TY - JOUR
AU - Gaherty, James, B
AB - SUMMARY We present new anisotropic phase-velocity maps of the Pacific basin for Rayleigh and Love waves between 25 and 250 s. The isotropic and anisotropic phase-velocity maps are obtained by inversion of a data set of single-station surface-wave phase-anomaly measurements recorded for paths crossing the Pacific basin. We develop an age-dependent gradient-damping scheme that allows us to reduce the amount of smoothness damping required in the inversion. The observed isotropic phase velocities have a strong age dependence, and our results are consistent with models of half-space cooling: simple phase-velocity models that depend only on seafloor age explain |$40\text{-}97\hbox{ per cent}$| of the data variance for Love waves and |$20\text{-}97\hbox{ per cent}$| for Rayleigh waves. These values represent a large fraction, ranging from 0.55 to 0.99, of the variance reduction of our best-fitting phase-velocity models. We find that 2ζ azimuthal anisotropy is required to fit our Rayleigh wave phase-anomaly data set but that our data do not require Love wave anisotropy. Rayleigh wave anisotropy also exhibits a clear age dependence, with a large decrease in the magnitude of 2ζ azimuthal anisotropy for seafloor older than 70 Ma that cannot be explained simply as a change in anisotropy direction between the lithosphere and asthenosphere. Long-period Rayleigh wave anisotropy directions align well overall with absolute-plate-motion directions, with a median angular misfit of 20° at 125 s. However, we observe large areas within the Pacific basin with a small but consistent offset of 10°–20° between the two directions. The disagreement between absolute plate motion and anisotropy for long-period waves suggests the presence of mantle flow beneath the base of the plate in a direction other than absolute plate motion. Pacific Ocean, Seismic anisotropy, Seismic tomography, Surface waves and free oscillations 1 INTRODUCTION Seismic tomography of the oceanic upper mantle informs our understanding of the thermal evolution of oceanic plates and the interactions between the lithosphere and the underlying asthenospheric mantle. Previous studies of the seismic structure of plates have observed that many seismic properties depend on seafloor age, including surface-wave phase velocities (Yu & Mitchell 1979; Nishimura & Forsyth 1989; Forsyth et al.1998; James et al.2014; Godfrey et al.2017), shear velocities (Ritzwoller et al.2004; Maggi et al.2006a; Nettles & Dziewonski 2008; Harmon et al.2009), and differential body-wave travel times (Goes et al.2013). The observation of age-dependent seismic velocities is consistent with simple models describing the thermal evolution of oceanic lithosphere, including half-space cooling (Parker & Oldenburg 1973; Turcotte & Schubert 2002) and plate models (McKenzie 1967; Parsons & Sclater 1977; Johnson & Carlson 1992; Stein & Stein 1992; Hasterok 2013). These models explain the dependence of seafloor depth and heat flow on the seafloor age and can be used to predict seismic velocities that are also a function of seafloor age (Faul & Jackson 2005; Stixrude & Lithgow-Bertelloni 2005). Observed seafloor flattening at older plate ages could be explained by asthenospheric flow or small-scale convection that provides a source of heat to the base of the plate (Haxby & Weissel 1986; Morgan & Smith 1992; Ritzwoller et al.2004; French et al.2013), and a simple thermal history may be complicated by occasional reheating events due to the influence of mantle plumes (Carlson & Johnson 1994; Nagihara et al.1996). Well-constrained seismic studies have the potential to distinguish between different models of the thermal history of oceanic lithosphere. Seismic properties of the oceanic basins also reflect the plate deformation history, and there are many observations of seismic anisotropy in the oceanic upper mantle. Early evidence of anisotropy included the discrepancy between Love and Rayleigh wave dispersion (Anderson 1966; Nataf et al.1984), the dependence of surface-wave phase and group velocity on propagation azimuth (Forsyth 1975; Montagner 1985; Suetsugu & Nakanishi 1987), and the dependence of Pn velocities on azimuth (Hess 1964; Backus 1965; Raitt et al.1969). Many studies have concluded that anisotropy is required in the upper mantle (e.g. Anderson & Dziewonski 1982; Montagner & Tanimoto 1991; Gaherty et al.1996; Ekström & Dziewonski 1998; Kustowski et al.2008; Lekić & Romanowicz 2011; French & Romanowicz 2014; Moulik & Ekström 2014) and that it is necessary to model seismic anisotropy to retrieve accurate