfiorito event ruptured a planar fault, to within −10°/+10° degrees. Figure 9. View largeDownload slide Down-dip curvature modelling results for 1997 September 26 Colfiorito earthquake. Caption as for Fig. 7. Figure 9. View largeDownload slide Down-dip curvature modelling results for 1997 September 26 Colfiorito earthquake. Caption as for Fig. 7. Some workers have described the faults in the Colfiorito area as having listric geometries (Boncio & Lavecchia 2000; Barchi & Mirabella 2009), because the coseismic faults do not project to the surface while maintaining their 35–45° dips, and exposed fault planes have measured dips of ∼60–70° (Cello et al. 2000; Chiaraluce et al. 2005). Additionally, it has been suggested that the normal faults bottom-out below ∼8 km, either onto pre-existing, low-angle structures (e.g. the Alto-Tiberino Fault; Boncio & Lavecchia 2000) or into horizons of Triassic evaporites (Mirabella et al. 2008; Barchi & Mirabella 2009), though there is a dearth of good quality seismic reflection data to test these suggestions (Chiaraluce et al. 2005; Mirabella et al. 2008). Although co-seismic displacements do seem to be taken up on high-angle fault strands at the surface—evinced by diffuse aftershock seismicity in the upper 1 km (Chiaraluce et al. 2004), complex patterns of surface deformation (e.g. Stramondo et al. 1999; Cello et al. 2000; Salvi et al. 2000; Vittori et al. 2000) and reconstruction of levelling-line displacements (Basili & Meghraoui 2001)—modelling of surface displacements indicates that the high-angle structures accommodating this slip only extend to ∼500 m beneath the surface (Basili & Meghraoui 2001). Therefore the faults activated in the Umbria-Marche sequence are not listric in the sense of a smooth decrease in dip with depth. Instead, the analysis presented here, and the close alignment of aftershock hypocentres, indicates that the faults are planar at the depths where they rupture in earthquakes (Amato et al. 1998; Chiaraluce 2003), that is, there is less than ±10° change in dip with depth between ∼2–8 km. The hypocentres of the larger events in the sequence, including the 1997 September 26 event modelled here, are located at depths close to the base of these aftershock clusters (Stramondo et al. 1999; Barba & Basili 2000), at the same depth as foreshock activity (Cattaneo et al. 2000), and close to the inferred intersection with pre-existing low-angle faults (Chiaraluce et al. 2005; Mirabella et al. 2008). A lack of seismicity at depths >8 km suggest this decollement, if it exists, is not seismically active. Both the modelling in this study and detailed studies by other workers establish that extension in the seismogenic layer is accommodated by rupture on planar faults in the Colfiorito region. 5.3 The 1995 May 13 Grevena earthquake, Greece On the 1995 May 13, a destructive Mw 6.4 normal-faulting earthquake hit northern Greece, approximately equidistant from the towns of Grevena and Kozani (Fig. 10). We obtained centroid source parameters consistent with other estimates from body waveform seismology (Hatzfeld et al. 1998), inversion of horizontal GPS displacements (Clarke et al. 1997) and InSAR studies (Resor et al. 2005) to within 10°, and the strike is similar to that measured for the only mapped fault with conspicuous surface rupture (the 250°-striking Paleochori Fault; Meyer et al. 1996). We obtained the same centroid depth (11 km) as Hatzfeld et al. (1998), and our estimated depth extent of the rupture (6–15 km) is consistent with their 14.2 km main-shock hypocentre and the distribution of aftershocks between 5–15 km. Figure 10. View largeDownload slide Map of Northern Greece.(a) Simplified tectonic setting. Major plate-bounding faults in black: NAF, North Anatolian Fault; HA, Hellenic Arc; CA, Cyprus Arc. The perimeter of box B is shown in grey. (b) Local topography map. The focal mechanism obtained for the 1995 May 13 Grevena earthquake in this study is shown offset from the EHB location. Settlements (black squares) and tectonic features are named in black. Simplified active faults, retraced after Resor et al. (2005), are delineated in black; location of surface fissures and ruptures mapped by Meyer et al. (1996) are in white; the trace of the major surface rupture, the Paleochori Fault (PF) is shown in red. Figure 10. View largeDownload slide Map of Northern Greece.(a) Simplified tectonic setting. Major plate-bounding faults in black: NAF, North Anatolian Fault; HA, Hellenic Arc; CA, Cyprus Arc. The perimeter of box B is shown in grey. (b) Local topography map. The focal mechanism obtained for the 1995 May 13 Grevena earthquake in this study is shown offset from the EHB location. Settlements (black squares) and tectonic features are named in black. Simplified active faults, retraced after Resor et al. (2005), are delineated in black; location of surface fissures and ruptures mapped by Meyer et al. (1996) are in white; the trace of the major surface rupture, the Paleochori Fault (PF) is shown in red. The planar solution from the body-waveform inversion generates synthetics that fit the shape and amplitude of SH-waveforms very well at 11 of 12 SH-stations within 30° of strike. There is therefore no indication that there may be down-dip curvature. Models with positive curvature produce complex SH-synthetics at these stations which have very different waveform shapes and/or the wrong initial polarity when compared with the observed waveforms (e.g. AAK; Fig. 11c)—this precludes any positive down-dip curvature. Models with negative curvature produce synthetic SH-waveforms with similar shapes to the recorded waveforms. Increasing the degree of negative curvature mainly affects the amplitudes, not the shape, of the synthetic waveforms, and yields a better fit of the resultant synthetic to the data for some stations (e.g. KURK −30°). However, for SH stations at azimuths 30°–65° from strike, models with more than −20° curvature generate synthetics with amplitudes much larger than the recorded data (e.g. SJG −40°). Synthetics for SH stations at azimuths >65° from strike have poor fits irrespectively of model fault geometry, as they lie close to an SH nodal surface and so have a poor signal-to-noise ratio. Stations with high take-off angles and lying roughly perpendicular to strike plot near one of the P nodal planes in a lower hemisphere projection. Small increases in negative curvature produce synthetic P-waveforms with the wrong initial polarity at these stations (e.g. NAI, ATD), ruling out more than −20° down-dip curvature. Plots of variance against curvature are skewed towards negative-curvature models (Fig. 11b), reflecting the extremely high misfits for positive-curvature models. Overall, both P and SH waveform data support a planar geometry and the down-dip curvature can be constrained to between −20° and 0°. Figure 11. View largeDownload slide Down-dip curvature modelling results for 1995 May 31 Grevena earthquake. Caption as for Fig. 7. Figure 11. View largeDownload slide Down-dip curvature modelling results for 1995 May 31 Grevena earthquake. Caption as for Fig. 7. Most published inversions suggest that the maximum slip and majority of the moment-release occurred on the deeper parts of a fault plane with parameters consistent with the focal mechanisms obtained using body waveform data (e.g. Meyer et al. 1996; Clarke et al. 1997; Rigo et al. 2004; Resor et al. 2005). It is therefore not surprising that the best-fit model from the teleseismic waveform modelling in this study is planar. The ability of the forward models to detect down-dip curvature is limited to the parts of the coseismic fault plane that produce a significant contribution to the overall moment. Therefore we do not expect to resolve the up-dip rupture propagation onto high-angle surface-breaking fault strands (if they exist) if they did not produce large offsets. It is likely that the deep main-shock fault connects in some way with the steeper exposed fault planes mapped at the surface, but the nature and geometry of this linkage is unclear. The availability of many different and detailed geologic, geodetic and seismological data sets has allowed several studies (e.g. Meyer et al. 1996; Resor et al. 2005) to build up a detailed picture of the fault network in the Kozani–Grevena region, and given the large moment-release it is not surprising that multiple fault strands, particularly those up-dip and in the hanging wall of the main shock, were activated by the Grevena earthquake. Despite the fine-scale complexity of the fault system, the results of the down-dip curvature modelling in this study suggest that the major coseismic displacements are consistent with rupture on a planar structure. 5.4 Ruptures with down-dip curvature Based on the analysis of the SH waveforms at stations within 30° of strike, there is a strong indication of down-dip curvature in 4 events. Two events (a Mw 5.7 and a Mw 5.8) were from an earthquake sequence that occurred on the Karonga Fault system, Lake Malawi, and which culminated in a Mw 5.9 (included here for completeness, but which does not show any evidence of down-dip curvature). The other two were 2004 and 2005 Mw 6.2 events that occurred in the Lunggar Rift region, Tibet. 5.4.1 The 2004 and 2005 Zhongba events, Lunggar Rift, Tibet We studied two Mw 6.2 normal-faulting events that occurred in Zhongba county in the Xizang region of southwestern Tibet, China (Fig. 12). Just north of the Indus suture the tectonics of southern Tibet are characterized by extension across N–S-trending grabens (Armijo et al. 1986). The 2004 July 11 and 2005 April 7 earthquakes described here were located in one of these active grabens, the South Lunggar Rift. Figure 12. View largeDownload slide Map of southwest Tibet. (a) Regional map and simplified structure. Major normal faults in red, strike-slip faults in black and suture zones dashed in white. NLR, North Lunggar Rift; SLR, South Lunggar Rift. Country boundaries are in grey, as is the perimeter of box B. The inset globe shows the location of box A in red. SRTM topography is coloured according to the scale on the right. (b) Topography and structure of the South Lunggar Rift. Focal mechanisms obtained in this study are offset from their EHB locations (red dot) and labelled with a date (yymmdd) identifier. Faults in red, after Styron et al. (2013). Outline of model fault planes and up-dip surface projections (green) from the uniform-slip InSAR models of Elliott et al. (2010) for the 2004 and 2005 events, and the 2008 doublet. Figure 12. View largeDownload slide Map of southwest Tibet. (a) Regional map and simplified structure. Major normal faults in red, strike-slip faults in black and suture zones dashed in white. NLR, North Lunggar Rift; SLR, South Lunggar Rift. Country boundaries are in grey, as is the perimeter of box B. The inset globe shows the location of box A in red. SRTM topography is coloured according to the scale on the right. (b) Topography and structure of the South Lunggar Rift. Focal mechanisms obtained in this study are offset from their EHB locations (red dot) and labelled with a date (yymmdd) identifier. Faults in red, after Styron et al. (2013). Outline of model fault planes and up-dip surface projections (green) from the uniform-slip InSAR models of Elliott et al. (2010) for the 2004 and 2005 events, and the 2008 doublet. The South Lunggar Rift is comprised of a ∼50 km wide central horst, the Surla Range, bounded on either side by the gentle west-dipping South Lunggar Detachment and steeper east-dipping Palung Co Fault (Styron et al. 2013). Small fault scarps are observed to cut glacial moraines along the northern portion of the Palung Co Fault (Styron et al. 2013), and the up-dip projections of InSAR-modelled fault planes for a 2008 normal-faulting doublet (Elliott et al. 2010) also coincide with the range front and mapped fault trace in the north, indicating that the fault is currently active. Elliott et al. (2010) performed a study of a series of large normal-faulting events in Tibet, including the two we model here, using InSAR and body waveform seismology. For both events, the surface deformation in InSAR interferograms was best fit by west-dipping faults located east of the Palung Co Fault (Elliott et al. 2010, and Fig. 12). The seismogenic thickness is ∼15 km in Tibet (Craig et al. 2012), and the magnitude and depth of the earthquakes suggest that they ruptured through most of the seismogenic crust. These two events seem to represent break-up of the hanging wall of the major basin-bounding Palung Co fault on antithetic faults. 2004 July 11 event. Synthetics from the planar solution obtained through body-waveform inversion fit SH-waveform data quite well at the nine stations within 30° of strike. However for the majority of these stations, the synthetics are consistently of a lower amplitude than the recorded signal, and do not match the fine detail of the waveform shape (the polarity of the small peaks in the initial part of the waveform) (e.g. OBN, ARU, SFJ; Fig. 13c). These small initial waveform peaks are a strong indication of down-dip curvature. Model geometries with some negative curvature (between −10° to −30°) consistently yield synthetics with better fits to the recorded waveform than for a planar model, particularly with respect to these details of SH-waveform shape and amplitude (e.g. ARU −20°, SFJ −30°). This improvement in fit is also reflected in the variance-curvature graphs for stations within 30° of strike (Fig. 13b); eight have minimum variances for models with negative curvature, and the average model variance is lowest for a model with −20° down-dip curvature. Figure 13. View largeDownload slide Down-dip curvature modelling results for the 2004 July 11 Zhongba earthquake. Caption as for Fig. 7. Figure 13. View largeDownload slide Down-dip curvature modelling results for the 2004 July 11 Zhongba earthquake. Caption as for Fig. 7. The shape and amplitude of SH-waveforms at all stations at azimuths >30° and <55° from strike are also better fit by synthetics from models with −10° to −30° curvature (e.g. MA2 −30°, GNI −20°; Fig. 13c). Stations at azimuths >55° from strike have complex, low-amplitude signals that are not well matched by any synthetics, due to the poor signal-to-noise ratio resulting from their being close to an SH nodal plane. From the synthetic modelling presented in Section 3, stations in this azimuth range are not expected to be sensitive to down-dip curvature. Models with any positive down-dip curvature produce synthetic SH-waveforms with complex wave shapes and initial peaks with the opposite polarity to the recorded signal at all stations within 47° of strike, ruling out any convex down-dip geometry for this event. For stations that plot near the E-dipping nodal plane in a lower hemisphere projection, models with −40° down-dip curvature or more produce synthetic P-waveforms with the wrong initial polarity (e.g. SSE, DAV; Fig. 13c). There is a good overall fit of both P and SH waveforms at models with −30° to 0° curvature. The results suggest that this event involves down-dip curvature, and the best-fit model is slightly listric, with −20° curvature. 2005 April 7 event. Synthetic SH-waveforms generated at five of six stations within 30° of strike for a model with planar down-dip geometry have much smaller amplitudes and different shapes compared to the recorded waveforms (e.g. KONO, KEV; Fig. 14c). Similar to the 2004 event, this is a strong indication of down-dip curvature. Synthetics generated from models with −30° to −10° negative down-dip curvature have very good fits to the data at these stations, in terms of the amplitude, overall shape and polarity of small initial peaks in the waveform (e.g. MBWA −30°, ARU −20°). The fit of the synthetics is significantly better for this range of negative-curvature models than for a planar model geometry. This feature is reflected in the shape of the graphs of variance against curvature for these stations, which have residual variances that tend to a minimum in this model range, and are lower than the variance for the planar model for 4 stations (Fig. 14b). In almost all cases the fit of synthetic SH-waveforms to the seismograms is very poor for all models with positive curvature. For strongly listric models (−40° down-dip curvature or more) synthetic SH-waveforms have very high amplitudes compared to the recorded waveforms, and the fit of the synthetic deteriorates with increasing negative curvature. The fit of synthetic P-waveforms at stations with high take-off angles and at azimuths that are roughly perpendicular to strike (e.g. MAJO, TATO) also becomes significantly worse in this range, as the synthetic waveform has the wrong initial polarity. For almost all stations at azimuths >30° and <50° from strike, models with −30° to −10° curvature also yield synthetics with a better fit to the recorded SH-waveform than synthetics from the planar model, in terms of both the detail of waveform shape and the amplitude of the peak. Based on the analysis of the SH waveforms, there is strong evidence for down-dip curvature in the range −10° to −30°. The best-fit model has −20° curvature. Figure 14. View largeDownload slide Down-dip curvature modelling results for the 2005 April 07 Zhongba earthquake.Caption as for Fig. 7. Figure 14. View largeDownload slide Down-dip curvature modelling results for the 2005 April 07 Zhongba earthquake.Caption as for Fig. 7. 5.4.2 The 2009 Karonga sequence, Lake Malawi We studied the three largest events (6th December Mw 5.7, 8th December Mw 5.8, and 19th December Mw 5.9) in an earthquake sequence that struck the Karonga region of northern Malawi, on the western shore of Lake Malawi, between November and December 2009 (Fig. 15). The rift basin is strongly asymmetric; the footwall of a steep west-dipping fault (the Livingstone Fault) forms a 2 km high escarpment on the eastern bank of the lake, and its hanging wall is broken up by minor west-dipping faults, mapped by offshore seismic reflection profiles (Flannery & Rosendahl 2009; Ebinger et al. 1999). The east-dipping Karonga Fault forms the westernmost boundary of the basin and divides the hilly topography and exposures of Precambrian to lower Palaeozoic basement rocks in the west from the flat alluvial plain in the east (Hamiel et al. 2012). Following the earthquake sequence, surface breaks were observed in an area north of Karonga city with no previous evidence of surface-rupturing faults, offsetting Quaternary sediments in the flat plain (Hamiel et al. 2012; Macheyeki et al. 2015). Biggs et al. (2010) used seismology and InSAR to demonstrate that the sequence occurred on shallow, west-dipping structures in the hanging wall of the Karonga Fault. It has been suggested that failure initiated on a favourably orientated pre-existing structure, and then migrated to adjacent planes of weakness as a result of static stress transfer (Fagereng 2013). Figure 15. View largeDownload slide Map of northern Lake Malawi.