TY - JOUR
AU - Phạm,, Thanh-Son
AB - SUMMARY Recorded globally, cross-correlated ground-motion time-series of the coda of large earthquakes enable the construction of a 2-D representation of correlation lapse time and inter-receiver distance—a global correlogram. A better understanding of how the features present in a correlogram are generated can revolutionize the characterization of planetary interiors. Here, we investigated correlograms based on individual large earthquakes and identified 12 events from the past decade with a multitude of prominent and some ‘exotic’ features in the first 3 hr following correlation origin. We found that the type of the source mechanism and energy-release dynamics are the key influencers responsible for individual correlograms equal in quality to a stack of hundreds of correlograms. A single event is sufficient in creating a correlogram resembling previous correlograms constructed from a large number of events, which reinforces the notion that the earthquake coda-correlation features are not ‘reconstructed’ body waves. Numerical simulations of the correlation wavefield can thus be based on exceptional-quality events, becoming more computationally affordable. Here, we explain more than 60 features of the global coda-correlogram, which presents the most extensive catalogue to date. Earthquake dynamics, Earthquake source observations, Seismic interferometry, Seismic noise 1 INTRODUCTION First attempts to correlate ambient noise from continuous records on a global scale consisted of removing the unwanted impact of earthquakes (e.g. Boué et al. 2013; Lin et al. 2013; Nishida 2013). It quickly appeared that the earthquake coda (a late part of the waveform, recorded hours after the first arrivals) was a major source of coherent energy. Recently introduced digital waveform processing flow enables turning cross-correlation functions of earthquake coda, simultaneously recorded worldwide, into global stacks that contain a wealth of prominent features. The Earth’s correlation wavefield is a mathematical expression of the seismic wavefield that can be presented as a 2-D stack of cross-correlation functions or global correlogram (Fig 1; for a glossary of terms, see Table 1). The processing, particularly improvements in conjunction with spectral normalization (Bensen et al. 2007; Phạm & Tkalčić 2017), results in correlograms of unprecedented quality (Phạm et al. 2018). Some of the features that had been previously considered spurious, but also some late arriving features that resemble the multiple reverberations through the Earth, are particularly prominent. The high-quality correlogram and improvements in processing have also led to a detection of feeble shear waves in the Earth’s inner core (Tkalčić & Phạm 2018). For a detailed review of the coda-correlation wavefield and recent advances, see Tkalčić et al. (2020). Figure 1. Open in new tabDownload slide (a) Frequency histogram of all available receiver pairs on the global scale for the 2010–2018 time interval. Inter-receiver distance is binned in 1° bins; the number of receivers is in excess of 50 000 for some bins. (b) Global correlogram calculated from the late-coda waveforms of the 12 earthquakes classified as the grade-A events in this study between 0 and 3600 s past the correlation-origin time, which we term the ‘regular’ range of the Earth’s correlation wavefield. (c) The same as (b) but with the superimposed theoretically predicted correlogram features. (d) Colour key for the theoretically predicted correlogram features. Figure 1. Open in new tabDownload slide (a) Frequency histogram of all available receiver pairs on the global scale for the 2010–2018 time interval. Inter-receiver distance is binned in 1° bins; the number of receivers is in excess of 50 000 for some bins. (b) Global correlogram calculated from the late-coda waveforms of the 12 earthquakes classified as the grade-A events in this study between 0 and 3600 s past the correlation-origin time, which we term the ‘regular’ range of the Earth’s correlation wavefield. (c) The same as (b) but with the superimposed theoretically predicted correlogram features. (d) Colour key for the theoretically predicted correlogram features. The global coda-correlogram features that look like seismic phases in the seismic wavefield (Boué et al. 2013, 2014; Huang et al. 2015; Wang et al. 2015) can be explained as high-tone normal modes (Poli et al. 2017) or through the contribution of many pairs of phases that arrive at two given recorders with the same slowness (Phạm et al. 2018). The latter study found that the features that had previously been called ‘spurious’ were formed due to the similarity of the pairs of phases that had a large part of ray path in common and differed only near two receivers. For example, the prominent non-causative feature in the correlogram named cS-cP can be formed due to the energy partitioning at the core–mantle boundary (CMB) between P and S waves, and the peak in the cross-correlation stack can be explained using the stationary principle; that is, the most prominent peak will be observed for the receivers recording P and S waves that originated in the stationary point at the CMB and arrived at those two receivers with the same slowness. Contribution from the near-stationary point phases is significant to all observed coda-correlogram features, which is evident from the fact that global earthquake sources are almost never located exactly in the stationary points for two given receivers. The quasi-stationarity has been argued recently to contribute to the generation of a correlation feature P-PKPab in the global ambient-noise correlograms that might originate from oceanic microseism sources (Li et al. 2020). By the same principle, all correlogram features including those that look like common seismic phases can be explained. We have therefore devised a new convention for all observed features in the global correlogram including a ‘*’ symbol for all features that look like the phases in the seismic wavefield (Tkalčić & Phạm 2018; Tkalčić et al. 2020). An important long-term goal to be achieved in the field of global coda-correlation studies is to fully understand the correlation wavefield and learn how to relate it with the Earth’s structure (Wang & Tkalčić 2020b). The main goal here is to understand the circumstances under which the global correlogram improves or worsens so that we can further enhance the clarity of the observed