estimates of isotropic seismic velocity (Anderson & Dziewonski 1982; Montagner & Tanimoto 1991; Ekström 2011). Several mechanisms may lead to observable seismic anisotropy. Layers and cracks with different isotropic velocities or aligned pockets of melt can cause anisotropy of the shape-preferred-orientation (SPO) style and are likely prevalent in the crust and lithosphere (Schlue & Knopoff 1976; Holtzman et al.2003; Kawakatsu et al.2009). Deformation in the Earth also leads to anisotropy of the lattice-preferred-orientation (LPO) style when individual crystals with some intrinsic anisotropy are aligned (Mainprice 2007; Long & Becker 2010). Olivine, the most abundant mineral in the upper mantle (Ringwood 1975), is strongly anisotropic; seismic waves propagating or polarized along the [100] axis travel faster than waves propagating along the [010] or [001] axes (Nicolas & Christensen 1987). Simple-shear experiments have shown that olivine crystals tend to rotate such that the fast crystallographic axis [100] is aligned with the direction of shear (A-type fabric; Zhang & Karato 1995; Karato et al.2008); in the asthenosphere, shear strain due to the relative motion between lithospheric plates and the underlying mantle will lead to this crystal rotation. A-type olivine fabrics are commonly observed in upper-mantle peridotites (Ben Ismail & Mainprice 1998). As a result, the orientation of LPO anisotropy reflects both past and present deformation in the mantle (e.g. Long & Becker 2010). Seismic tomography of anisotropy can provide a useful test of models of anisotropy formation in oceanic regions. Due to the abundance of olivine in the upper mantle, LPO anisotropy is the most likely mechanism for the formation of anisotropy in the oceanic lithosphere and asthenosphere (Nicolas & Christensen 1987). Assuming A-type olivine fabric, the anisotropy observed in oceanic lithosphere should reflect the orientation of mantle flow at the time of lithosphere formation and cooling, while anisotropy in the asthenosphere should be controlled by the current or geologically recent orientation of shear between the plate and the mantle below. As a result, an observed change in the orientation of the fast axis of anisotropy may be a proxy for the depth of the transition from lithosphere to asthenosphere (e.g. Plomerová et al.2002; Yuan & Romanowicz 2010; Debayle & Ricard 2013; Burgos et al.2014; Schaeffer et al.2016). Some observations of the azimuthal anisotropy of Rayleigh waves in the oceans suggest that the fast propagation direction approximately aligns with fossil spreading directions at short periods and with absolute plate motion at long periods (Forsyth 1975; Nishimura & Forsyth 1988, 1989; Smith et al.2004; Maggi et al.2006a). However, local observations in the central Pacific have found an anisotropy fast axis that does not align with absolute plate motion, suggesting weak shear beneath the base of the plate (Lin et al.2016). Becker et al. (2014) argue that large-scale buoyancy-driven flow is required to match geodynamic models to patterns of azimuthal anisotropy. Studies have argued both for (Debayle & Ricard 2013; Burgos et al.2014; Schaeffer et al.2016) and against (Beghein et al.2014) an age dependence of the depth at which there is a transition in anisotropy orientation, and have related this transition to discontinuities within the oceanic lithosphere (Gaherty et al.1996; Beghein et al.2014). One reason for the discrepancies between 3-D models of anisotropic velocity structure is the complexity inherent in modelling a large number of parameters, where many choices of regularization and parameter scaling must be made. Even recent 2-D, anisotropic phase-velocity models (e.g. Trampert & Woodhouse 2003; Ekström 2011) show surprisingly large discrepancies in the orientation and strength of azimuthal anisotropy, including in oceanic regions that might be expected to exhibit relatively simple patterns of isotropic and anisotropic variability. In this study, we investigate the isotropic and anisotropic elastic structure of the Pacific upper mantle using surface waves, and focus on retrieving robust estimates of azimuthally anisotropic phase velocity. We use data sensitive only to velocity variations in the Pacific basin and conduct a regional inversion. This simplifies the tomographic problem, allowing us to use prior knowledge about oceanic crust and mantle structure in order to inform our modelling. Both sediment thickness and water depth are well known, and oceanic crust is relatively uniform (Oxburgh & Parmentier 1977; McKenzie & Bickle 1988; White et