(a) Regional map of the southern part of the Western Branch of the East African Rift. Country boundaries are in grey, major normal faults mentioned in the text are in red. The traces of the Kanda (KF), Livingstone (LF) and Bilila-Mtakataka (BMF) Faults are after Versfelt & Rosendahl (1989), Jackson & Blenkinsop (1997) and Vittori et al. (1997), respectively. The perimeter of box B is shown in grey and the inset globe shows the location of box A in red. (b) SRTM30 topography of northern Lake Malawi (scale to top left). Focal mechanisms obtained in this study are offset from their EHB locations (red dot) and labelled with a date (yymmdd) identifier. The location of Karonga is marked with a black square; KFS is the Karonga Fault system. Faults, delineated in black, are retraced from Biggs et al. (2010); the surface ruptures of Macheyeki et al. (2015) are in white with a black outline (just N of Karonga). The trend of basement foliations are marked in purple, after Versfelt & Rosendahl (1989) Figure 15. View largeDownload slide Map of northern Lake Malawi.(a) Regional map of the southern part of the Western Branch of the East African Rift. Country boundaries are in grey, major normal faults mentioned in the text are in red. The traces of the Kanda (KF), Livingstone (LF) and Bilila-Mtakataka (BMF) Faults are after Versfelt & Rosendahl (1989), Jackson & Blenkinsop (1997) and Vittori et al. (1997), respectively. The perimeter of box B is shown in grey and the inset globe shows the location of box A in red. (b) SRTM30 topography of northern Lake Malawi (scale to top left). Focal mechanisms obtained in this study are offset from their EHB locations (red dot) and labelled with a date (yymmdd) identifier. The location of Karonga is marked with a black square; KFS is the Karonga Fault system. Faults, delineated in black, are retraced from Biggs et al. (2010); the surface ruptures of Macheyeki et al. (2015) are in white with a black outline (just N of Karonga). The trend of basement foliations are marked in purple, after Versfelt & Rosendahl (1989) 2009 December 19 event. Unlike the other earthquakes we modelled from this sequence (6th December Mw 5.7 and 8th December Mw 5.8 events), there was no evidence of down-dip curvature for this event. Of nine stations within 30° of strike, the planar solution from the body-waveform inversion generates synthetics with good fits to the shape and amplitude of SH-waveforms at five stations (e.g. MAW, TUE, KIEV; Fig. 16c). At the other four, the synthetic wave shape has a poorer fit and the amplitude is lower than the recorded data (e.g. TAM, BFO). Down-dip curvature modelling does yield synthetics with better fits than the planar model, for these stations. However, it also results in SH-synthetics with increasingly worse fits to the waveform data for the five stations that are well-matched by the initial planar solution. Positive-curvature models generate very different synthetic SH wave shapes, which in some cases have the wrong initial polarity compared to the recorded data (e.g. BFO +20°). Models with negative curvature produce synthetic SH-waveforms with high amplitudes, which yield individual best-fit models for some stations (e.g. BFO −30°), but very poor fits for others (e.g. MAW −30°, DPC −30°). The minimum-variance model for most of the ∼along-strike SH-stations is between −10° to +10° (Fig. 16b). The average is −10°, however this is most likely skewed by the result for EIL, for which the observed waveform data is not fit well by any model, irrespective of geometry, presumably due to noise in the data. Figure 16. View largeDownload slide Down-dip curvature modelling results for the 2009 December 19 Karonga earthquake.Caption as for Fig. 7. Figure 16. View largeDownload slide Down-dip curvature modelling results for the 2009 December 19 Karonga earthquake.Caption as for Fig. 7. SH-waveforms at stations at azimuths >30° from strike are less sensitive to down-dip curvature and are overall well-matched by the initial planar solution. Increasing degrees of down-dip curvature generates synthetics with poorer fits (e.g. XMIS, UOSS; Fig. 16c). The complexity, polarities and reduced amplitudes of synthetic P-waveforms at stations with high take-off angles and that lie at high angles from strike precludes geometries with >30° down-dip curvature (e.g. KAPI, RCBR). The overall fit of synthetic SH-waveforms is significantly worse outside the range −30° to +10°. We therefore suggest that this event in the Karonga sequence ruptured a planar fault. 2009 December 8 event. The planar solution from the body-waveform inversion generates synthetics with similar waveform shapes, but much smaller amplitudes than the recorded SH-waveform at all five stations within 30° of strike (e.g. TUE, IDI; Fig. 17c). This is a strong indication of down-dip curvature. Synthetics generated from models with negative down-dip curvature have excellent fits to the data at these stations, both for the waveform amplitude and shape, particularly in the −30° to −60° range. The fit of the synthetics is significantly better for this range of negative-curvature models than for a planar model geometry. This is reflected in the shape of the graphs of variance against curvature for these stations (Fig. 17b). For all five stations, models with negative down-dip curvature yield lower variances than that for the single-plane solution and their respective minimum variances lie in the range −50° to −20°. Figure 17. View largeDownload slide Down-dip curvature modelling results for the 2009 December 8 Karonga earthquake.Caption as for Fig. 7. Figure 17. View largeDownload slide Down-dip curvature modelling results for the 2009 December 8 Karonga earthquake.Caption as for Fig. 7. For stations at azimuths >30° from strike, there is a wide range of model geometries over which the fit of the synthetic (in terms of waveform shape and amplitude) to the observed SH-waveform is adequate. In general the fit is equally good or slightly better for negative-curvature models (e.g. SYO −30°; Fig. 17c), and equally good or slightly worse for positive-curvature models (e.g. SYO +10°). Although the overall fit of SH-synthetics is best for models with strong negative curvature (−50°), the fit of synthetic P-waveforms at stations with high take-off angles and at azimuths that are roughly perpendicular to strike (e.g. CHTO, DGAR and XMIS) becomes significantly worse as the synthetic waveforms have the wrong initial polarity. The overall fit of all P and SH synthetics is good for models with geometries in the −40° to −10° curvature range. Due to the location of this event, much of the region lying to the south and within the teleseismic distance range is covered by ocean (Fig. 17a), therefore there are large (∼90°) azimuth gaps in the S-wave data-coverage. It would be preferable to have a more even distribution of station data, particularly for SH-waveform data, however there is strong evidence from the SH-waveform data that does exist (particularly from the along-strike stations to the north, and the one SH-station to the south, SYO) that this event ruptured a fault with negative down-dip curvature. From this evidence, and considering the fit to all available P and SH waveforms, our preferred model is −30° curvature. 2009 December 6 event. The planar solution from the body-waveform inversion generates SH-synthetics with similar waveform shapes and amplitudes to the observed models for the 9 stations at azimuths within 30° of strike (e.g. GNI, KBA; Fig. 18c). There is therefore no strong indication of down-dip curvature. However, the minimum-variance model for all but one station has a geometry with negative curvature (Fig. 18b), and models with some negative curvature (−30° to −10°) produce synthetics with similarly good wave shapes and amplitudes as the synthetics for the planar model. For all stations at azimuths >30° from strike, models with strong negative curvature yield synthetics with a better fit to the recorded SH-waveform than synthetics from the planar model, in terms of both the detail of waveform shape and the amplitude of the peak (e.g. UOSS −50°, DBIC −50°). At stations with high take-off angles and at azimuths that are perpendicular to strike (e.g. UOSS, PALK and SHEL), synthetic P-waveforms have small amplitudes and initial peaks with the wrong polarity compared to the recorded waveforms for models with −40° or more down-dip curvature, ruling out an extremely listric fault geometry. The fit synthetic SH-waveforms deteriorates for all stations for models with increasing positive curvature. Figure 18. View largeDownload slide Down-dip curvature modelling results for the 2009 December 6 Karonga earthquake. Caption as for Fig. 7. Figure 18. View largeDownload slide Down-dip curvature modelling results for the 2009 December 6 Karonga earthquake. Caption as for Fig. 7. Due to the small size (Mw 5.7) and the location of this event, there is not a good azimuthal coverage of SH-stations at teleseismic distances (Fig. 18a), especially south of the event. There is a possibility that this event may have down-dip curvature, especially given its proximity to the 8th December event, however we are unable to constrain the geometry further than to say models with down-dip curvature in the range of −30° to +10° (including a planar geometry), give equally good overall fits to P and SH waveforms. 6 DISCUSSION As described in the sections above, the down-dip curvature modelling results suggest that continental normal-faulting earthquakes that are large enough to penetrate to the bottom of the seismogenic layer rupture planar faults; most events showed no strong evidence for down-dip curvature, had dips between 30° and 60°, and could be constrained to be planar to within ±20°. In both the Apennines and the Aegean, recent large normal-faulting earthquakes have generated very little surface rupture in regions with complex mapped faults. The rise of geodetic observational techniques (InSAR and GPS) has resulted in numerous studies that produced competing models of if, and how, the seismogenic slip is accommodated in the upper ≤1 km of crust, and on which faults. Fault plane measurements taken at the surface often show relatively steep dips (e.g. Jackson et al. 1982; Cello et al. 2000; Chiaraluce et al. 2005) compared to the source parameters estimated from seismology, resulting in authors describing faults as listric. However, this view is misleading. It is expected that normal fault planes steepen in upper ∼500 m as the rupture propagates towards a free surface, because this portion of the crust often fails in tension; exposed fault planes may also dip steeply due to unloading effects. This logic implies that there will be a significant underestimation of seismic hazard from surface studies, and that the structures accommodating slip in the near-surface do not reflect the geometry of the main seismogenic fault at depth. Fault planes may be expected to flatten at depth, if they detaches into a subhorizontal, rheologically weak unit. It is not unexpected that some seismogenic slip propagates onto these segments, however they generally do not make a significant contribution to the coseismic signal (e.g. Meyer et al. 1996). Indeed, our method will only resolve down-dip curvature if there is a significant moment contribution from these upper and lower portions of the fault plane. The advantage of the seismological technique presented in this paper is that we resolve the structure of the fault at depth, and on a gross scale, that is, the technique is only sensitive to the parts of the fault that are important in generating earthquakes and the picture is not obscured by the (entirely expected) complexity of surface faulting and deformation. Partly due to the small magnitudes of the earthquakes, and partly due to the global distribution of seismometers, we have had very limited success in modelling oceanic earthquakes. For example, for events on the Mid-Atlantic Ridge there are large azimuthal gaps in station coverage at teleseismic distances, particularly along-strike to the north and south, as these regions are covered by ocean. Also, the amplitude of water multiples are often of a similar magnitude to the direct arrivals, which makes our analysis difficult. Both of the oceanic events that we studied are located in regions where there is no detailed bathymetry data to confirm whether or not core complexes (the uplifted, domed and corrugated footwalls of large-offset normal faults that expose mantle rocks) are present. It is impossible to distinguish on the basis of ocean floor bathymetry alone whether rift-parallel ridged relief forms as a result of simple domino-style extension and rotation of successive planar normal faults, or whether it is formed from the steep surface breakaways of listric detachment faults (Smith et al. 2008). Resolving the down-dip geometry of oceanic normal-faulting earthquakes offers a way to discriminate between models. Based on the observed waveforms, we inferred that both of the oceanic events we studied (Tables 1 and 2, and Appendix D in the Supporting Information) ruptured through the full seismogenic layer on planar faults. In contrast to the majority of events we studied, there is strong evidence for listric down-dip curvature in some events from Tibet and East Africa. For events showing down-dip curvature, the maximum change in dip is 20°–30°. Although resolving this change in dip is a significant observation, it should be noted that the overall change is much less than that for the strongly listric fault geometries (≥50° change in dip) that are often drawn on geological cross-sections. The tightness of the constraints on the geometry is similar to the planar events, that is, within 10°–30° of the best-fitting model geometry. The ruptures we studied that displayed down-dip curvature occurred on antithetic faults, or minor faults within the hanging wall of a rift. The location and the inferred depth extent of the rupture for both the 2004 and 2005 Zhongba (Tibet) events indicate that these earthquakes occurred on faults that cut through the hanging wall of a major rift-bounding normal fault. Our best-fit models, of −20° curvature, indicate the lower portion of the active faults may dip at ∼30°. This angle is similar to the ∼28° dip of the basal detachment Kapp et al. (2008) inferred to underlie the North Lunggar Rift, ∼100 km north-northwest of the Zhongba epicentres. The deeper structure of the South Lunggar Rift (where the Zhongba earthquakes were located) is not known. West of the Zhongba epicentres, the South Lunggar Detachment dips at 20° at the surface and exhumes mylonites and foliated rocks with a normal sense of shear (Styron et al. 2013). However, we have found no evidence for seismogenic slip on very low-angle normal faults (≤20° dip) in the Lunggar Rift, as has been debated for metamorphic core complexes in other parts of the world (Wernicke 1995; Axen 1999; Collettini 2011). The 2009 Karonga earthquakes ruptured a series of ∼6–8 km long fault segments in the hanging wall of the Karonga Fault (which is antithetic to the major basin-bounding Livingstone Fault), each with a small depth extent compared to the ≥40 km seismogenic thickness in this area (Foster & Jackson 1998; Ebinger et al. 1999; Maggi et al. 2000; Craig et al. 2011). For one event there is strong evidence of down-dip curvature, with a suggestion of possible curvature for a second. In the Karonga area the pre-existing structure is complex (Fig. 15b), and two opposing basement fabrics converge (Versfelt & Rosendahl 1989). It has been suggested that failure initiated on a favourably orientated pre-existing structure, and then migrated to adjacent planes of weakness as a result of static stress transfer (Fagereng 2013). Therefore it is possible that the varying down-dip geometries are an inherited feature, and result from the reactivation of old fabrics. However, the scale of the Livingstone Fault (i.e. the great width of the basin and the large topographic step resulting from the cumulative displacement across the fault), together with a low spreading rate (Saria et al. 2014) and long earthquake cycle, means that it must dominate the stress-state in the rift (Foster & Nimmo 1996; Ebinger et al. 1999), which may also be highly spatially variable. In this setting, it is perhaps not surprising that the minor faults are curved. 7 CONCLUSIONS We have developed a new seismological technique to assess the down-dip shape of earthquake-generating faults through the analysis of body waveforms, and have successfully applied the technique to earthquakes in a variety of extensional environments. We have found that most normal-faulting earthquakes that rupture through the full seismogenic layer are planar and have dips of 30°–60°. 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Any queries (other than missing material) should be directed to the corresponding author for the paper. © The Author(s) 2017. Published by Oxford University Press on behalf of The Royal Astronomical Society. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Geophysical Journal International Oxford University Press

Seismological constraints on the down-dip shape of normal faults

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The Royal Astronomical Society
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© The Author(s) 2017. Published by Oxford University Press on behalf of The Royal Astronomical Society.