features and employ them in future applications of the correlation wavefield. Another important goal of this work is to provide a catalogue of all observed features, some of which are already known from previous studies and others emerge as the quality of the correlogram improves. It has been shown that the correlation wavefield evolves in a similar way to the seismic wavefield (Kennett 2001; Ruigrok et al. 2008; Poli et al. 2017; Kennett & Phạm 2018). Previous studies (Lin & Tsai 2013; Lin et al. 2013; Nishida 2013; Boué et al. 2014; Sens-Schönfelder et al. 2015) also showed that the emergence of global correlation features is closely related to the nature of reverberation in earthquake coda (Aki 1969; Aki & Chouet 1975). Lin et al. (2013) discussed the impact of earthquakes and showed that it strongly depends on the processing applied to the continuing data. Boué et al. (2014) explored the difference in global correlograms for seismically active and quiet days and suggested a strong causal relationship between the correlation features and large earthquakes. It remains critical, however, to decipher the nature of seismic sources that most effectively produce high-quality correlograms. Therefore, here we systematically examine many seismic events, including the most recent large earthquakes, in order to identify those that contribute most constructively and those that diminish the quality of the global correlogram. We first describe the data considered in this study along with data analysis and methods used to produce global correlograms from individual events (Section 2). We then discuss the quality of correlograms derived from individual earthquakes in the context of earthquake dynamics (Section 3). This is followed by a description of the new catalogue of the correlogram features derived from a compilation of the highest-quality correlograms (Section 4). We end with concluding remarks (Section 5). 2 DATA ANALYSIS: THE WORLD’S LARGEST EARTHQUAKES Our study is based on the analysis of the world’s largest earthquakes. Previously, we included in the data processing more than 150 world’s earthquakes with Mw ≥ 6.8 between 2010 and 2016 recorded at about 160 receivers in the global seismic network and the Australian seismic network to produce a global correlogram (Phạm et al. 2018; Tkalčić & Phạm 2018). Here, we expand our data set to include earthquakes until 2018 and all available broad-band recordings worldwide (about 2000 receivers for most earthquakes). 2.1 Data selection To achieve the goals set out above, we systematically analysed available waveform data. Hence, data were obtained via a request from IRIS DMC using JWEED, and only events with Mw ≥ 6.8 were requested because such large seismic events should create more detectable arrivals in the global correlogram. We limited our search to the events from 2010 January 1 to 2018 January 1. This resulted in 183 events. The waveforms that were requested were made to be 10 hr long from the events’ origin times. For the analysis here, only the vertical channels were used. As a result, the number of available receivers for some events increased to about 2200. 2.2 Construction of global correlograms The instrument responses were removed so that the waveform correlation corresponded to the Earth’s response, rather than each of the individual instruments. The main processing procedure for each earthquake included single-receiver processing, followed by cross-correlating receiver pairs. Single receiver processing involves temporal and spectral normalization of the waveform data. Temporal normalization aims to reduce the effect of earthquakes, non-stationary noise sources and instrumental irregularities near to the station (Bensen et al. 2007). In the case of the earthquake coda, the temporal normalization mostly corrects natural amplitude decay due to geometrical spreading and attenuation. The method we used here involves running the absolute-mean to suppress unwanted signals in the data as well as to balance the temporal trend in waveform amplitudes. During this stage, the raw velocity seismograms are filtered and smoothed to provide the envelope functions. To complete the temporal-normalization process, these are then weighted by the inverse of the envelope functions. More details about this method can be found in Lin et al. (2007). Spectral normalization removes a bias due to the lack of high-frequency relative to low-frequency content for teleseismic propagation. We used the method of spectral whitening as described in Bensen et al. (2007) and in our previous work (Phạm & Tkalčić 2017) to amplify the high-frequency content. We optimized the averaging window width to increase the signal-to-noise ratio and the clarity of cross-correlations (Phạm & Tkalčić 2018). The output obtained, following spectral and temporal normalization, was a list of pre-computed, whitened complex spectra for all stations. We computed correlograms for up to 10 800 s beyond the correlation-origin time and initially used the time interval 0–3600 s. When computing the cross-correlation, we calculated the angular inter-receiver distance for each receiver pair and computed their cross-correlation function in the spectral domain using the whitened spectra. Inverse Fourier transforms were used to obtain a one-sided symmetric cross-correlation function. The angular inter-receiver distance was then split into bins and the cross-correlation functions were stacked for each bin. This produces a 2-D matrix; that is, the global correlogram, a representation of the Earth’s correlation wavefield (Figs 1, 4 and 5, and Supporting Information Figs S2–S5). Figure 2. Open in new tabDownload slide A geographic map of the locations of receivers and A- and B-grade earthquakes used in this study. The earthquakes are indicated by the corresponding ‘beach-ball’ diagrams. The size of the ‘beach balls’ is proportional to the earthquakes’ moment magnitudes. They are coloured according to the geographical region shown in the legend of Fig. 3. Figure 2. Open in new tabDownload slide A geographic map of the locations of receivers and A- and B-grade earthquakes used in this study. The earthquakes are indicated by the corresponding ‘beach-ball’ diagrams. The size of the ‘beach balls’ is proportional to the earthquakes’ moment magnitudes. They are coloured according to the geographical region shown in the legend of Fig. 3. Figure 3. Open in new tabDownload slide Blob chart of large earthquakes that