al.1992; Bassin et al.2000). We choose to focus on the Pacific ocean because it is large and there are many earthquake sources and stations surrounding the basin, leading to good coverage by surface-wave paths. We present a new set of well-resolved anisotropic phase-velocity maps of the Pacific for Rayleigh and Love waves between 25 and 250 s. 2 DATA We primarily use a subset of the global surface-wave phase-anomaly data set collected by Ekström (2011). The global dispersion data set consists of single-station fundamental-mode phase anomalies measured at periods from 25 − 250 s using the phase-matched filter algorithm of Ekström et al. (1997). The technique is based on the iterative minimization of residual dispersion between the observed seismogram and a synthetic fundamental-mode seismogram, with window lengths for the analysis dependent on frequency. The resulting dispersion curve is required to remain smooth, to avoid cycle skips. It is well known that measurements of fundamental-mode Love wave phase velocity have the potential to be contaminated by interference from higher-mode Love waves with similar group speeds. Several of the processing steps employed in the Ekström et al. (1997) approach, including data selection, seismogram matching, windowing, and the requirement that the dispersion curve remain smooth across a wide frequency band, are designed to reduce the potential for contamination. Nettles & Dziewoński (2011) found, using this measurement technique, that errors introduced by overtone interference are small and do not bias the resulting phase-velocity maps when measurements from a range of epicentral distances are available. Measurements were made on seismograms from shallow (depth <50 km) earthquakes at epicentral distances ≥25°, for events with magnitude Mw ≥ 5.5 between 2000 and 2009. The global data set includes phase anomalies measured for a large number of paths, including minor-arc paths for periods of 25–250 s and both minor- and major-arc paths for periods ≥150 s (Table 1). The global dispersion model GDM52 was constructed with this data set (Ekström 2011). Our focus here is on the structure of the Pacific oceanic lithosphere and asthenosphere, which is illuminated well by surface waves. Global models must accept trade-offs due to some areas having lower resolution than others, which effectively limits resolution in the best-covered regions. We select the borders of the Pacific basin to be the outer edges of the Pacific, Philippine Sea, Nazca, Cocos, Caroline, Mariana, Easter, Juan Fernandez, Galapagos, Juan de Fuca and Rivera plates as defined by the Bird (2003) compilation of plate boundaries. We select paths from the global data set that have lengths |$\gt 90\hbox{ per cent}$| within the boundaries of the Pacific basin. Due to the large number of earthquake sources and receivers surrounding the Pacific, this subset contains many paths at all periods (Table 1). On average, |$10\hbox{ per cent}$| of paths from the global data set meet our criteria at each period. Data coverage and the azimuthal distribution of paths are good throughout the Pacific basin (Fig. 1). The best sampling occurs in the north-central Pacific. The least-well-sampled region is in the southern Pacific. Figure 1. View largeDownload slide Number of rays crossing each 5° × 5° pixel for (a) 25-s Love waves and (b) 125-s Rayleigh waves, respectively the worst- and best-resolved models. Local resolution for (c) 125-s Love waves and (d) 125-s Rayleigh waves, as described in Section 5.2. A low value for the local resolution indicates the model is well resolved. Blue triangles show the stations contributing to the main data set (Table 1). Red triangles show NoMelt stations (Table 2). Figure 1. View largeDownload slide Number of rays crossing each 5° × 5° pixel for (a) 25-s Love waves and (b) 125-s Rayleigh waves, respectively the worst- and best-resolved models. Local resolution for (c) 125-s Love waves and (d) 125-s Rayleigh waves, as described in Section 5.2. A low value for the local resolution indicates the model is well resolved. Blue triangles show the stations contributing to the main data set (Table 1). Red triangles show NoMelt stations (Table 2). Table 1. Number of Love and Rayleigh wave observations in the GDM52 phase-anomaly data set (N), and the number of observations with |$\gt 90\hbox{ per cent}$| of the path length within the boundaries of the Pacific basin (Nr). Period (s) N (Love) Nr (Love) N (Rayleigh) Nr (Rayleigh) 25 18670 2481 103633 16340 27 19034 2538 104820 16412 30 19187 2561 105796 16476 32 35858 4149 178997 20302 35 35935 4152 179296 