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Abstract

Summary We present a seismological technique for determining the down-dip shape of seismogenic normal faults. Synthetic models of non-planar source geometries reveal the important signals in teleseismic P and SH waveforms that are diagnostic of down-dip curvature. In particular, along-strike SH waveforms are the most sensitive to variations in source geometry, and have significantly more complex and larger-amplitude waveforms for curved source geometries than planar ones. We present the results of our forward-modelling technique for 13 earthquakes. Most continental normal-faulting earthquakes that rupture through the full seismogenic layer are planar and have dips of 30°–60°. There is evidence for faults with a listric shape from some of the earthquakes occurring in two regions; Tibet and East Africa. These ruptures occurred on antithetic faults, or minor faults within the hanging walls of the rifts affected, which may suggest a reason for the down-dip curvature. For these earthquakes, the change in dip across the seismogenic part of the fault plane is ≤30°. Body waves, Earthquake source observations, Dynamics and mechanics of faulting 1 INTRODUCTION It is not known whether major earthquake-generating normal faults are dominantly planar, or whether the dip of the fault changes with depth so that they have significant curvature. Seismic reflection profiles and geological exposures commonly reveal both listric and planar normal faults in sedimentary units. There is ongoing debate regarding whether faults with steep surface dips flatten into subhorizontal detachment horizons around the depth of the brittle-ductile transition (e.g. Velasco et al. 2010). High-resolution bathymetric studies have revealed in great detail the corrugated, domed footwalls exposed in oceanic core complexes, but the geometrical evolution of these structures, and whether or not they slip in earthquakes, remains enigmatic (Escartín et al. 2008; MacLeod et al. 2009; Smith et al. 2014). The loss in resolution of geodetic techniques (e.g. GPS and InSAR) at depth, together with the non-uniqueness involved in inverting surface measurements for fault geometry and slip, means that it is difficult, using geodetic techniques, to determine the down-dip shape of seismogenic faults, particularly at the depths at which earthquakes nucleate. In this paper, we present a seismological technique for constraining the down-dip curvature of active normal faults. The advantage of using seismology is that it sheds light on the shape of the seismogenic part of the fault at the time it was active, and the technique is only sensitive to the parts of the fault that are important in generating earthquakes. The wider implications of this work lie in several areas. First, normal fault curvature controls the geometry of basins and affects mechanisms of crustal thinning. For example, curved faults bounding regions which deform internally can accommodate significantly more extension than a series of planar faults bounding rigid crustal blocks (Jackson & McKenzie 1983; Jackson & White 1989). Second, the processes that initiate, drive, impede and finally stop earthquake ruptures are intrinsically linked to the physical attributes of faults (e.g. Sibson 1985; Scholz 1998), therefore knowledge of the shape of faults is important in investigations of fault rheology and mechanics. Third, the down-dip shape of normal faults has implications for assessing earthquake hazard, from the perspective of the location of energy release and the down-dip width of fault available to rupture. First, we discuss our approach and model set-up, and how our method differs from that of Braunmiller & Nábělek (1996), on whose work we build. We then present a synthetic example to highlight the features of teleseismic waveforms that are indicative of the presence or absence of down-dip curvature. Finally, we describe the application of our method to a catalogue of continental and oceanic normal-faulting events, and present the results of the modelling along with a discussion of the constraints on the down-dip shape of the fault for each earthquake. Though we focus on normal faults, our technique is equally applicable to thrust earthquakes. 2 DATA AND FAULT MODELS If an earthquake occurs on a fault plane with down-dip curvature, as the rupture proceeds through time and advances across the fault surface, different portions of the fault, which have different dips, will contribute to the signal recorded at a seismometer. If the rupture is of sufficient duration then the moment contributions from different parts of the fault plane, which contain information about the source geometry, are separate enough in time to be detected in seismic waveforms. We exploit this complexity in the waveforms in this study. We define down-dip fault curvature as the difference in dip between the upper and lower portions of the fault. A listric geometry, that is, decreasing dip with increasing depth, is defined as having negative curvature; a convex-up surface has positive curvature; and a plane has zero curvature. A curved surface can be approximated by a series of connected planes with different dips. For simplicity, and building upon the work of Braunmiller & Nábělek (1996), we model earthquakes using three subsources (Fig. 1). In this model, the rupture surface is approximated by three planes (tri-planar), and the subsources are offset in time and space, to represent the progress of the rupture through different parts of the fault. Figure 1. View largeDownload slide Setup of tri-planar model geometry. Left: Initial planar model. For real earthquakes, the moment obtained for the point-source centroid (red dot) parameters is used to estimate the dimensions of a planar rupture patch of dimensions L × L. Right: We use three-subsource models to simulate curvature: the planar rupture is broken into three rectangular patches, of dimensions L × $$\frac{L}{3}$$, and a subsource centroid (numbered orange dots) is located at the centre of each. The relative timing of each subsource is determined by the size of the estimated rupture plane and a rupture velocity of 2.5 km s−1. The length of the source time function (STF) for each subsource (orange triangles labelled with numbered orange dot) is constrained so that the overall duration of the three-subsource event is the same as the length of the source time function obtained for the point-source inversion (red triangle). Figure 1. View largeDownload slide Setup of tri-planar model geometry. Left: Initial planar model. For real earthquakes, the moment obtained for the point-source centroid (red dot) parameters is used to estimate the dimensions of a planar rupture patch of dimensions L × L. Right: We use three-subsource models to simulate curvature: the planar rupture is broken into three rectangular patches, of dimensions L × $$\frac{L}{3}$$, and a subsource centroid (numbered orange dots) is located at the centre of each. The relative timing of each subsource is determined by the size of the estimated rupture plane and a rupture velocity of 2.5 km s−1. The length of the source time function (STF) for each subsource (orange triangles labelled with numbered orange dot) is constrained so that the overall duration of the three-subsource event is the same as the length of the source time function obtained for the point-source inversion (red triangle). Our study is restricted to events with magnitudes >Mw 5.5, below which we commonly do not see clear waveforms in broadband seismograms, and <Mw 6.5, above which the waveform complexity resulting from the rupture of multiple fault segments results in trade-offs with the fault geometry. Unlike field-based, InSAR or seismic reflection studies, our resolution is not limited by the depth extent of the rupture, or by geographic considerations (such as site access, errors due to topographic or meteorological effects, or whether the epicentre is on land or under the oceans). The seismological technique we present is a forward-modelling method, based on the comparison of recorded waveforms with synthetic waveforms for tri-planar faults with planar and curved geometries. To construct the geometry of the three subsources for the tri-planar models, we estimate the dimensions of the rupture plane using the seismic moment of the centroid solution and fault scaling laws (as described below). For real earthquakes, we invert for these centroid parameters using P- and SH-waveform inversions, using the MT5 programme of Zwick et al. (1994) and McCaffrey et al. (1991) (discussed further below). For the synthetic earthquake, discussed in the next section, the value of the moment (and other source parameters) is chosen to be representative of the real earthquakes that we investigate. We refer to this initial centroid solution, on which the tri-planar models are based, as the planar model or single-plane solution. We estimate the dimensions of a square fault plane using the seismic moment and a displacement-to-length ratio of 5 × 10−5 (Scholz 1982). This rupture plane is broken into three rectangular patches of length, L, and down-dip width, $$\frac{L}{3}$$ (Fig. 1). The centroids of the respective subsources are positioned at the centre of each subplane, and each subsource has a moment of $$\frac{M_0}{3}$$. The relative positions and depths of the three subsources are recalculated for each degree of fault curvature that we model, while enforcing that the combined parameters of the three-source models average to the centroid solution, and that the structural contiguity of the fault model is maintained. As we prescribe each subsource with the same moment, the moment-averaged source parameters are also the same as the centroid solution. These steps ensure that our models are of physically plausible fault ruptures that are consistent with the overall centroid parameters of the events. All subsources have strike and rake fixed to that of the centroid solution. The dip of the middle subsource is fixed to that of the centroid solution. To simulate down-dip curvature, the dips of the upper and lower subsources are varied in tandem, such that the average dip of the tri-planar model is the same as for the single-plane solution. The degree of curvature is the difference in dip between the upper and lower subsources (−80° is very listric, +80° is very convex-up). Dips are altered in 5° increments, resulting in models at 10° intervals of curvature, up to a maximum degree of curvature where the dip of the upper or lower subsource approaches vertical or horizontal. Rupture of a curved surface is simulated by setting a time delay between subsources. We assume rupture nucleates at depth (initiating with the deepest subsource, S1) and propagates upwards. We show in Appendix B in the Supporting Information the effects of rupture propagating from the surface downwards. The time delay between subsources is calculated using the model geometry and assuming a rupture velocity, vr, of 2.5 km s−1. Each subsource has the same source time function, defined by a single triangular element, the duration of which is set so that the overall duration of the tri-planar event matches that of the centroid solution. We carried out synthetic tests (Appendix B in the Supporting Information) that show that variations in the timing of moment-release (due to our choice of rupture velocity and source time function parameters) have only a minor effect on the waveforms compared to changes in the down-dip geometry, and that our assumptions therefore do not affect our ability to resolve down-dip curvature. 2.1 Previous work Braunmiller & Nábělek (1996) also used teleseismic body waveform data to examine the fault geometries in 6 normal-faulting earthquakes in Greece and western Turkey. They used three-subsource models to produce synthetic waveforms for rupture on faults with down-dip curvature, and found that SH wave shapes and polarities were strongly affected by down-dip curvature when observed at teleseismic stations lying approximately along-strike of the event. We build on their work to produce a new set of synthetic waveforms and present a technique for both identifying and constraining down-dip curvature from teleseismic data. We replicated the synthetic study of Braunmiller & Nábělek (1996) using the MT5 programme of Zwick et al. (1994) (which is detailed in Appendix A in the Supporting Information), and our method reproduces the differences in amplitude and polarity in the initial parts of P and SH waveforms between a planar rupture model and a curved fault plane (with 40° listric curvature) that they observed. We improve upon the study of Braunmiller & Nábělek (1996) by investigating the effects of the choice of model rupture velocity, source duration and propagation direction, which we describe in Appendix B in the Supporting Information. Different to Braunmiller and Nábělek, we also include the important and high-amplitude depth-phases (i.e. near-source surface reflections) in our synthetic waveforms, and we prescribe the subsource parameters such that our curved fault models are consistent with the centroid solution obtained through body waveform inversion. 