occurred in the 2010–2018 time interval. (a) Centroid moment tensor solutions (beach-ball diagrams) of earthquakes with magnitude Mw ≥ 7.0 positioned along the vertical axis according to the difference between the origin and centroid times. The size of the ‘beach balls’ is proportional to the earthquakes’ moment magnitudes. Only the earthquakes categorized as grade A (see Table 2 and Fig. 2 for the locations) are coloured according to the geographical region shown in the legend. Earthquakes other than grade A are shown in grey. (b) The same as (a), but the earthquakes are positioned along the vertical axis based on the duration of their source-time function (STF). The earthquakes categorized both as grade A and grade B (see Table 2 and Supporting Information Table S1) are coloured according to the geographical region shown in the legend. Figure 3. Open in new tabDownload slide Blob chart of large earthquakes that occurred in the 2010–2018 time interval. (a) Centroid moment tensor solutions (beach-ball diagrams) of earthquakes with magnitude Mw ≥ 7.0 positioned along the vertical axis according to the difference between the origin and centroid times. The size of the ‘beach balls’ is proportional to the earthquakes’ moment magnitudes. Only the earthquakes categorized as grade A (see Table 2 and Fig. 2 for the locations) are coloured according to the geographical region shown in the legend. Earthquakes other than grade A are shown in grey. (b) The same as (a), but the earthquakes are positioned along the vertical axis based on the duration of their source-time function (STF). The earthquakes categorized both as grade A and grade B (see Table 2 and Supporting Information Table S1) are coloured according to the geographical region shown in the legend. 2.3 Classification of correlograms Instead of stacking correlograms over all events, we compute and analyse events’ correlograms qualitatively, on individual basis, to gain a better insight into the influence of the kinematics and dynamics of earthquake sources. Finally, we classify the events, based on their quality to Grade A, Grade B, Grade C, and so on, from the highest to the lowest quality. A-grade correlograms are characterized by the prominence of the first-order correlation features and the presence of a number of the second-order features. The first-order features are shown in the last column of Supporting Information Table S2 and we refer the reader to the legend of Fig. 1 in the main text to identify the features in the global correlogram. I*, I2*, I3* (F0–2) and the higher multiples are termed the ‘1* group’, and K*, K2*, K3* (F8–10) and the higher multiples are termed the ‘K* group’ of the correlation wavefield. A strongly expressed K* is also responsible for the following features: cK* (F35) and ScSK* (F37) in the right part of the correlogram. The grade-A correlograms are expected to have highly prominent ScS* (F24), c* (F26), cS-cP (F27) and the lower multiples of I* and K* groups, and they are not specifically mentioned in Supporting Information Table S1 unless there is something unusual about these observations. Another feature that is of interest is K-ScS (F20), which appears as a non-causative feature (arriving before the theoretical arrival of P waves) in the lower right portion of the correlogram. SKP* (F11) that appears around 250 s above K* is prominent in most correlograms, resulting also in related features in the upper central part of the correlogram, SKPK* (F12) and SKPK2* (F13). The most prominent second-order features are in the exotic part of the correlogram: I4*, I5* and I6* (F44–46), and they are well pronounced in the final stack and in some individual correlograms, particularly those corresponding to deep events. Other examples of second-order features are SKPK3* (F50) and SKPK4* (F51). B-grade correlograms are characterized by the prominence of almost all first-order correlation features, but a lower quality or a complete absence of some of them. Another property that distinguishes the grade-A from the grade-B correlograms is not just how well the features are expressed in the first 0-3600 s, but also how prominent the exotic features appear in the later times (3600–7200 s and 7200–10 800 s). The classification and the difference between grade-A and grade-B correlograms remain somewhat subjective, and the final ranking is based on a thorough visual analysis of hundreds of correlograms that were considered in the paper. Upon an initial inspection, we found that events with 6.8 ≤ Mw ≤ 7.0 in our chosen time interval (183 events in total) produced noisy first-order features and a relatively smaller number of the second-order features (see the Supporting Information for a more detailed description of how we classified the correlogram features), and did not contribute to the quality of the correlograms except for a single event (the Mw = 7.0 event near the coast of northern Chile on 2014 April 1). We therefore focused on the events with Mw ≥ 7.1, and their total number consequently reduced to 97—the number we can manage. Out of those 97 events, there were 7 events with Mw ≥ 8.0 or 13 events with Mw ≥ 7.9. We identified a total of 12 events (Table 2, Fig. 2) that passed our quality selection criteria as the grade-A events (the events of the highest quality). Their correlograms are characterized by the prominence of the first-order features and also met our criterion for the number of the second-order features. It is worth noting here that we made a deliberate choice to study correlograms of individual events first, and then classified them according to their quality before examining their depths, focal mechanisms, source-time functions (STF; moment-rate release) and other characteristics (see the next section for more details). We identified nine more events that yielded the grade-B correlograms (of good quality), although with some imperfections (see Supporting Information Figs S3–S5 and Tables S1–S3 and compare the notes on the quality of individual features). Interestingly, both the grade-A and grade-B events (21 in total) were not among the largest events that occurred, with two exceptions. Out of the 13 events with Mw ≥ 7.9, a single event (Mw = 8.2, Solomon Islands region on 2017 January 22) was selected as the grade-A event and a single event (Mw = 8.2, near the coast of Chiapas, Mexico on 2017 September 8) was among the grade-B events based on the correlograms they produced. Figure 4. Open in new