3 SYNTHETICS We examine the effect on P and SH waveforms of changes in the down-dip geometry of a synthetic Mw 5.9 normal-faulting event, by computing synthetic seismograms for a suite of tri-planar models covering a −80° to +80° range of curvatures (Fig. 2), using the MT5 algorithm of McCaffrey et al. (1991) and Zwick et al. (1994). The synthetic stations were chosen to represent the typical epicentral distance ranges of teleseismic data used in body waveform inversions, and the magnitude of the synthetic earthquake was chosen to be similar to the real events discussed later. Figs 3 and 4 compare the synthetic SH and P waveforms for a planar fault model, with those for curved fault models at ±10°, 20°, 40°, 60° and 80° curvature. We investigate how waveform amplitude and complexity is affected by fault geometry and station location, and discuss the implications of our results for examining real data. Figure 2. View largeDownload slide Geometry of synthetic Mw 5.9 normal-faulting event and curvature models. Left: Red dot marks the point-source location (centroid) of the synthetic earthquake at a centroid depth, zc, on a cross-section perpendicular to the event strike. The source parameters are shown above and the P and SH focal spheres are to the left. The point-source event is envisaged to occur on a planar fault surface with the same parameters as the source centroid (which we later refer to as the planar model, or single-plane solution). The centroid sits at the centre of this fault plane (black line). Right: Tri-planar models are generated by splitting the single-plane solution into three equal-sized rectangles, the dips of which are varied in order to simulate curvature. The cross-sections are perpendicular to strike and show the down-dip geometry of the tri-planar models in grey, relative to the single-plane solution centroid depth (dashed red line). Rupture of a tri-planar fault model is simulated using three point sources (subsources) with $$\frac{1}{3}$$ the moment of the single-plane solution, which are offset in space and time from each other. In the model rupture propagates from the bottom up, so the first subsource (1) is the deepest, the last (3) the shallowest. The location of each subsource centroid (orange dot) is at the centre of each of the three rectangular planes. Each cross-section is labelled with the amount of model down-dip curvature (difference in dip between the upper and lower planes) on the top right. On the bottom left, each cross-section has a P focal sphere showing the nodal planes of subsource 1 (solid), 2 (dashed) and 3 (dotted). Figure 2. View largeDownload slide Geometry of synthetic Mw 5.9 normal-faulting event and curvature models. Left: Red dot marks the point-source location (centroid) of the synthetic earthquake at a centroid depth, zc, on a cross-section perpendicular to the event strike. The source parameters are shown above and the P and SH focal spheres are to the left. The point-source event is envisaged to occur on a planar fault surface with the same parameters as the source centroid (which we later refer to as the planar model, or single-plane solution). The centroid sits at the centre of this fault plane (black line). Right: Tri-planar models are generated by splitting the single-plane solution into three equal-sized rectangles, the dips of which are varied in order to simulate curvature. The cross-sections are perpendicular to strike and show the down-dip geometry of the tri-planar models in grey, relative to the single-plane solution centroid depth (dashed red line). Rupture of a tri-planar fault model is simulated using three point sources (subsources) with $$\frac{1}{3}$$ the moment of the single-plane solution, which are offset in space and time from each other. In the model rupture propagates from the bottom up, so the first subsource (1) is the deepest, the last (3) the shallowest. The location of each subsource centroid (orange dot) is at the centre of each of the three rectangular planes. Each cross-section is labelled with the amount of model down-dip curvature (difference in dip between the upper and lower planes) on the top right. On the bottom left, each cross-section has a P focal sphere showing the nodal planes of subsource 1 (solid), 2 (dashed) and 3 (dotted). Figure 3. View largeDownload slide Synthetic SH waveforms generated for a Mw 5.9 normal-faulting earthquake, with a strike, average dip and rake of 000°/45°/270°. SH waveforms were generated at the synthetic stations shown here, at an epicentral distance of 55°, which is typical of the epicentral distance ranges of teleseismic data used in body waveform inversions. The station position (intersection of the ray path with the lower hemisphere projection of the focal sphere) is shown with a solid black dot on the SH focal sphere. Synthetic waveforms are plotted around the SH focal sphere (which shows the nodal surfaces for an event with 0° down-dip curvature) at the approximate station azimuth, and labelled with the alphanumeric station name (bold) and azimuth. Synthetic SH waveforms, generated from tri-planar models, are shown for events with ±10°, 20°, 40°, 60° and 80° curvature in blue. Solid blue lines are for negative curvature (listric), dotted blue for positive curvature (convex up). Model curvature increases radially outwards, that is, the inner ring shows waveforms for models with 10° curvature, the outer 80°. Synthetics for curved models (blue) are plotted on top of a synthetic single-plane, 1-source centroid model (black) with 0° curvature. Figure 3. View largeDownload slide Synthetic SH waveforms generated for a Mw 5.9 normal-faulting earthquake, with a strike, average dip and rake of 000°/45°/270°. SH waveforms were generated at the synthetic stations shown here, at an epicentral distance of 55°, which is typical of the epicentral distance ranges of teleseismic data used in body waveform inversions. The station position (intersection of the ray path with the lower hemisphere projection of the focal sphere) is shown with a solid black dot on the SH focal sphere. Synthetic waveforms are plotted around the SH focal sphere (which shows the nodal surfaces for an event with 0° down-dip curvature) at the approximate station azimuth, and labelled with the alphanumeric station name (bold) and azimuth. Synthetic SH waveforms, generated from tri-planar models, are shown for events with ±10°, 20°, 40°, 60° and 80° curvature in blue. Solid blue lines are for negative curvature (listric), dotted blue for positive curvature (convex up). Model curvature increases radially outwards, that is, the inner ring shows waveforms for models with 10° curvature, the outer 80°. Synthetics for curved models (blue) are plotted on top of a synthetic single-plane, 1-source centroid model (black) with 0° curvature. Figure 4. View largeDownload slide Synthetic P waveforms generated for a Mw 5.9 normal-faulting earthquake, with a strike, average dip and rake of 000°/45°/270°. Key as for Fig. 3, but curved model synthetics are in red and the P focal sphere is shown, with compressional quadrants shaded in grey. The P stations are at an epicentral distance of 60°, and the station position (intersection of the ray path with the lower hemisphere projection of the P focal sphere) is shown with a solid black dot. Figure 4. View largeDownload slide Synthetic P waveforms generated for a Mw 5.9 normal-faulting earthquake, with a strike, average dip and rake of 000°/45°/270°. Key as for Fig. 3, but curved model synthetics are in red and the P focal sphere is shown, with compressional quadrants shaded in grey. The P stations are at an epicentral distance of 60°, and the station position (intersection of the ray path with the lower hemisphere projection of the P focal sphere) is shown with a solid black dot. 3.1 Synthetic waveforms The synthetic seismograms at stations within ∼30° of fault strike have significantly more complex SH waveforms for all curved fault models than for the planar case, even those with only ±10° curvature (Fig. 3). The SH waveforms at these stations also have much higher amplitudes for curved models, and along-strike nodal stations (stations S1 and S13) show waveforms whereas none are present for the planar model. These effects are more pronounced for models with greater curvature. At stations with azimuths at high angle to strike, SH waveforms for curved models are not as complex, and have similar amplitudes to (and are harder to distinguish by eye from) those for the planar fault model. However, for models with high curvature, the dip of the lowermost plane (subsource S1) may be high or low enough that the nodal plane for this subsource lies on the opposite side of where these stations plot on the focal sphere, that is, the station projects to a different quadrant of the SH focal sphere. In this case the SH waveform shows a small amplitude peak with the opposite sign to that of the waveform for the planar model (Fig. 5). At nodal stations perpendicular to strike (stations S6 and S20), there is no SH arrival in any model. These features arise because the SH nodal planes cut through the centre of the focal sphere, passing through parts of the focal sphere that are sampled by seismometers at teleseismic distances. Changes in dip within the source rotate the SH focal sphere such that the nodal planes sweep across the region in the lower hemisphere projection covered by the take-off angles of teleseismic waves. This effect makes SH waveforms highly sensitive to changes in down-dip curvature. Small changes in curvature therefore have a large effect on the SH waveforms at stations within ∼30° of fault strike. Therefore, to detect down-dip curvature in real earthquakes it is essential to include SH data from stations in the along-strike directions. This finding is consistent with the observations made by Braunmiller & Nábělek (1996). Figure 5. View largeDownload slide The effect of a high degree of model curvature on synthetic waveforms. This figure illustrates that stations at azimuths >30° from strike may also be sensitive to down-dip curvature. Left: Model fault geometry and P and SH focal spheres for synthetic single-source planar Mw 5.9 event, as for Fig. 2. Example synthetic waveforms for stations P7 and S9 are shown to the right of the appropriate focal sphere. For both the P and SH focal spheres, quadrants with positive waveform arrivals are shaded grey, and the appropriate station ray path intersection is marked with a black dot. Station labels are as for Figs 3 and 4. Right: Tri-planar models with 60° down-dip curvature, as for Fig. 2. The synthetic P (red) and SH (blue) waveforms for stations P7 and S9 are shown to the right; solid line for negative curvature, dotted for positive. The synthetic waveforms are the signal resulting from the summed contribution of the radiated energy from all three subsources, however we show the P and SH focal spheres for only the first (deepest) subsource, S1, which affects the initial part of the waveform. The quadrants with positive arrivals from S1 are shaded and the intersection of the ray path for station P7 and S9 on the focal sphere is shown with a black dot. The dip of S1 affects the position of the nodal surfaces relative to the station position, and the resultant polarity of the initial part of the waveform. Figure 5. View largeDownload slide The effect of a high degree of model curvature on synthetic waveforms. This figure illustrates that stations at azimuths >30° from strike may also be sensitive to down-dip curvature. Left: Model fault geometry and P and SH focal spheres for synthetic single-source planar Mw 5.9 event, as for Fig. 2. Example synthetic waveforms for stations P7 and S9 are shown to the right of the appropriate focal sphere. For both the P and SH focal spheres, quadrants with positive waveform arrivals are shaded grey, and the appropriate station ray path intersection is marked with a black dot. Station labels are as for Figs 3 and 4. Right: Tri-planar models with 60° down-dip curvature, as for Fig. 2. The synthetic P (red) and SH (blue) waveforms for stations P7 and S9 are shown to the right; solid line for negative curvature, dotted for positive. The synthetic waveforms are the signal resulting from the summed contribution of the radiated energy from all three subsources, however we show the P and SH focal spheres for only the first (deepest) subsource, S1, which affects the initial part of the waveform. The quadrants with positive arrivals from S1 are shaded and the intersection of the ray path for station P7 and S9 on the focal sphere is shown with a black dot. The dip of S1 affects the position of the nodal surfaces relative to the station position, and the resultant polarity of the initial part of the waveform. The shape of synthetic P waveforms is much less sensitive to station azimuth and degree of curvature (Fig. 4), because the P-wave nodal planes of normal-faulting earthquakes cut through parts of the focal sphere that are distant from the take-off angles of seismic waves received at stations at teleseismic distances. There are small changes in the width and location of peaks in the waveform, however the main effect is on the amplitude of the waveform, particularly at stations that lie perpendicular to strike. Considering the true (E-dipping) nodal plane that represents our synthetic normal fault, for positive curvature models (convex), stations that lie in the down-dip (East) direction have smaller amplitude and more complex P waveforms than stations in the up-dip (West) direction. The opposite is true for negative curvature (listric) models. This effect is stronger for models with greater curvature, as the dip of one subsource is steep and the projection of the relevant nodal plane passes close to stations in the focal sphere, resulting in less energy being received and smaller amplitudes being recorded at those stations (Fig. 5). 3.2 Implications for modelling real events If seismogenic faults have only small degrees of down-dip curvature, the diagnostic signals (SH waveform complexity and/or initial low-amplitude peaks with the wrong polarity) will only be detectable at stations lying at positions at or very close to along-strike. Identifying the shapes of the waveforms correctly requires picking the precise onset times for P and SH arrivals. Stations that lie near an SH nodal surface receive a lower energy signal and show lower amplitude SH arrivals in seismograms than stations lying elsewhere in the SH focal sphere. Along-strike broadband data must be examined carefully for clear arrivals that can be distinguished from the background noise. Picking the wrong SH arrival time would skew any attempt to resolve down-dip curvature. For this reason we pick the waveform arrivals by hand, and when modelling real earthquakes we include data from as many along-strike stations as possible, so that one wrong or uncertain SH arrival pick will not adversely distort the results. 4 APPLICATION TO REAL EARTHQUAKES We present a seismological, forward-modelling technique for determining the down-dip geometry of earthquake-generating dip-slip faults, based upon the synthetic models described above. We have applied this method to a catalogue of continental and oceanic events and present the results of the modelling in the next section. 4.1 Event selection We performed body-waveform inversions for a catalogue of normal-faulting events (Table 1), from a wide range of extensional environments. We then selected suitable earthquakes on which to apply our seismological technique for determining down-dip curvature. Events were chosen based on (1) magnitude, (2) source time function, and (3) station signal-to-noise ratio and distribution. Events need to be large enough (≥Mw 5.5) that the seismic contributions from different parts of the rupture plane are distinct and separate in space and time; and small enough (≤Mw 6.5) that the approximation of the earthquakes as a point source (centroid), on which the initial waveform inversion is based, is still valid. Factors such as changes in the rupture propagation direction, uneven moment release, or earthquake doublets, have a large effect on the resultant waveforms recorded at teleseismic distances. This level of complexity leads to multiple trade-offs with down-dip fault geometry. Therefore we select events that are one-segment ruptures, with relatively simple source time functions. In order to perform the modelling effectively there must be a good azimuthal distribution of stations at teleseismic distances, a high density of stations at close to along-strike azimuths, and seismograms with clear arrivals and a high signal-to-noise ratio. Table 1. Events used in this study. Event  Best-fit centroid parameters      Name  Region  Lat  Long  yymmdd  hh:mm:ss  Mw  M0  Strike  Dip  Rake  Depth      (°)  (°)        (N m)  (°)  (°)  (°)  (km)  L’Aquila  Italy  42.370  13.319  090406  01:32:42  6.2  2.60 × 1018  134  46  261  4.6  Colfiorito  Italy  43.079  12.781  970926  09:40:27  5.8  6.67 × 1017  123  40  270  5.4  Aegion  Greece  38.440  22.307  950615  00:15:50  6.2  2.34 × 1018  290  27  305  11.6  Grevena  Greece  40.143  21.717  950513  08:47:14  6.4  4.39 × 1018  245  39  271  11.2  Simav  Turkey  39.128  29.070  110519  20:15:25  5.8  7.02 × 1017  116  37  274  9.5                7.02 × 1017  291  53  269  9.5  Palu  Indonesia  −1.085  119.878  090302  00:03:41  5.6  2.82 × 1017  313  39  273  7.4                2.82 × 1017  128  51  265  7.4  MAR  Mid-Atlantic  26.552  −44.629  070301  23:11:52  5.9  7.84 × 1017  204  50  289  7    Ridge            7.84 × 1017  024  42  293  7  Gakkel  Arctic Sea  84.913  99.618  050306  05:21:40  6.2  2.95 × 1018  133  44  264  9.4  Ridge              2.95 × 1018  315  48  267  9.4  Zhongba 1  Tibet  30.681  83.650  040711  23:08:44  6.2  2.23 × 1018  163  40  268  10.5  Zhongba 2  Tibet  30.481  83.657  050407  20:04:40  6.2  2.26 × 1018  165  44  266  7.8  Karonga 1  Malawi  −10.158  33.825  091206  17:36:37  5.7  4.44 × 1017  164  38  270  4.2  Karonga 2  Malawi  −9.983  33.819  091208  03:08:57  5.8  5.77 × 1017  146  44  248  5.4  Karonga 3  Malawi  −10.019  33.831  091219  23:19:17  5.9  8.25 × 1017  158  43  262  5.3  Event  Best-fit centroid parameters      Name  Region  Lat  Long  yymmdd  hh:mm:ss  Mw  M0  Strike  Dip  Rake  Depth      (°)  (°)        (N m)  (°)  (°)  (°)  (km)  L’Aquila  Italy  42.370  13.319  090406  01:32:42  6.2  2.60 × 1018  134  46  261  4.6  Colfiorito  Italy  43.079  12.781  970926  09:40:27  5.8  6.67 × 1017  123  40  270  5.4  Aegion  Greece  38.440  22.307  950615  00:15:50  6.2  2.34 × 1018  290  27  305  11.6  Grevena  Greece  40.143  21.717  950513  08:47:14  6.4  4.39 × 1018  245  39  271  11.2  Simav  Turkey  39.128  29.070  110519  20:15:25  5.8  7.02 × 1017  116  37  274  9.5                7.02 × 1017  291  53  269  9.5  Palu  Indonesia  −1.085  119.878  090302  00:03:41  5.6  2.82 × 1017  313  39  273  7.4                2.82 × 1017  128  51  265  7.4  MAR  Mid-Atlantic  26.552  −44.629  070301  23:11:52  5.9  7.84 × 1017  204  50  289  7    Ridge            7.84 × 1017  024  42  293  7  Gakkel  Arctic Sea  84.913  99.618  050306  05:21:40  6.2  2.95 × 1018  133  44  264  9.4  Ridge              2.95 × 1018  315  48  267  9.4  Zhongba 1  Tibet  30.681  83.650  040711  23:08:44  6.2  2.23 × 1018  163  40  268  10.5  Zhongba 2  Tibet  30.481  83.657  050407  20:04:40  6.2  2.26 × 1018  165  44  266  7.8  Karonga 1  Malawi  −10.158  33.825  091206  17:36:37  5.7  4.44 × 1017  164  38  270  4.2  Karonga 2  Malawi  −9.983  33.819  091208  03:08:57  5.8  5.77 × 1017  146  44  248  5.4  Karonga 3  Malawi  −10.019  33.831  091219  23:19:17  5.9  8.25 × 1017  158  43  262  5.3  Hypocentre locations and times were retrieved from the ISC; location data for events occurring prior to 2009 is from the EHB bulletin. The centroid parameters were obtained through body waveform inversion in this study. If the true fault plane is not known, parameters for both nodal planes are shown. View Large 4.2 Procedure The main stages of the method are as follows: Perform a body waveform inversion to obtain point-source centroid focal parameters, moment and source time function for the chosen event. Use centroid solution to estimate source dimensions and set up geometry of tri-planar models. Generate synthetic waveforms for tri-planar models with a range of down-dip curvatures. Compare model synthetics with observed seismograms to constrain down-dip curvature. 4.2.1 Body waveform inversion procedure Teleseismic data was downloaded using the IRIS (Incorporated Research Institutions for Seismology) Wilber III system and P and SH arrivals were manually picked on broadband seismograms. A full list of stations we used, along with their network codes, is found in Appendix C in the Supporting Information. We used data from all networks with suitable records, and restrict the station epicentral distance range to 30°–90° and 30°–80° for P and SH data respectively. This ensures that the P and S signals are not affected by arrivals of waves that have diffracted, reflected or travelled through the core, and that they have not been affected by shallow lithospheric phases (e.g. Moho head waves). The broadband seismograms are first deconvolved from their instrumental response, and then reconvolved with the response of a long-period (15–100 s) World-Wide Standardized Seismograph Network (WWSSN) instrument. This procedure means that earthquakes of magnitudes Mw 5.0–6.5 can be modelled as a finite-duration rupture at a point source (centroid). We then used the MT5 programme of Zwick et al. (1994), based on the algorithm of McCaffrey & Abers (1988) and McCaffrey et al. (1991), to jointly invert P and SH waveforms for earthquake source parameters (strike, dip, rake, centroid depth, moment and source time function). Given an initial model (taken from the GCMT catalogue) and our arrival time picks, we generate synthetic P and SH waveforms and solve iteratively for the source parameters that give a minimum misfit between the observed waveform and synthetics within the inversion window. The inversion window starts at the picked arrival time and the length is set for P and SH data so that it includes only the body waveforms and their depth phases, and no additional phases. P, pP and sP phases are modelled on vertical component seismograms and S and sS phases on transverse component seismograms. Synthetics are computed based on the source parameters and calculated take-off angles (with amplitudes corrected for geometrical spreading and attenuation). We solve for the strike, dip and rake of the source (which dominantly affect the shape of the waveforms), and the centroid depth and source time function (which chiefly control the length and amplitude of the waveforms). The source is constrained to be purely double-couple. A full description of this procedure can be found in Taymaz et al. (1991) and Nábělek (1984), and similar waveform inversion techniques are used extensively in the literature (Bergman & Solomon 1985; Braunmiller & Nábělek 1996; Craig et al. 2011; Sloan et al. 2011). This technique refines the accuracy of source parameter estimates made by routine catalogues such as the GCMT, particularly for the centroid depth. The degree to which each focal parameter can be resolved is determined by fixing a parameter, for example, depth, at a series of values away from the best fit, and re-inverting for all other parameters. The fit of the synthetic to the observed seismograms is then compared at successive values of the fixed parameter to determine the range over which a reasonable fit has been found. Typical errors are ±4 km for depth, ±10° for strike, ±5° for dip and ±10° for rake (Molnar & Lyon-Caen 1989; Taymaz et al. 1991; Craig et al. 2014). We used a simple crustal velocity model consisting of a half-space of Vp = 6.5 km s−1, Vs = 3.7 km s−1, ρ = 2800 kg m−3. Discrepancies between the model velocity structure and the actual (unknown) velocity profile at the location of each earthquake (e.g. due to shallow, low-velocity sedimentary layers above the source) affect the estimated centroid depth, but not the geometry of the nodal planes (e.g. Bergman & Solomon 1985; Nelson et al. 1987; Taymaz et al. 1990; Middleton & Copley 2013). The lack of sensitivity of the orientation of the focal planes to the velocity model results from the constraint that the source be comprised of double-couple subsources, and the simultaneous inversion of P and SH waves at all stations (Fredrich et al. 1988). 4.2.2 Constraining down-dip geometry Having obtained a centroid solution for the earthquakes we study, we use the same procedure as that for the synthetic event (described above) to set up tri-planar models with down-dip curvature (Fig. 1). The MT5 programme (Zwick et al. 1994) is used to generate synthetic P and SH waveforms for the curved tri-planar models at all stations used in the initial inversion. As a first indicator of down-dip curvature in the source, we look for complex SH waveform shapes with higher than expected amplitudes at stations within 30° of the along-strike azimuth. We then attempt to put constraints on the down-dip geometry by determining the range of down-dip curvature models that produce an acceptable fit to all the waveform data. For each SH station (including those >30° from strike) and for every tri-planar curvature model, synthetic waveforms are compared to the observed seismogram, and the synthetic from the planar solution, in order to determine whether the synthetics produced with a curved fault plane yield a better fit to the observed data, and over what range of curvature there is an acceptable fit to the waveforms. We calculate the variance of the residuals between the recorded signals and the synthetic waveforms within the inversion window, and plot graphs of variance against curvature for SH-waveforms recorded at stations within 30° of strike. The important observations are how the misfit varies as a function of curvature for each station. The waveforms are visually inspected to check for features that may skew the plots or produce a misleading variance, such as synthetics that fit most of the waveform but have the wrong first motion (which would give a low variance of the residuals, despite having the wrong first motion), or the presence of noise in some seismograms (which may result in a high variance, even if the synthetic broadly fits the observed waveform). In order to constrain the down-dip curvature of an event, we examine the visual fit of synthetics together with the graphs of variance against curvature. If down-dip curvature is present, we expect to see a consistent agreement across the SH stations, with improved fits at curved models; though we expect the stations >30° from strike to be much less sensitive. Finally, to determine a preferred model, and to avoid biases due to uneven azimuthal distribution of stations or biases in favour of fitting SH-waveforms at the expense of P-waveforms, we examine the fit of the curved models as a whole, to all P- and SH-waveforms. Looking for common features among multiple stations is diagnostic of source, rather than receiver, effects. 5 RESULTS We present the results of body-waveform inversions (Table 1) and the constraints on the down-dip geometry (Table 2) of 13 events. We begin by presenting the source parameters and modelling results for a well-studied event, the 2009 L’Aquila earthquake. There are multiple independent geophysical inversion and aftershock studies for this event, against which we compare the results of our seismological technique, and test that the method is robust. We then describe the constraints on the down-dip geometry for the additional events that we studied; seven in the main text and five others in Appendix D in the Supporting Information. Table 2. Results from down-dip curvature modelling. Plain grey bars delimit range of down-dip curvature investigated for each event. Grey boxes indicate the extent to which down-dip geometry can be constrained—they show cross-sections of the model geometries that produce synthetics with an acceptable fit to recorded broadband seismograms. The red line marks the modelled centroid depth with respect to the model fault plane. Red dots mark the centroids for the events that show no resolvable evidence for down-dip curvature; orange dots mark the subsource centroids for our preferred tri-planar fault model for events where there is evidence for down-dip curvature. If the true fault plane (FP) is not known, modelling results for both nodal planes are shown (NP1 and NP2).     View Large We first detail the events with no evidence of down-dip curvature and describe to what extent the down-dip geometry can be constrained. We then describe the results for two groups of earthquakes (the Karonga sequence, East Africa, and the Zhongba earthquakes, Tibet) for which there is evidence of down-dip curvature in some events, and present the solution for our preferred model. For every event, the full solution of the initial body-waveform inversion (planar) and the solution for our preferred model geometry (if different) is in Appendix E in the Supporting Information, modelling of auxiliary planes (if the true fault plane is not known) is presented in in Appendix F in the Supporting Information, and synthetic P- and SH-waveforms for all models and stations are presented in Appendix G in the Supporting Information. 5.1 Test case: the 2009 April 6 L’Aquila earthquake, Italy The 2009 April 6 Mw 6.2 L’Aquila earthquake ruptured part of an NW–SE-trending fault system (Fig. 6) running through the central Apennines. Body-waveform seismology (e.g. Walters et al. 2009; Pondrelli et al. 2010; Scognamiglio et al. 2010; Herrmann et al. 2011), InSAR (e.g. Atzori et al. 2009; Walters et al. 2009), GPS (Anzidei et al. 2009; Cheloni et al. 2010; Serpelloni et al. 2011), GPS and strong motion (Cirella et al. 2009) and aftershock location (Chiarabba et al. 2009; Chiaraluce et al. 2011; Valoroso et al. 2013) studies agree on the first order source parameters (normal motion with a small component of right-lateral slip on a fault striking 127°–144°, dipping 45°–56° to the southwest), which are consistent with the those presented in this study (Fig. 7a). Geologic mapping and analysis of coseismic surface ruptures (EMERGEO Working Group 2009; Falcucci et al. 2009; Boncio et al. 2010; Bonini et al. 2014), up-dip surface projections of fault plane solutions and analysis of the ground displacements measured by InSAR and GPS (Atzori et al. 2009; Walters et al. 2009) demonstrate that the main shock ruptured the Paganica Fault. There is some disagreement on whether coseismic slip only occurred up-dip of the 8–10 km hypocentre (Herrmann et al. 2011; D’Agostino et al. 2012) or whether there was also a deeper slip patch between 9–14 km (Cirella et al. 2009; Cheloni et al. 2010), however most of the slip was shallower than the hypocentre. Our modelled centroid depth of 5 km, and the depth extent of model fault geometries (1–10 km) are consistent with the estimates of the extent of the fault plane in the source parameter studies mentioned above (1–15 km depth). Figure 6. View largeDownload slide Map of the Abruzzo Region, central Apennines, Italy (a) Regional map. The perimeter of box B is shown in dark grey. (b) Topography of the 2009 April 6 L’Aquila earthquake epicentral region. The focal mechanism obtained in this study is shown offset from the EHB location. Settlements (black squares) and major features are named. Known and active faults are in black, after Roberts & Michetti (2004); Chiarabba et al. (2009); EMERGEO Working Group (2009). The surface trace of the main-shock fault, the Paganica Fault (Pf), is marked in red. Part of the Campotosto Fault (Cf) was activated by an aftershock. Figure 6. View largeDownload slide Map of the Abruzzo Region, central Apennines, Italy (a) Regional map. The perimeter of box B is shown in dark grey. (b) Topography of the 2009 April 6 L’Aquila earthquake epicentral region. The focal mechanism obtained in this study is shown offset from the EHB location. Settlements (black squares) and major features are named. Known and active faults are in black, after Roberts & Michetti (2004); Chiarabba et al. (2009); EMERGEO Working Group (2009). The surface trace of the main-shock fault, the Paganica Fault (Pf), is marked in red. Part of the Campotosto Fault (Cf) was activated by an aftershock. Figure 7. View largeDownload slide Down-dip curvature modelling results for the 2009 April 6 L’Aquila earthquake.Figure overleaf. (a) Event location map, focal mechanism and distribution of stations. Centroid parameters obtained through body waveform inversion (planar solution) are shown above the map; the focal mechanism is plotted at the location of the epicentre. Stations used in the inversion are named. (b) Plots of variance against curvature for SH-stations within 30° of strike. Variance was calculated for the residuals between synthetic and recorded SH-waveforms, within the inversion window used to obtain the initial