tabDownload slide The ‘exotic’ range of the Earth’s correlation wavefield between 3600 and 7200 s past the correlation-origin time. (a) Global correlogram calculated from the late-coda waveforms of the grade-A earthquakes only. (b) The same as (a) but with the superimposed theoretically predicted correlogram features. The colour key for the theoretically predicted correlogram features is the same as in Fig. 1. Figure 4. Open in new tabDownload slide The ‘exotic’ range of the Earth’s correlation wavefield between 3600 and 7200 s past the correlation-origin time. (a) Global correlogram calculated from the late-coda waveforms of the grade-A earthquakes only. (b) The same as (a) but with the superimposed theoretically predicted correlogram features. The colour key for the theoretically predicted correlogram features is the same as in Fig. 1. Figure 5. Open in new tabDownload slide Three representative events with the histograms of all available receiver pairs (top) and the corresponding correlogram and focal mechanism (bottom). (a) The Mw = 9.0, Tohoku, 2011 March 11 earthquake. This event is not among the selected events of grade A or B. (b) The Mw = 7.3, Colombia, 2012 September 30 earthquake. This event is classified as grade A (see Table 1). (c) The Mw = 5.2, Democratic People’s Republic of Korea nuclear test (NKT6) on 2017 September 3. This event is not among the selected events of grade A or B. Figure 5. Open in new tabDownload slide Three representative events with the histograms of all available receiver pairs (top) and the corresponding correlogram and focal mechanism (bottom). (a) The Mw = 9.0, Tohoku, 2011 March 11 earthquake. This event is not among the selected events of grade A or B. (b) The Mw = 7.3, Colombia, 2012 September 30 earthquake. This event is classified as grade A (see Table 1). (c) The Mw = 5.2, Democratic People’s Republic of Korea nuclear test (NKT6) on 2017 September 3. This event is not among the selected events of grade A or B. Table 1. Glossary of most relevant terms relevant for the global correlation studies. For more glossary terms, please see the extended glossary in Tkalčić et al. (2020). Glossary term . Description . Correlation wavefield A term coined to represent an abstract wavefield resulting from cross-correlation of seismograms from the regular seismic wavefield Correlogram A 2-D graphical representation of stacked cross-correlation functions in inter-receiver angular-distance bins Correlation features Visible prominent and less prominent signals that are coherently seen over a range of distances in the correlogram, often resembling traveltime curves of specific seismic phases in the seismic sections. Regarding the nomenclature of a correlation feature, if the feature has similar timing property with a regular seismic phase, we use the standard nomenclature of that seismic phase with an asterisk. For example, the correlation feature PcP* is a result of the maxima in the correlation functions generated by the waveform similarity among body waves involving PcP. Otherwise, a correlation feature is named by a differential naming convention of two involving phases. For example, cS-cP refers to a prominent correlation feature that has no equivalence in the seismic wavefield. Cross-correlation A process of measuring similarity between two time-series (of ground displacement, velocity or acceleration seismograms in our context) as a function of the time displacement of one time-series relative to the other Cross-correlation function A function in which cross-correlation, typically normalized between −1 and 1, is associated with the time displacement between the two input time-series to which cross-correlation is applied Cross-correlation stack A stack (sum) of a set of cross-correlation functions, for example, for a single receiver pair over many events, or for many receiver-pairs within the same inter-receiver angular-distance bin Seismic phases Surface of body waves recorded on seismograms and denoted by different symbols depending on the geometry of their source-receiver paths through the Earth. For example, the phase PcP stands for body waves that travel from the source as P waves (P), reflect from the Earth’s core (c) and travel to a receiver also as P waves (P). Seismic wavefield A volume taken up by seismic waves that propagate from a seismic source that is manifested as a ground-motion time-series recorded at a receiver Glossary term . Description . Correlation wavefield A term coined to represent an abstract wavefield resulting from cross-correlation of seismograms from the regular seismic wavefield Correlogram A 2-D graphical representation of stacked cross-correlation functions in inter-receiver angular-distance bins Correlation features Visible prominent and less prominent signals that are coherently seen over a range of distances in the correlogram, often resembling traveltime curves of specific seismic phases in the seismic sections. Regarding the nomenclature of a correlation feature, if the feature has similar timing property with a regular seismic phase, we use the standard nomenclature of that seismic phase with an asterisk. For example, the correlation feature PcP* is a result of the maxima in the correlation functions generated by the waveform similarity among body waves involving PcP. Otherwise, a correlation feature is named by a differential naming convention of two involving phases. For example, cS-cP refers to a prominent correlation feature that has no equivalence in the seismic wavefield. Cross-correlation A process of measuring similarity between two time-series (of ground displacement, velocity or acceleration seismograms in our context) as a function of the time displacement of one time-series relative to the other Cross-correlation function A function in which cross-correlation, typically normalized between −1 and 1, is associated with the time displacement between the two input time-series to which cross-correlation is applied Cross-correlation stack A stack (sum) of a set of cross-correlation functions, for example, for a single receiver pair over many events, or for many receiver-pairs within the same inter-receiver angular-distance bin Seismic phases Surface of body waves recorded on seismograms and denoted by different symbols depending on the geometry of their source-receiver paths through the Earth. For example, the phase PcP stands for body waves that travel from the source as P waves (P), reflect from the Earth’s