centroid solution, for each station and tri-planar model. (c) Down-dip curvature modelling results and synthetics for select stations. Cross-sections through model fault geometry are shown above. The range of curvature constrained by the data is highlighted in black, the best-fit model geometry in blue. Synthetic waveforms calculated for three-subsource models for select stations are plotted below (red for P-, blue for SH-waveforms), on top of the recorded waveform (black). For the 0°-curvature model, the synthetic from the point-source planar solution (grey) is plotted on top of the recorded waveform. The station positions are shown on the relevant focal sphere. Figure 7. View largeDownload slide Down-dip curvature modelling results for the 2009 April 6 L’Aquila earthquake.Figure overleaf. (a) Event location map, focal mechanism and distribution of stations. Centroid parameters obtained through body waveform inversion (planar solution) are shown above the map; the focal mechanism is plotted at the location of the epicentre. Stations used in the inversion are named. (b) Plots of variance against curvature for SH-stations within 30° of strike. Variance was calculated for the residuals between synthetic and recorded SH-waveforms, within the inversion window used to obtain the initial centroid solution, for each station and tri-planar model. (c) Down-dip curvature modelling results and synthetics for select stations. Cross-sections through model fault geometry are shown above. The range of curvature constrained by the data is highlighted in black, the best-fit model geometry in blue. Synthetic waveforms calculated for three-subsource models for select stations are plotted below (red for P-, blue for SH-waveforms), on top of the recorded waveform (black). For the 0°-curvature model, the synthetic from the point-source planar solution (grey) is plotted on top of the recorded waveform. The station positions are shown on the relevant focal sphere. Of eight stations within 30° of strike, six have SH-synthetics with a good fit to the observed data for the planar solution (e.g. RAYN, WCI; Fig. 7c). Models with >10° of curvature produce synthetic SH-waveforms for which the overall waveform shape and/or peak amplitudes and polarities are significantly different to the observed waveforms at these stations, that is, the recorded data precludes fault geometries of ≥20° of curvature for this event. Recorded waveforms at the other two stations in this azimuth range (MSEY and DWPF) are not fit well by the planar solution synthetics (most likely due to station noise of unknown origin); varying the down-dip geometry does not yield a better fit. Synthetics generated from some curved models yield fits that are equally good or better than the planar case for individual stations (e.g. WCI +30°; Fig. 7c). However, as all the stations record the same event, it is important to find a model that is consistent with the recorded P and SH waveforms at the majority of stations, rather than a model that yields excellent fits at only some of the along-strike SH stations. There is no consistent trend among the stations as a whole favouring either positive or negative curvature, and minor improvements in fit at individual stations are likely due to fitting noise. This feature is demonstrated by the differing minimum-variance model for each of the SH-stations within 30° of strike (Fig. 7b). The average variance of the residuals for these stations is lowest for a model with 0° curvature (i.e. planar). SH-stations at azimuths >30° from strike have wider ranges of down-dip curvature over which the model produces synthetics with an acceptable fit to the recorded data (e.g. TIXI; Fig. 7c); those that lie roughly perpendicular to strike are insensitive to changes in model geometry (e.g. HIA). Increasing the down-dip curvature produces only small amplitude changes in synthetic P-waveforms at most stations (e.g. TSUM), but large changes in stations with high take-off angles and that lie near a P nodal plane (e.g. KBS, ARU). For these stations, models with >20° curvature produce synthetic P-waveforms with larger amplitudes compared to the other stations (and compared to the planar model). We do not observe this azimuthal variation in the recorded P-waveform data. Taken as a whole, all these observations combined mean that we infer that the L’Aquila earthquake ruptured a planar fault. If there is a change in dip in the down-dip direction, it is not more than ±10°. Chiarabba et al. (2009), Chiaraluce et al. (2011) and Valoroso et al. (2013) relocated large catalogues of foreshocks and aftershocks associated with the L’Aquila main shock. All three studies showed tight clustering of the relocated events along a plane dipping ∼50° to the southwest. Their close spatial alignment argues for the Paganica Fault having a planar down-dip geometry, consistent with the results of our analysis of teleseismic body waveforms and down-dip curvature modelling. The corroboration of our result by other geophysical methods demonstrates the robustness of the technique. Based on modelling of regional broadband waveforms and extensive finite-fault models of velocity and accelerometer data, Herrmann et al. (2011) concluded that the major moment release in the L’Aquila earthquake occurred up-dip of and, 4–7 s after, the rupture initiation at the hypocentre. Cirella et al. (2009) jointly invert strong motion and GPS data and find that slip propagated up-dip with a velocity of 2.2–2.8 km s−1. These independent analyses further support our model assumptions; an upwards-propagating rupture, and the choice of a 2.5 km s−1 rupture velocity. 5.2 Planar ruptures Our analysis shows that the majority of normal-faulting earthquakes that are large enough to rupture through the seismogenic layer occur on planar faults. These events showed no strong evidence for down-dip curvature, had dips between 30°–60°, and could be constrained to be planar to within ±20°. We describe in detail below the 1997 September 26 Colfiorito earthquake, Italy, and the 1995 May 13 Grevena earthquake, northern Greece. A full description of our results for the additional planar ruptures (1995 June 15 Aegion earthquake, Greece; 2011 May 19 Simav earthquake, Turkey; 2009 March 2 Palu earthquake, Indonesia; 2007 March 1 earthquake, Mid-Atlantic Ridge; 2005 March 6 earthquake, Gakkel Ridge, Arctic Sea) is presented in Appendix D in the Supporting Information. 5.2.1 The 1997 September 26 Colfiorito earthquake, Italy The 1997 September 26 Colfiorito earthquake was largest of six 5 < Mw <6 events that struck the Abruzzo region (Fig. 8) of central Italy during September–October 1997, known as the Umbria-Marche sequence (Chiaraluce 2003). Our modelled centroid dip (40°) agrees well with that obtained by other authors through waveform inversion (Ekström et al. 1998; Morelli et al. 2000), the alignment of relocated aftershocks (Amato et al. 1998; Deschamps et al. 2000; Chiaraluce 2003) and various geodetic analyses (Hunstad et al. 1999; Stramondo et al. 1999; Salvi et al. 2000; De Martini et al. 2003). We obtain a centroid depth of 5 km, consistent with the 4–5.5 km depth of maximum slip obtained by Lundgren & Stramondo (2002) through joint inversion of GPS and InSAR data, and infer the depth extent of faulting to extend between >1 km to <8 km. This depth distribution is supported by observations that very little slip reached the surface (Cinti et al. 1999; Cello et al. 2000; Basili & Meghraoui 2001), aftershock hypocentres delineate a cut-off in seismicity beneath 8–9 km depth (Deschamps et al. 2000; Chiaraluce 2003), and forward-modelling of coseismic displacements on a fault plane with a similar depth extent adequately reproduces measured GPS and InSAR surface displacements (Hunstad et al. 1999; Salvi et al. 2000). Figure 8. View largeDownload slide Map of the Umbria-Marche Region, central Apennines, Italy.(a) Regional map. The perimeter of box B is shown in grey. (b) Topography of the 1997 September 26 Colfiorito earthquake epicentral region, overlaid with a simplified fault map (after Chiaraluce 2003). Settlements (black squares) and major features are named. Pre-exisiting, inactive thrusts are in grey, SW-dipping normal faults in black, and the trace of the major NE-dipping, Alto-Tiberino normal fault (ATF) is bold. The focal mechanism obtained in this study is shown offset from the EHB location. Figure 8. View largeDownload slide Map of the Umbria-Marche Region, central Apennines, Italy.(a) Regional map. The perimeter of box B is shown in grey. (b) Topography of the 1997 September 26 Colfiorito earthquake epicentral region, overlaid with a simplified fault map (after Chiaraluce 2003). Settlements (black squares) and major features are named. Pre-exisiting, inactive thrusts are in grey, SW-dipping normal faults in black, and the trace of the major NE-dipping, Alto-Tiberino normal fault (ATF) is bold. The focal mechanism obtained in this study is shown offset from the EHB location. Our planar solution yields synthetics with moderately good fits to the shape and amplitude of SH-waveforms recorded at all stations within 30° of strike (Fig. 9c). Models with ≥20° of curvature produce complex synthetic SH-waveforms that do not fit the observed data at these 6 stations, particularly for stations lying SE of the event (e.g. MSEY; Figs 9a and c). The average variance of SH-stations within 30° of strike is lowest for models with 0° to +10° curvature (Fig. 9b). For stations >30° from strike, the SH-waveforms are less sensitive to changes in the down-dip geometry (e.g. ALE; Fig. 9c), and individual stations have a wider range of curvatures over which the model generates a synthetic that fits the recorded waveform equally well. In general, increasing down-dip curvature has only a small effect on the amplitude of P-waveforms (e.g. FURI, FFC; Fig. 9c). Stations with high take-off angles and that lie near a P nodal plane (e.g. KBS, ARU; Fig. 9c) exclude geometries with ≥30° of curvature; for these geometries the initial dip is high or low enough that the P-synthetic produced at these stations may have the wrong initial polarity and/or a substantially different amplitude compared to P-synthetics for other stations and the observed data. There is no evidence to suspect down-dip curvature for this event. The data allows for a maximum of ±10° curvature; outside of this range the fit of synthetics at key stations deteriorates. We therefore infer that the Colfiorito event ruptured a planar fault, to within −10°/+10° degrees. Figure 9. View largeDownload slide Down-dip curvature modelling results for 1997 September 26 Colfiorito earthquake. Caption as for Fig. 7. Figure 9. View largeDownload slide Down-dip curvature modelling results for 1997 September 26 Colfiorito earthquake. Caption as for Fig. 7. Some workers have described the faults in the Colfiorito area as having listric geometries (Boncio & Lavecchia 2000; Barchi & Mirabella 2009), because the coseismic faults do not project to the surface while maintaining their 35–45° dips, and exposed fault planes have measured dips of ∼60–70° (Cello et al. 2000; Chiaraluce et al. 2005). Additionally, it has been suggested that the normal faults bottom-out below ∼8 km, either onto pre-existing, low-angle structures (e.g. the Alto-Tiberino Fault; Boncio & Lavecchia 2000) or into horizons of Triassic evaporites (Mirabella et al. 2008; Barchi & Mirabella 2009), though there is a dearth of good quality seismic reflection data to test these suggestions (Chiaraluce et al. 2005; Mirabella et al. 2008). Although co-seismic displacements do seem to be taken up on high-angle fault strands at the surface—evinced by diffuse aftershock seismicity in the upper 1 km (Chiaraluce et al. 2004), complex patterns of surface deformation (e.g. Stramondo et al. 1999; Cello et al. 2000; Salvi et al. 2000; Vittori et al. 2000) and reconstruction of levelling-line displacements (Basili & Meghraoui 2001)—modelling of surface displacements indicates that the high-angle structures accommodating this slip only extend to ∼500 m beneath the surface (Basili & Meghraoui 2001). Therefore the faults activated in the Umbria-Marche sequence are not listric in the sense of a smooth decrease in dip with depth. Instead, the analysis presented here, and the close alignment of aftershock hypocentres, indicates that the faults are planar at the depths where they rupture in earthquakes (Amato et al. 1998; Chiaraluce 2003), that is, there is less than ±10° change in dip with depth between ∼2–8 km. The hypocentres of the larger events in the sequence, including the 1997 September 26 event modelled here, are located at depths close to the base of these aftershock clusters (Stramondo et al. 1999; Barba & Basili 2000), at the same depth as foreshock activity (Cattaneo et al. 2000), and close to the inferred intersection with pre-existing low-angle faults (Chiaraluce et al. 2005; Mirabella et al. 2008). A lack of seismicity at depths >8 km suggest this decollement, if it exists, is not seismically active. Both the modelling in this study and detailed studies by other workers establish that extension in the seismogenic layer is accommodated by rupture on planar faults in the Colfiorito region. 5.3 The 1995 May 13 Grevena earthquake, Greece On the 1995 May 13, a destructive Mw 6.4 normal-faulting earthquake hit northern Greece, approximately equidistant from the towns of Grevena and Kozani (Fig. 10). We obtained centroid source parameters consistent with other estimates from body waveform seismology (Hatzfeld et al. 1998), inversion of horizontal GPS displacements (Clarke et al. 1997) and InSAR studies (Resor et al. 2005) to within 10°, and the strike is similar to that measured for the only mapped fault with conspicuous surface rupture (the 250°-striking Paleochori Fault; Meyer et al. 1996). We obtained the same centroid depth (11 km) as Hatzfeld et al. (1998), and our estimated depth extent of the rupture (6–15 km) is consistent with their 14.2 km main-shock hypocentre and the distribution of aftershocks between 5–15 km. Figure 10. View largeDownload slide Map of Northern Greece.(a) Simplified tectonic setting. Major plate-bounding faults in black: NAF, North Anatolian Fault; HA, Hellenic Arc; CA, Cyprus Arc. The perimeter of box B is shown in grey. (b) Local topography map. The focal mechanism obtained for the 1995 May 13 Grevena earthquake in this study is shown offset from the EHB location. Settlements (black squares) and tectonic features are named in black. Simplified active faults, retraced after Resor et al. (2005), are delineated in black; location of surface fissures and ruptures mapped by Meyer et al. (1996) are in white; the trace of the major surface rupture, the Paleochori Fault (PF) is shown in red. Figure 10. View largeDownload slide Map of Northern Greece.