core (c) and travel to a receiver also as P waves (P). Seismic wavefield A volume taken up by seismic waves that propagate from a seismic source that is manifested as a ground-motion time-series recorded at a receiver Open in new tab Table 1. Glossary of most relevant terms relevant for the global correlation studies. For more glossary terms, please see the extended glossary in Tkalčić et al. (2020). Glossary term . Description . Correlation wavefield A term coined to represent an abstract wavefield resulting from cross-correlation of seismograms from the regular seismic wavefield Correlogram A 2-D graphical representation of stacked cross-correlation functions in inter-receiver angular-distance bins Correlation features Visible prominent and less prominent signals that are coherently seen over a range of distances in the correlogram, often resembling traveltime curves of specific seismic phases in the seismic sections. Regarding the nomenclature of a correlation feature, if the feature has similar timing property with a regular seismic phase, we use the standard nomenclature of that seismic phase with an asterisk. For example, the correlation feature PcP* is a result of the maxima in the correlation functions generated by the waveform similarity among body waves involving PcP. Otherwise, a correlation feature is named by a differential naming convention of two involving phases. For example, cS-cP refers to a prominent correlation feature that has no equivalence in the seismic wavefield. Cross-correlation A process of measuring similarity between two time-series (of ground displacement, velocity or acceleration seismograms in our context) as a function of the time displacement of one time-series relative to the other Cross-correlation function A function in which cross-correlation, typically normalized between −1 and 1, is associated with the time displacement between the two input time-series to which cross-correlation is applied Cross-correlation stack A stack (sum) of a set of cross-correlation functions, for example, for a single receiver pair over many events, or for many receiver-pairs within the same inter-receiver angular-distance bin Seismic phases Surface of body waves recorded on seismograms and denoted by different symbols depending on the geometry of their source-receiver paths through the Earth. For example, the phase PcP stands for body waves that travel from the source as P waves (P), reflect from the Earth’s core (c) and travel to a receiver also as P waves (P). Seismic wavefield A volume taken up by seismic waves that propagate from a seismic source that is manifested as a ground-motion time-series recorded at a receiver Glossary term . Description . Correlation wavefield A term coined to represent an abstract wavefield resulting from cross-correlation of seismograms from the regular seismic wavefield Correlogram A 2-D graphical representation of stacked cross-correlation functions in inter-receiver angular-distance bins Correlation features Visible prominent and less prominent signals that are coherently seen over a range of distances in the correlogram, often resembling traveltime curves of specific seismic phases in the seismic sections. Regarding the nomenclature of a correlation feature, if the feature has similar timing property with a regular seismic phase, we use the standard nomenclature of that seismic phase with an asterisk. For example, the correlation feature PcP* is a result of the maxima in the correlation functions generated by the waveform similarity among body waves involving PcP. Otherwise, a correlation feature is named by a differential naming convention of two involving phases. For example, cS-cP refers to a prominent correlation feature that has no equivalence in the seismic wavefield. Cross-correlation A process of measuring similarity between two time-series (of ground displacement, velocity or acceleration seismograms in our context) as a function of the time displacement of one time-series relative to the other Cross-correlation function A function in which cross-correlation, typically normalized between −1 and 1, is associated with the time displacement between the two input time-series to which cross-correlation is applied Cross-correlation stack A stack (sum) of a set of cross-correlation functions, for example, for a single receiver pair over many events, or for many receiver-pairs within the same inter-receiver angular-distance bin Seismic phases Surface of body waves recorded on seismograms and denoted by different symbols depending on the geometry of their source-receiver paths through the Earth. For example, the phase PcP stands for body waves that travel from the source as P waves (P), reflect from the Earth’s core (c) and travel to a receiver also as P waves (P). Seismic wavefield A volume taken up by seismic waves that propagate from a seismic source that is manifested as a ground-motion time-series recorded at a receiver Open in new tab A map of the grade-A and grade-B events, as well as the receivers and their locations, is shown in Fig. 2. Supporting Information Fig. S1 shows how the number of seismograms changed as a function of time. Following the addition of all possible networks and stations, there is a large increase in the number of receivers at very small inter-receiver distances. 2.4 Source-time function database The STFs calculated by the SCARDEC method are described in Vallée et al. (2011) and Vallée & Douet (2016). The method is based on the deconvolution of synthetic point-source signals, which produces the apparent STFs. We devised a scheme for measuring a duration of STFs (or moment-rate release) shown in Fig. 3(b) based on identifying significant peaks in the SCARDEC moment-rate function. The significant peaks are higher than a certain per cent of the maximum moment rate, with a threshold percentage as a control input parameter. The duration is the distance between the outermost slopes of the significant peaks. 2.5 Theoretical traveltime curves of correlogram features We use the Taup Toolkit (Crotwell et al. 1999) to generate prediction lines in Figs 1 and 4 and Supporting Information Figs S2–S5. For phases that have timing properties similar to regular seismic phases, the program can be used to produce the traveltime curves. For phases that have no counterparts in the direct wavefield, we calculated differential traveltime in the slowness domain as described in Phạm et al. (2018) and Tkalčić et al. (2020). 