(a) Simplified tectonic setting. Major plate-bounding faults in black: NAF, North Anatolian Fault; HA, Hellenic Arc; CA, Cyprus Arc. The perimeter of box B is shown in grey. (b) Local topography map. The focal mechanism obtained for the 1995 May 13 Grevena earthquake in this study is shown offset from the EHB location. Settlements (black squares) and tectonic features are named in black. Simplified active faults, retraced after Resor et al. (2005), are delineated in black; location of surface fissures and ruptures mapped by Meyer et al. (1996) are in white; the trace of the major surface rupture, the Paleochori Fault (PF) is shown in red. The planar solution from the body-waveform inversion generates synthetics that fit the shape and amplitude of SH-waveforms very well at 11 of 12 SH-stations within 30° of strike. There is therefore no indication that there may be down-dip curvature. Models with positive curvature produce complex SH-synthetics at these stations which have very different waveform shapes and/or the wrong initial polarity when compared with the observed waveforms (e.g. AAK; Fig. 11c)—this precludes any positive down-dip curvature. Models with negative curvature produce synthetic SH-waveforms with similar shapes to the recorded waveforms. Increasing the degree of negative curvature mainly affects the amplitudes, not the shape, of the synthetic waveforms, and yields a better fit of the resultant synthetic to the data for some stations (e.g. KURK −30°). However, for SH stations at azimuths 30°–65° from strike, models with more than −20° curvature generate synthetics with amplitudes much larger than the recorded data (e.g. SJG −40°). Synthetics for SH stations at azimuths >65° from strike have poor fits irrespectively of model fault geometry, as they lie close to an SH nodal surface and so have a poor signal-to-noise ratio. Stations with high take-off angles and lying roughly perpendicular to strike plot near one of the P nodal planes in a lower hemisphere projection. Small increases in negative curvature produce synthetic P-waveforms with the wrong initial polarity at these stations (e.g. NAI, ATD), ruling out more than −20° down-dip curvature. Plots of variance against curvature are skewed towards negative-curvature models (Fig. 11b), reflecting the extremely high misfits for positive-curvature models. Overall, both P and SH waveform data support a planar geometry and the down-dip curvature can be constrained to between −20° and 0°. Figure 11. View largeDownload slide Down-dip curvature modelling results for 1995 May 31 Grevena earthquake. Caption as for Fig. 7. Figure 11. View largeDownload slide Down-dip curvature modelling results for 1995 May 31 Grevena earthquake. Caption as for Fig. 7. Most published inversions suggest that the maximum slip and majority of the moment-release occurred on the deeper parts of a fault plane with parameters consistent with the focal mechanisms obtained using body waveform data (e.g. Meyer et al. 1996; Clarke et al. 1997; Rigo et al. 2004; Resor et al. 2005). It is therefore not surprising that the best-fit model from the teleseismic waveform modelling in this study is planar. The ability of the forward models to detect down-dip curvature is limited to the parts of the coseismic fault plane that produce a significant contribution to the overall moment. Therefore we do not expect to resolve the up-dip rupture propagation onto high-angle surface-breaking fault strands (if they exist) if they did not produce large offsets. It is likely that the deep main-shock fault connects in some way with the steeper exposed fault planes mapped at the surface, but the nature and geometry of this linkage is unclear. The availability of many different and detailed geologic, geodetic and seismological data sets has allowed several studies (e.g. Meyer et al. 1996; Resor et al. 2005) to build up a detailed picture of the fault network in the Kozani–Grevena region, and given the large moment-release it is not surprising that multiple fault strands, particularly those up-dip and in the hanging wall of the main shock, were activated by the Grevena earthquake. Despite the fine-scale complexity of the fault system, the results of the down-dip curvature modelling in this study suggest that the major coseismic displacements are consistent with rupture on a planar structure. 5.4 Ruptures with down-dip curvature Based on the analysis of the SH waveforms at stations within 30° of strike, there is a strong indication of down-dip curvature in 4 events. Two events (a Mw 5.7 and a Mw 5.8) were from an earthquake sequence that occurred on the Karonga Fault system, Lake Malawi, and which culminated in a Mw 5.9 (included here for completeness, but which does not show any evidence of down-dip curvature). The other two were 2004 and 2005 Mw 6.2 events that occurred in the Lunggar Rift region, Tibet. 5.4.1 The 2004 and 2005 Zhongba events, Lunggar Rift, Tibet We studied two Mw 6.2 normal-faulting events that occurred in Zhongba county in the Xizang region of southwestern Tibet, China (Fig. 12). Just north of the Indus suture the tectonics of southern Tibet are characterized by extension across N–S-trending grabens (Armijo et al. 1986). The 2004 July 11 and 2005 April 7 earthquakes described here were located in one of these active grabens, the South Lunggar Rift. Figure 12. View largeDownload slide Map of southwest Tibet. (a) Regional map and simplified structure. Major normal faults in red, strike-slip faults in black and suture zones dashed in white. NLR, North Lunggar Rift; SLR, South Lunggar Rift. Country boundaries are in grey, as is the perimeter of box B. The inset globe shows the location of box A in red. SRTM topography is coloured according to the scale on the right. (b) Topography and structure of the South Lunggar Rift. Focal mechanisms obtained in this study are offset from their EHB locations (red dot) and labelled with a date (yymmdd) identifier. Faults in red, after Styron et al. (2013). Outline of model fault planes and up-dip surface projections (green) from the uniform-slip InSAR models of Elliott et al. (2010) for the 2004 and 2005 events, and the 2008 doublet. Figure 12. View largeDownload slide Map of southwest Tibet. (a) Regional map and simplified structure. Major normal faults in red, strike-slip faults in black and suture zones dashed in white. NLR, North Lunggar Rift; SLR, South Lunggar Rift. Country boundaries are in grey, as is the perimeter of box B. The inset globe shows the location of box A in red. SRTM topography is coloured according to the scale on the right. (b) Topography and structure of the South Lunggar Rift. Focal mechanisms obtained in this study are offset from their EHB locations (red dot) and labelled with a date (yymmdd) identifier. Faults in red, after Styron et al. (2013). Outline of model fault planes and up-dip surface projections (green) from the uniform-slip InSAR models of Elliott et al. (2010) for the 2004 and 2005 events, and the 2008 doublet. The South Lunggar Rift is comprised of a ∼50 km wide central horst, the Surla Range, bounded on either side by the gentle west-dipping South Lunggar Detachment and steeper east-dipping Palung Co Fault (Styron et al. 2013). Small fault scarps are observed to cut glacial moraines along the northern portion of the Palung Co Fault (Styron et al. 2013), and the up-dip projections of InSAR-modelled fault planes for a 2008 normal-faulting doublet (Elliott et al. 2010) also coincide with the range front and mapped fault trace in the north, indicating that the fault is currently active. Elliott et al. (2010) performed a study of a series of large normal-faulting events in Tibet, including the two we model here, using InSAR and body waveform seismology. For both events, the surface deformation in InSAR interferograms was best fit by west-dipping faults located east of the Palung Co Fault (Elliott et al. 2010, and Fig. 12). The seismogenic thickness is ∼15 km in Tibet (Craig et al. 2012), and the magnitude and depth of the earthquakes suggest that they ruptured through most of the seismogenic crust. These two events seem to represent break-up of the hanging wall of the major basin-bounding Palung Co fault on antithetic faults. 2004 July 11 event. Synthetics from the planar solution obtained through body-waveform inversion fit SH-waveform data quite well at the nine stations within 30° of strike. However for the majority of these stations, the synthetics are consistently of a lower amplitude than the recorded signal, and do not match the fine detail of the waveform shape (the polarity of the small peaks in the initial part of the waveform) (e.g. OBN, ARU, SFJ; Fig. 13c). These small initial waveform peaks are a strong indication of down-dip curvature. Model geometries with some negative curvature (between −10° to −30°) consistently yield synthetics with better fits to the recorded waveform than for a planar model, particularly with respect to these details of SH-waveform shape and amplitude (e.g. ARU −20°, SFJ −30°). This improvement in fit is also reflected in the variance-curvature graphs for stations within 30° of strike (Fig. 13b); eight have minimum variances for models with negative curvature, and the average model variance is lowest for a model with −20° down-dip curvature. Figure 13. View largeDownload slide Down-dip curvature modelling results for the 2004 July 11 Zhongba earthquake. Caption as for Fig. 7. Figure 13. View largeDownload slide Down-dip curvature modelling results for the 2004 July 11 Zhongba earthquake. Caption as for Fig. 7. The shape and amplitude of SH-waveforms at all stations at azimuths >30° and <55° from strike are also better fit by synthetics from models with −10° to −30° curvature (e.g. MA2 −30°, GNI −20°; Fig. 13c). Stations at azimuths >55° from strike have complex, low-amplitude signals that are not well matched by any synthetics, due to the poor signal-to-noise ratio resulting from their being close to an SH nodal plane. From the synthetic modelling presented in Section 3, stations in this azimuth range are not expected to be sensitive to down-dip curvature. Models with any positive down-dip curvature produce synthetic SH-waveforms with complex wave shapes and initial peaks with the opposite polarity to the recorded signal at all stations within 47° of strike, ruling out any convex down-dip geometry for this event. For stations that plot near the E-dipping nodal plane in a lower hemisphere projection, models with −40° down-dip curvature or more produce synthetic P-waveforms with the wrong initial polarity (e.g. SSE, DAV; Fig. 13c). There is a good overall fit of both P and SH waveforms at models with −30° to 0° curvature. The results suggest that this event involves down-dip curvature, and the best-fit model is slightly listric, with −20° curvature. 2005 April 7 event. Synthetic SH-waveforms generated at five of six stations within 30° of strike for a model with planar down-dip geometry have much smaller amplitudes and different shapes compared to the recorded waveforms (e.g. KONO, KEV; Fig. 14c). Similar to the 2004 event, this is a strong indication of down-dip curvature. Synthetics generated from models with −30° to −10° negative down-dip curvature have very good fits to the data at these stations, in terms of the amplitude, overall shape and polarity of small initial peaks in the waveform (e.g. MBWA −30°, ARU −20°). The fit of the synthetics is significantly better for this range of negative-curvature models than for a planar model geometry. This feature is reflected in the shape of the graphs of variance against curvature for these stations, which have residual variances that tend to a minimum in this model range, and are lower than the variance for the planar model for 4 stations (Fig. 14b). In almost all cases the fit of synthetic SH-waveforms to the seismograms is very poor for all models with positive curvature. For strongly listric models (−40° down-dip curvature or more) synthetic SH-waveforms have very high amplitudes compared to the recorded waveforms, and the fit of the synthetic deteriorates with increasing negative curvature. The fit of synthetic P-waveforms at stations with high take-off angles and at azimuths that are roughly perpendicular to strike (e.g. MAJO, TATO) also becomes significantly worse in this range, as the synthetic waveform has the wrong initial polarity. For almost all stations at azimuths >30° and <50° from strike, models with −30° to −10° curvature also yield synthetics with a better fit to the recorded SH-waveform than synthetics from the planar model, in terms of both the detail of waveform shape and the amplitude of the peak. Based on the analysis of the SH waveforms, there is strong evidence for down-dip curvature in the range −10° to −30°. The best-fit model has −20° curvature. Figure 14. View largeDownload slide Down-dip curvature modelling results for the 2005 April 07 Zhongba earthquake.Caption as for Fig. 7. Figure 14. View largeDownload slide Down-dip curvature modelling results for the 2005 April 07 Zhongba earthquake.Caption as for Fig. 7. 5.4.2 The 2009 Karonga sequence, Lake Malawi We studied the three largest events (6th December Mw 5.7, 8th December Mw 5.8, and 19th December Mw 5.9) in an earthquake sequence that struck the Karonga region of northern Malawi, on the western shore of Lake Malawi, between November and December 2009 (Fig. 15). The rift basin is strongly asymmetric; the footwall of a steep west-dipping fault (the Livingstone Fault) forms a 2 km high escarpment on the eastern bank of the lake, and its hanging wall is broken up by minor west-dipping faults, mapped by offshore seismic reflection profiles (Flannery & Rosendahl 2009; Ebinger et al. 1999). The east-dipping Karonga Fault forms the westernmost boundary of the basin and divides the hilly topography and exposures of Precambrian to lower Palaeozoic basement rocks in the west from the flat alluvial plain in the east (Hamiel et al. 2012). Following the earthquake sequence, surface breaks were observed in an area north of Karonga city with no previous evidence of surface-rupturing faults, offsetting Quaternary sediments in the flat plain (Hamiel et al. 2012; Macheyeki et al. 2015). Biggs et al. (2010) used seismology and InSAR to demonstrate that the sequence occurred on shallow, west-dipping structures in the hanging wall of the Karonga Fault. It has been suggested that failure initiated on a favourably orientated pre-existing structure, and then migrated to adjacent planes of weakness as a result of static stress transfer (Fagereng 2013). Figure 15. View largeDownload slide Map of northern Lake Malawi.(a) Regional map of the southern part of the Western Branch of the East African Rift. Country boundaries are in grey, major normal faults mentioned in the text are in red. The traces of the Kanda (KF), Livingstone (LF) and Bilila-Mtakataka (BMF) Faults are after Versfelt & Rosendahl (1989), Jackson & Blenkinsop (1997) and Vittori et al. (1997), respectively. The perimeter of box B is shown in grey and the inset globe shows the location of box A in red. (b) SRTM30 topography of northern Lake Malawi (scale to top left). Focal mechanisms obtained in this study are offset from their EHB locations (red dot) and labelled with a date (yymmdd) identifier. The location of Karonga is marked with a black square; KFS is the Karonga Fault system. Faults, delineated in black, are retraced from Biggs et al. (2010); the surface ruptures of Macheyeki et al. (2015) are in white with a black outline (just N of Karonga). The trend of basement foliations are marked in purple, after Versfelt & Rosendahl (1989) Figure 15. View largeDownload slide Map of northern Lake Malawi.(a) Regional map of the southern part of the Western Branch of the East African Rift. Country boundaries are in grey, major normal faults mentioned in the text are in red. The traces of the Kanda (KF), Livingstone (LF) and Bilila-Mtakataka (BMF) Faults are after Versfelt & Rosendahl (1989), Jackson & Blenkinsop (1997) and Vittori et al. (1997), respectively. The perimeter of box B is shown in grey and the inset globe shows the location of box A in red. (b) SRTM30 topography of northern Lake Malawi (scale to top left). Focal mechanisms obtained in this study are offset from their EHB locations (red dot) and labelled with a date (yymmdd) identifier. The location of Karonga is marked with a black square; KFS is the Karonga Fault system. Faults, delineated in black, are retraced from Biggs et al. (2010); the surface ruptures of Macheyeki et al. (2015) are in white with a black outline (just N of Karonga). The trend of basement foliations are marked in purple, after Versfelt & Rosendahl (1989) 2009 December 19 event. Unlike the other earthquakes we modelled from this sequence (6th December Mw 5.7 and 8th December Mw 5.8 events), there was no evidence of down-dip curvature for this event. Of nine stations within 30° of strike, the planar solution from the body-waveform inversion generates synthetics with good fits to the shape and amplitude of SH-waveforms at five stations (e.g. MAW, TUE, KIEV; Fig. 16c). At the other four, the synthetic wave shape has a poorer fit and the amplitude is lower than the recorded data (e.g. TAM, BFO). Down-dip curvature modelling does yield synthetics with better fits than the planar model, for these stations. However, it also results in SH-synthetics with increasingly worse fits to the waveform data for the five stations that are well-matched by the initial planar solution. Positive-curvature models generate very different synthetic SH wave shapes, which in some cases have the wrong initial polarity compared to the recorded data (e.g. BFO +20°). Models with negative curvature produce synthetic SH-waveforms with high amplitudes, which yield individual best-fit models for some stations (e.g. BFO −30°), but very poor fits for others (e.g. MAW −30°, DPC −30°). The minimum-variance model for most of the ∼along-strike SH-stations is between −10° to +10° (Fig. 16b). The average is −10°, however this is most likely skewed by the result for EIL, for which the observed waveform data is not fit well by any model, irrespective of geometry, presumably due to noise in the data. Figure 16. View largeDownload slide Down-dip curvature modelling results for the 2009 December 19 Karonga earthquake.Caption as for Fig. 7. Figure 16. View largeDownload slide Down-dip curvature modelling results for the 2009 December 19 Karonga earthquake.Caption as for Fig. 7. SH-waveforms at stations at azimuths >30° from strike are less sensitive to down-dip curvature and are overall well-matched by the initial planar solution. Increasing degrees of down-dip curvature generates synthetics with poorer fits (e.g. XMIS, UOSS; Fig. 16c). The complexity, polarities and reduced amplitudes of synthetic P-waveforms at stations with high take-off angles and that lie at high angles from strike precludes geometries with >30° down-dip curvature (e.g. KAPI, RCBR). The overall fit of synthetic SH-waveforms is significantly worse outside the range −30° to +10°. We therefore suggest that this event in the Karonga sequence ruptured a planar fault. 2009 December 8 event. The planar solution from the body-waveform inversion generates synthetics with similar waveform shapes, but much smaller amplitudes than the recorded SH-waveform at all five stations within 30° of strike (e.g. TUE, IDI; Fig. 17c). This is a strong indication of down-dip curvature. Synthetics generated from models with negative down-dip curvature have excellent fits to the data at these stations, both for the waveform amplitude and shape, particularly in the −30° to −60° range. The fit of the synthetics is significantly better for this range of negative-curvature models than for a planar model geometry. This is reflected in the shape of the graphs of variance against curvature for these stations (Fig. 17b). For all five stations, models with negative down-dip curvature yield lower variances than that for the single-plane solution and their respective minimum variances lie in the range −50° to −20°. Figure 17. View largeDownload slide Down-dip curvature modelling results for the 2009 December 8 Karonga earthquake.Caption as for Fig. 7. Figure 17. View largeDownload slide Down-dip curvature modelling results for the 2009 December 8 Karonga earthquake.Caption as for Fig. 7. For stations at azimuths >30° from strike, there is a wide range of model geometries over which the fit of the synthetic (in terms of waveform shape and amplitude) to the observed SH-waveform is adequate. In general the fit is equally good or slightly better for negative-curvature models (e.g. SYO −30°; Fig. 17c), and equally good or slightly worse for positive-curvature models (e.g. SYO +10°). Although the overall fit of SH-synthetics is best for models with strong negative curvature (−50°), the fit of synthetic P-waveforms at stations with high take-off angles and at azimuths that are roughly perpendicular to strike (e.g. CHTO, DGAR and XMIS) becomes significantly worse as the synthetic waveforms have the wrong initial polarity. The overall fit of all P and SH synthetics is good for models with geometries in the −40° to −10° curvature range. Due to the location of this event, much of the region lying to the south and within the teleseismic distance range is covered by ocean (Fig. 17a), therefore there are large (∼90°) azimuth gaps in the S-wave data-coverage. It would be preferable to have a more even distribution of station data, particularly for SH-waveform data, however there is strong evidence from the SH-waveform data that does exist (particularly from the along-strike stations to the north, and the one SH-station to the south, SYO) that this event ruptured a fault with negative down-dip curvature. From this evidence, and considering the fit to all available P and SH waveforms, our preferred model is −30° curvature. 2009 December 6 event. The planar solution from the body-waveform inversion generates SH-synthetics with similar waveform shapes and amplitudes to the observed models for the 9 stations at azimuths within 30° of strike (e.g. GNI, KBA; Fig. 18c). There is therefore no strong indication of down-dip curvature. However, the minimum-variance model for all but one station has a geometry with negative curvature (Fig. 18b), and models with some negative curvature (−30° to −10°) produce synthetics with similarly good wave shapes and amplitudes as the synthetics for the planar model. For all stations at azimuths >30° from strike, models with strong negative curvature yield synthetics with a better fit to the recorded SH-waveform than synthetics from the planar model, in terms of both the detail of waveform shape and the amplitude of the peak (e.g. UOSS −50°, DBIC −50°). At stations with high take-off angles and at azimuths that are perpendicular to strike (e.g. UOSS, PALK and SHEL), synthetic P-waveforms have small amplitudes and initial peaks with the wrong polarity compared to the recorded waveforms for models with −40° or more down-dip curvature, ruling out an extremely listric fault geometry. The fit synthetic SH-waveforms deteriorates for all stations for models with increasing positive curvature. Figure 18. View largeDownload slide Down-dip curvature modelling results for the 2009 December 6 Karonga earthquake. Caption as for Fig. 7. Figure 18. View largeDownload slide Down-dip curvature modelling results for the 2009 December 6 Karonga earthquake. Caption as for Fig. 7. Due to the small size (Mw 5.7) and the location of this event, there is not a good azimuthal coverage of SH-stations at teleseismic distances (Fig. 18a), especially south of the event. There is a possibility that this event may have down-dip curvature, especially given its proximity to the 8th December event, however we are unable to constrain the geometry further than to say models with down-dip curvature in the range of −30° to +10° (including a planar geometry), give equally good overall fits to P and SH waveforms. 6 DISCUSSION As described in the sections above, the down-dip curvature modelling results suggest that continental normal-faulting earthquakes that are large enough to penetrate to the bottom of the seismogenic layer rupture planar faults; most events showed no strong evidence for down-dip curvature, had dips between 30° and 60°, and could be constrained to be planar to within ±20°. In both the Apennines and the Aegean, recent large normal-faulting earthquakes have generated very little surface rupture in regions with complex mapped faults. The rise of geodetic observational techniques (InSAR and GPS) has resulted in numerous studies that produced competing models of if, and how, the seismogenic slip is accommodated in the upper ≤1 km of crust, and on which faults. Fault plane measurements taken at the surface often show relatively steep dips (e.g. Jackson et al. 1982; Cello et al. 2000; Chiaraluce et al. 2005) compared to the source parameters estimated from seismology, resulting in authors describing faults as listric. However, this view is misleading. It is expected that normal fault planes steepen in upper ∼500 m as the rupture propagates towards a free surface, because this portion of the crust often fails in tension; exposed fault planes may also dip steeply due to unloading effects. This logic implies that there will be a significant underestimation of seismic hazard from surface studies, and that the structures accommodating slip in the near-surface do not reflect the geometry of the main seismogenic fault at depth. Fault planes may be expected to flatten at depth, if they detaches into a subhorizontal, rheologically weak unit. It is not unexpected that some seismogenic slip propagates onto these segments, however they generally do not make a significant contribution to the coseismic signal (e.g. Meyer et al. 1996). Indeed, our method will only resolve down-dip curvature if there is a significant moment contribution from these upper and lower portions of the fault plane. The advantage of the seismological technique presented in this paper is that we resolve the structure of the fault at depth, and on a gross scale, that is, the technique is only sensitive to the parts of the fault that are important in generating earthquakes and the picture is not obscured by the (entirely expected) complexity of surface faulting and deformation. Partly due to the small magnitudes of the earthquakes, and partly due to the global distribution of seismometers, we have had very limited success in modelling oceanic earthquakes. For example, for events on the Mid-Atlantic Ridge there are large azimuthal gaps in station coverage at teleseismic distances, particularly along-strike to the north and south, as these regions are covered by ocean. Also, the amplitude of water multiples are often of a similar magnitude to the direct arrivals, which makes our analysis difficult. Both of the oceanic events that we studied are located in regions where there is no detailed bathymetry data to confirm whether or not core complexes (the uplifted, domed and corrugated footwalls of large-offset normal faults that expose mantle rocks) are present. It is impossible to distinguish on the basis of ocean floor bathymetry alone whether rift-parallel ridged relief forms as a result of simple domino-style extension and rotation of successive planar normal faults, or whether it is formed from the steep surface breakaways of listric detachment faults (Smith et al. 2008). Resolving the down-dip geometry of oceanic normal-faulting earthquakes offers a way to discriminate between models. Based on the observed waveforms, we inferred that both of the oceanic events we studied (Tables 1 and 2, and Appendix D in the Supporting Information) ruptured through the full seismogenic layer on planar faults. In contrast to the majority of events we studied, there is strong evidence for listric down-dip curvature in some events from Tibet and East Africa. For events showing down-dip curvature, the maximum change in dip is 20°–30°. Although resolving this change in dip is a significant observation, it should be noted that the overall change is much less than that for the strongly listric fault geometries (≥50° change in dip) that are often drawn on geological cross-sections. The tightness of the constraints on the geometry is similar to the planar events, that is, within 10°–30° of the best-fitting model geometry. The ruptures we studied that displayed down-dip curvature occurred on antithetic faults, or minor faults within the hanging wall of a rift. The location and the inferred depth extent of the rupture for both the 2004 and 2005 Zhongba (Tibet) events indicate that these earthquakes occurred on faults that cut through the hanging wall of a major rift-bounding normal fault. Our best-fit models, of −20° curvature, indicate the lower portion of the active faults may dip at ∼30°. This angle is similar to the ∼28° dip of the basal detachment Kapp et al. (2008) inferred to underlie the North Lunggar Rift, ∼100 km north-northwest of the Zhongba epicentres. The deeper structure of the South Lunggar Rift (where the Zhongba earthquakes were located) is not known. West of the Zhongba epicentres, the South Lunggar Detachment dips at 20° at the surface and exhumes mylonites and foliated rocks with a normal sense of shear (Styron et al. 2013). However, we have found no evidence for seismogenic slip on very low-angle normal faults (≤20° dip) in the Lunggar Rift, as has been debated for metamorphic core complexes in other parts of the world (Wernicke 1995; Axen 1999; Collettini 2011). The 2009 Karonga earthquakes ruptured a series of ∼6–8 km long fault segments in the hanging wall of the Karonga Fault (which is antithetic to the major basin-bounding Livingstone Fault), each with a small depth extent compared to the ≥40 km seismogenic thickness in this area (Foster & Jackson 1998; Ebinger et al. 1999; Maggi et al. 2000; Craig et al. 2011). For one event there is strong evidence of down-dip curvature, with a suggestion of possible curvature for a second. In the Karonga area the pre-existing structure is complex (Fig. 15b), and two opposing basement fabrics converge (Versfelt & Rosendahl 1989). It has been suggested that failure initiated on a favourably orientated pre-existing structure, and then migrated to adjacent planes of weakness as a result of static stress transfer (Fagereng 2013). Therefore it is possible that the varying down-dip geometries are an inherited feature, and result from the reactivation of old fabrics. However, the scale of the Livingstone Fault (i.e. the great width of the basin and the large topographic step resulting from the cumulative displacement across the fault), together with a low spreading rate (Saria et al. 2014) and long earthquake cycle, means that it must dominate the stress-state in the rift (Foster & Nimmo 1996; Ebinger et al. 1999), which may also be highly spatially variable. In this setting, it is perhaps not surprising that the minor faults are curved. 7 CONCLUSIONS We have developed a new seismological technique to assess the down-dip shape of earthquake-generating faults through the analysis of body waveforms, and have successfully applied the technique to earthquakes in a variety of extensional environments. We have found that most normal-faulting earthquakes that rupture through the full seismogenic layer are planar and have dips of 30°–60°. 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