3 EXCITATION OF SEISMIC ENERGY Next, we focused our attention on determining what made our grade-A correlograms and their corresponding events unique. Fig. 3 is a blob chart that shows the analysed earthquakes’ focal mechanisms, moment magnitudes, hypocentral-locations region (for the grade-A events) and the time difference between the origin and the centroid times according to the data available in the global centroid moment tensor (GCMT) catalogue (Dziewonski et al. 1981; Ekström et al. 2012), plotted as a function of the origin time. The chart reveals that the selected grade-A earthquakes (shown in colour according to their hypocentral locations) were not the largest earthquakes that occurred. Furthermore, a common characteristic of the selected grade-A events is that they had either reverse (compressional environment) or normal (extensional environment) focal mechanisms, which were efficient to radiate significant seismic energy to the deep Earth. This is aligned with our previous findings that steeply arriving seismic phases with similar slowness tend to contribute to the most prominent correlogram features. However, many of the large earthquakes do so, and there were larger events with normal or reverse focal mechanisms that did not produce correlograms of the highest quality. Lastly, all except one (Mw = 7.8, South Island, New Zealand on 2016 November 13) of the selected grade-A events had a time difference between the origin and the centroid time of less than about 15 s. This suggests a highly concentrated slip area, but prompts a further analysis of the STFs of all events. It is intuitive that a short and less-complicated STFs would lead to a better correlation. Indeed, we found that the duration of STFs and, most likely, their slip distribution play a critical role in producing the exceptional-quality correlograms. All of our grade-A events had moment-rate releases less than about 20 s. We found that the Mw = 7.8, 2016 November 13 South Island, New Zealand event, had an emergent and long start of about 60 s, and then a significant amount of energy was released in the last 20 s (see the 10th event listed in Table 1). Moreover, when we plotted both the grade-A and grade-B events on a similar type of a blob chart as shown in Fig. 3(a), but this time as a function of STF duration, all selected events collapsed to the bottom of the chart (Fig. 3b), suggesting that an impulsive release of energy is a prerequisite for the highest cross-correlation between the seismic phases in the radiated seismic wavefield (Figs 1 and 4). A somewhat surprising outcome of our analysis is that there are no more deep earthquakes among the grade-A events—only three events exceeded the depth of 100 km (Table 2). Thus, we performed an auxiliary analysis in which we re-examined deep earthquakes to investigate further why there were no more deeper earthquakes among the events of the highest quality. There are two possible reasons that we were able to identify: (i) a disproportionally larger number of shallow than deep earthquakes and (ii) a complete absence of the expression of the PKP-ScS feature (F20) for deep earthquakes (the lower-right corner of the correlogram in Fig. 1). In conjunction with (i), we analysed the global data set of ScS-S traveltimes (Houser et al. 2008), with over 40 000 measurements, and we found that over 80 per cent of ScS-S traveltime data measured through cross-correlation correspond to earthquakes shallower than 80 km. With regard to (ii), we speculate that the main cause is that most deep earthquakes that release P-wave energy steeply down—a prerequisite to create favourable conditions for multiple reverberated phases and pronounced cross-correlations—do not have a significant release of S-wave energy in the same direction due to the nature of the radiation pattern for P and S waves. Table 2. Earthquakes (2010–2018) resulting in the most prominent (grade-A) correlograms. They are listed in a chronological order. The last two columns show the focal mechanism (scaled with the moment magnitude and coloured by the region as in Fig. 3) from the GCMT catalogue (Dziewonski et al. 1981; Ekström et al. 2012) and the source-time functions (0–90 s) from the SCARDEC catalogue (Vallée et al. 2011; Vallée & Douet 2016). Event . Date . Time . Mw . Lat (°) . Lon (°) . Depth (km) . Location . FM . STF . 1 9 May 2010 05:59:51 7.2 3.36 95.78 37 Northern Sumatra, Indonesia 2 21 Dec 2010 17:19:53 7.4 27.10 143.76 16 Bonin Islands, Japan Region 3 20 Mar 2012 18:02:24 7.5 16.60 −98.39 15 Guererro Mexico, near coast 4 5 Sep 2012 14:42:43 7.6 10.00 −85.64 30 Costa Rica 5 30 Sep 2012 16:31:45 7.2 1.89 −76.22 174 Columbia 6 1 Apr 2014 23:58:11 7.0 −19.85 −71.39 21 Northern Chile, near coast 7 14 Oct 2014 03:51:44 7.3 12.33 −88.45 41 Central America, off coast 8 26 Oct 2015 09:09:47 7.5 36.55 70.42 209 Hindu-Kush Region, Afghanistan 9 4 Dec 2015 22:25:09 7.1 −47.74 85.23 29 Southeast Indian Ridge 10 13 Nov 2016 11:03:53 7.8 −42.03 173.85 19 New Zealand, South Island 11 25 Dec 2016 14:22:38 7.6 −43.41 −74.43 33 Southern Chile 12 22 Jan 2017 04:30:38 7.9 −6.03 154.94 142 Solomon Islands Event . Date . Time . Mw . Lat (°) . Lon (°) . Depth (km) . Location . FM . STF . 1 9 May 2010 05:59:51 7.2 3.36 95.78 37 Northern Sumatra, Indonesia 2 21 Dec 2010 17:19:53 7.4 27.10 143.76 16 Bonin Islands, Japan Region 3 20 Mar 2012 18:02:24 7.5 16.60 −98.39 15 Guererro Mexico, near coast 4 5 Sep 2012 14:42:43 7.6 10.00 −85.64 30 Costa Rica 5 30 Sep 2012 16:31:45 7.2 1.89 −76.22 174 Columbia 6 1 Apr 2014 23:58:11 7.0 −19.85 −71.39 21 Northern Chile, near coast 7 14 Oct 2014 03:51:44 7.3 12.33 −88.45 41 Central America, off coast 8 26 Oct 2015 09:09:47 7.5 36.55 70.42 209 Hindu-Kush Region, Afghanistan 9 4 Dec 2015 22:25:09 7.1 −47.74 85.23 29 Southeast Indian Ridge 10 13 Nov 2016 11:03:53 7.8 −42.03 173.85 19 New Zealand, South Island 11 25 Dec 2016 14:22:38 7.6 −43.41 −74.43 33 Southern Chile 12 22 Jan 2017 04:30:38 7.9 −6.03 154.94 142 Solomon Islands Open in new tab Table 2. Earthquakes (2010–2018) resulting in the most prominent (grade-A) correlograms. They are listed in a chronological order. The last two columns show the focal mechanism (scaled with the moment magnitude and coloured by the region as in Fig. 3) from the GCMT catalogue (Dziewonski et al. 1981; Ekström et al. 2012) and the source-time functions (0–90 s) from the SCARDEC catalogue (Vallée et al. 2011; Vallée & Douet 2016). Event . Date . Time . Mw . Lat (°) . Lon (°) . Depth (km) . Location . FM . STF . 1 9 May 2010 05:59:51 7.2 3.36 95.78 37 Northern Sumatra, Indonesia 2 21 Dec 2010 17:19:53 7.4 27.10 143.76 16 Bonin Islands, Japan Region 3 20 Mar 2012 18:02:24 7.5 16.60 −98.39 15 Guererro Mexico, near coast 4 5 Sep 2012 14:42:43 7.6 10.00 −85.64 30 Costa Rica 5 30 Sep 2012 16:31:45 7.2 1.89 −76.22 174 Columbia 6 1 Apr 2014 23:58:11 7.0 −19.85 −71.39 21 Northern Chile, near coast 7 14 Oct 2014 03:51:44 7.3 12.33 −88.45 41 Central America, off coast 8 26 Oct 2015 09:09:47 7.5 36.55 70.42 209 Hindu-Kush Region, Afghanistan 9 4 Dec 2015 22:25:09 7.1 −47.74 85.23 29 Southeast Indian Ridge 10 13 Nov 2016 11:03:53 7.8 −42.03 173.85 19 New Zealand, South Island 11 25 Dec 2016 14:22:38 7.6 −43.41 −74.43 33 Southern Chile 12 22 Jan 2017 04:30:38 7.9 −6.03 154.94 142 Solomon Islands Event . Date . Time . Mw . Lat (°) . Lon (°) . Depth (km) . Location . FM . STF . 1 9 May 2010 05:59:51 7.2 3.36 95.78 37 Northern Sumatra, Indonesia 2 21 Dec 2010 17:19:53 7.4 27.10 143.76 16 Bonin Islands, Japan Region 3 20 Mar 2012 18:02:24 7.5 16.60 −98.39 15 Guererro Mexico, near coast 4 5 Sep 2012 14:42:43 7.6 10.00 −85.64 30 Costa Rica 5 30 Sep 2012 16:31:45 7.2 1.89 −76.22 174 Columbia 6 1 Apr 2014 23:58:11 7.0 −19.85 −71.39 21 Northern Chile, near coast 7 14 Oct 2014 03:51:44 7.3 12.33 −88.45 41 Central America, off coast 8 26 Oct 2015 09:09:47 7.5 36.55 70.42 209 Hindu-Kush Region, Afghanistan 9 4 Dec 2015 22:25:09 7.1 −47.74 85.23 29 Southeast Indian Ridge 10 13 Nov 2016 11:03:53 7.8 −42.03 173.85 19 New Zealand, South Island 11 25 Dec 2016 14:22:38 7.6 −43.41 −74.43 33 Southern Chile 12 22 Jan 2017 04:30:38 7.9 −6.03 154.94 142 Solomon Islands Open in new tab In Fig. 5, we compare three characteristic events to further illustrate the dependence of the quality of correlograms on the type of focal mechanism and the magnitude and dynamics of moment release. The first event is the largest earthquake (Mw = 9.0, Tohoku, near the east coast of Honshu, Japan on 2011 March 11). The second event is the Mw = 7.3, Columbia on 2012 September 30 earthquake, a grade-A event listed as the fifth in Table 1. The third event is the Mw = 5.2 nuclear test (NKT6) in the Democratic People’s Republic of Korea on 2017 September 3 (Alvizuri & Tape 2018; Wang et al. 2018). Although much larger, the Tohoku event does not contain as prominent features in the lower part of the correlogram as the Columbia event. Many of the features are significantly diminished in quality in comparison with the Columbia event, or completely missing. For example, K2* (F9), K-ScS (F20), c* (F26), cPPcP-cS (F29) and cK2* (F36) are significantly stronger for the Columbia event. Additionally, the exotic features such as I4* (F44) and I5* (F45) are not expressed. We attribute the diminished quality of the Tohoku-event correlogram to the fact that its STF is spread over 120 s. The correlogram associated with the NKT6 event is void of any significant features. Apart from its relatively low moment magnitude in comparison with the other two events, the features in the NKT6-event correlogram are not expressed because of its explosive focal mechanism, which means that only a part of released energy is radiated steeply down in comparison to a maximal energy release to the Earth’s deep interior for reverse or normal earthquakes. 4 PROMINENT AND EXOTIC FEATURES IN THE EARTH’S CORRELATION WAVEFIELD We computed correlograms for up to 10 800 s beyond the correlation-origin time and split the time intervals to 0–3600, 3600–7200 and 7200–10 800 s to increase the visual clarity of the correlogram features. Correlograms of all individual earthquakes were analysed visually to identify prominent features. We also computed the stacks of the grade-A and the grade-B correlograms and compared them with the correlograms from the previously published data set that consisted of 160 events. Finally, we computed predictions of all correlogram features according to the formalism developed in our previous work (Phạm et al. 2018; Tkalčić & Phạm 2018). This resulted in 61 predicted time curves of the features (marked F1–F61), which is the most extensive catalogue of global correlogram features to date. We examine all correlograms in a set of three consecutive time intervals with and without theoretically predicted time curves, clearly marked using a colour key that suggests how the feature is formed. Fig. 1 shows the first 3600 s of the correlogram computed by stacking the grade-A correlograms featured in Table 1 and the superimposed theoretical time curves. This correlogram is supplemented with the 3600–7200 (Fig. 4) and 7200–10 800 s sections (Supporting Information Fig. S2) showing the correlograms with and without the predicted time curves. Our newly computed correlograms are characterized by the multitude of visible features appearing up to about 10 000 s past the correlation origin-time, including I7* (F47), nearly 8500 s past the correlation origin-time. Here we comment only on some of the most important features that guided our classification of the correlograms. Most of these phases are observed at caustic inter-receiver distances, which enhances the formation of the global correlation features (Snieder & Sens-Schönfelder 2015). We term I*, I2*, I3* (F0–2) and the higher multiples as the ‘I* group’, and K*, K2*, K3* (F8–10) and the higher multiples as the ‘K* group’ of the correlation wavefield. A strongly expressed K* is also responsible for cK* (F35) and ScSK* (F37) features in the right-hand part of the correlogram. The grade-A correlograms are expected to have highly prominent ScS* (F24), c* (F26), cS-cP (F27) and the lower multiples of I* and K* groups, and they are not specifically mentioned in Supporting Information Tables S2 and S3 unless there was something unusual about those observations. Another feature that is of interest is K-ScS (F20), which appears as an early feature in the lower-right portion of the correlogram. The strength of this feature is usually correlated with the strength of ScS* (F24) and the K* group. Finally, SKP* (F11), which appears around 250 s above K*, is prominent in most correlograms, resulting also in related features in the upper central part of the correlogram, SKPK* (F12) and SKPK2* (F13). What distinguishes the grade-A (Table 1) from the grade-B events (Supporting Information Table S1) is not just how well the features are expressed in the first 0–3600 s, but also how prominent the exotic features appear in the later times (3600–7200 s). Supporting Information Tables S2 and S3 show our remarks about the observed features in the correlograms. For example, I4*, I5* and I6* (F44–46) are well pronounced in the final stack and in some individual correlograms, particularly those corresponding to deep events. There is also a significant presence of SKPK3* (F50) and SKPK4* (F51). The inclusion or exclusion of localized, dense networks such as the USArray affects the quality of correlograms at small inter-receiver distances. We analysed this effect by calculating a correlogram using the grade-A event 2 for all global receiver pairs. Apparent changes at small inter-receiver distances are associated with the reduction of contributing correlation pairs. Dense regional networks can introduce localized effects of the Earth’s heterogeneity. However, at larger distances, the contributions remain averaged globally as there is a benefit of the diversity of receiver-pair geometry. Thus, the exclusion of the USArray and the selection of the highest-quality events would result in the same selection of grade-A and grade-B events. The influence of the receiver locations with respect to the null planes for a particular event is minimal. This is because we correlate late earthquake-coda in which the incidence of seismic energy is steep and related to the core reflections (Sens-Schönfelder et al. 2015). Therefore, when an earthquake radiates a significant amount of energy towards the deep Earth (such is the case in our selected normal and thrust events), the radiation pattern in the late coda will be azimuthally homogeneous. However, the relative position of an earthquake with respect to the great-circle plane formed by a receiver pair strongly influences the contribution to the global correlogram. In-plane pairs contribute significantly to the global stack, in contrast to the out-of-plane pairs. This effect is discussed in a greater detail in Wang & Tkalčić (2020a). 5 CONCLUDING REMARKS We demonstrated that when energy from a single seismic event is radiated in a favourable way (a reverse or normal fault, and a short source-time-function duration), it generates the correlation wavefield manifested in the form of a high-quality correlogram. The fact that a single event is sufficient in creating a correlogram resembling previous correlograms constructed from a large number of events reinforces the notion that the earthquake coda-correlation features are not ‘reconstructed’ body waves. We can predict all the observed features in the correlogram using the principle of the same slowness and ak135, the model of a spherically symmetrical Earth (Kennett et al. 1995). This attests to the accuracy with which we know the Earth’s averaged spherical structure as represented by current spherically symmetric Earth models [ak135 (Kennett et al. 1995); PREM (Dziewoński & Anderson 1981)] at these periods (15–50 s). Whereas most features are formed due to a similarity among prominent phases in the seismic wavefield, some of the observed exotic features do not have their observed counterpart in the seismic wavefield (for example, I3*, K*, I4*, K4* and higher multiples of the I* and K* groups). What remains to be done is to further refine the quality of the global correlogram in order to advance global seismology for various practical uses. One priority is to improve the overall quality of the global correlogram by supplying more cross-correlations at podal and antipodal inter-receiver distances. A more uniform number of receiver pairs across the entire inter-receiver distance range should improve the clarity of the observed features in the global correlogram, especially near its edges (that is, towards the inter-receiver distances of 0° and 180°). One of the most practical consequences of our findings is that numerical simulations of the seismic and correlation wavefields do not need to include a large number of seismic events to be efficient: our modelling of the observed features in the correlograms can be reduced to a simulation of correlograms corresponding to single events and a fixed configuration of receivers around the globe. Possible future applications include but are not limited to tomography and planetary seismology in which we envisage imaging of all terrestrial planets using a large number of receivers and a single natural or forced event. SUPPORTING INFORMATION Tkalcic_Pham_GJI-S-20-0432_Revised_Supplement.pdf Figure S1. The number of seismograms available from the IRIS Data Management Center for the analysis as a function of event origin time. Figure S2. The ‘exotic range’ of the Earth’s correlation wavefield between 7,200 and 10,800 seconds past the correlation-origin time calculated using the selected grade-A events (see Figs 1 and 4 for the earlier sections of the correlogram). Figure S3. The ‘regular range’ of the Earth’s correlation wavefield between 3,600 and 7,200 seconds past the correlation-origin time calculated from late-coda waveforms of the selected grade-B events in this study (see S1). Figure S4. The ‘exotic range’ of the Earth’s correlation wavefield between 3,600 and 7,200 seconds past the correlation-origin time calculated using the selected grade-B events. Figure S5. The ‘exotic range’ of the Earth’s correlation wavefield between 7,200 and 10,800 seconds past the correlation-origin time calculated using the selected grade-B events. Table S1. Earthquakes (2010–2018) resulting in grade-B correlograms. Table S2. Earthquakes (2010–2018) resulting in grade-A correlograms with detailed notes (see Table 1). Table S3. Earthquakes (2010–2018) resulting in grade-B correlograms with detailed notes (see Table S1). Please note: Oxford University Press is not responsible for the content or functionality of any supporting materials supplied by the authors. Any queries (other than missing material) should be directed to the corresponding author for the paper. ACKNOWLEDGEMENTS We are greatful to two anonymous reviewers for their constructive comments that improved the original manuscript. 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TI - Excitation of the global correlation wavefield by large earthquakes
JO - Geophysical Journal International
DO - 10.1093/gji/ggaa369
DA - 2020-10-15
UR - https://www.deepdyve.com/lp/oxford-university-press/excitation-of-the-global-correlation-wavefield-by-large-earthquakes-5UrOzD0ut9
SP - 1769
EP - 1779
VL - 223
IS - 3
DP - DeepDyve
ER -