20306 40 35977 4149 179657 20308 45 36022 4152 179802 20313 50 82958 7762 282579 25262 60 85646 8040 286132 25364 75 85742 8035 286302 25374 100 83463 7740 282996 24996 125 62829 6109 247410 21946 150 43999 1739 83093 3159 200 30870 924 82518 3131 250 36991 1351 78291 2941 Period (s) N (Love) Nr (Love) N (Rayleigh) Nr (Rayleigh) 25 18670 2481 103633 16340 27 19034 2538 104820 16412 30 19187 2561 105796 16476 32 35858 4149 178997 20302 35 35935 4152 179296 20306 40 35977 4149 179657 20308 45 36022 4152 179802 20313 50 82958 7762 282579 25262 60 85646 8040 286132 25364 75 85742 8035 286302 25374 100 83463 7740 282996 24996 125 62829 6109 247410 21946 150 43999 1739 83093 3159 200 30870 924 82518 3131 250 36991 1351 78291 2941 View Large Table 1. Number of Love and Rayleigh wave observations in the GDM52 phase-anomaly data set (N), and the number of observations with |$\gt 90\hbox{ per cent}$| of the path length within the boundaries of the Pacific basin (Nr). Period (s) N (Love) Nr (Love) N (Rayleigh) Nr (Rayleigh) 25 18670 2481 103633 16340 27 19034 2538 104820 16412 30 19187 2561 105796 16476 32 35858 4149 178997 20302 35 35935 4152 179296 20306 40 35977 4149 179657 20308 45 36022 4152 179802 20313 50 82958 7762 282579 25262 60 85646 8040 286132 25364 75 85742 8035 286302 25374 100 83463 7740 282996 24996 125 62829 6109 247410 21946 150 43999 1739 83093 3159 200 30870 924 82518 3131 250 36991 1351 78291 2941 Period (s) N (Love) Nr (Love) N (Rayleigh) Nr (Rayleigh) 25 18670 2481 103633 16340 27 19034 2538 104820 16412 30 19187 2561 105796 16476 32 35858 4149 178997 20302 35 35935 4152 179296 20306 40 35977 4149 179657 20308 45 36022 4152 179802 20313 50 82958 7762 282579 25262 60 85646 8040 286132 25364 75 85742 8035 286302 25374 100 83463 7740 282996 24996 125 62829 6109 247410 21946 150 43999 1739 83093 3159 200 30870 924 82518 3131 250 36991 1351 78291 2941 View Large We make additional measurements of fundamental-mode surface-wave dispersion for events recorded on stations of the NoMelt network (Sarafian et al.2015; Lin et al.2016), a temporary deployment of broad-band ocean-bottom seismometers on ∼70 Ma lithosphere between the Clarion and Clipperton fracture zones in the central Pacific. We make single-station dispersion measurements between 25 and 125 s using the technique of Ekström et al. (1997) for the 57 shallow earthquakes of Mw > 6 recorded on the NoMelt network. This is the first time the Ekström et al. (1997) measurement technique has been applied to ocean-bottom data. Without modification of the algorithm, we are able to make several hundred high-quality measurements of Rayleigh waves, as well as a small number of Love wave measurements (Table 2). Love waves are more difficult to observe on ocean-bottom seismometers due to large amounts of tilt noise on the horizontal components (e.g. Webb 1998). As for the larger phase-anomaly data set, we select paths for our NoMelt data set that have lengths |$\gt 90\hbox{ per cent}$| within the Pacific basin (Table 2). These data are used after inversion as a test of our preferred phase-velocity models. Table 2. Number of Love and Rayleigh wave observations obtained from the 16 available stations of the NoMelt network (N), and the number of observations with |$\gt 90\hbox{ per cent}$| of the path length within the boundaries of the Pacific basin (Nr). Period (s) N (Love) Nr (Love) N (Rayleigh) Nr (Rayleigh) 25 2 1 321 232 27 2 1 321 233 30 2 1 321 233 32 6 4 449 281 35 6 4 449 281 40 6 4 449 281 45 6 4 449 281 50 20 11 652 343 60 20 12 652 349 75 20 12 652 351 100 20 10 652 341 125 20 9 652 307 Period (s) N (Love) Nr (Love) N (Rayleigh) Nr (Rayleigh) 25 2 1 321 232 27 2 1 321 233 30 2 1 321 233 32 6 4 449 281 35 6 4 449 281 40 6 4 449 281 45 6 4 449 281 50 20 11 652 343 60 20 12 652 349 75 20 12 652 351 100 20 10 652 341 125 20 9 652 307 View Large Table 2. Number of Love and Rayleigh wave observations obtained from the 16 available stations of the NoMelt network (N), and the number of observations with |$\gt 90\hbox{ per cent}$| of the path length within the boundaries of the Pacific basin (Nr). Period (s) N (Love) Nr (Love) N (Rayleigh) Nr (Rayleigh) 25 2 1 321 232 27 2 1 321 233 30 2 1 321 233 32 6 4 449 281 35 6 4 449 281 40 6 4 449 281 45 6 4 449 281 50 20 11 652 343 60 20 12 652 349 75 20 12 652 351 100 20 10 652 341 125 20 9 652 307 Period (s) N (Love) Nr (Love) N (Rayleigh) Nr (Rayleigh) 25 2 1 321 232 27 2 1 321 233 30 2 1 321 233 32 6 4 449 281 35 6 4 449 281 40 6 4 449 281 45 6 4 449 281 50 20 11 652 343 60 20 12 652 349 75 20 12 652 351 100 20 10 652 341 125 20 9 652 307 View Large 3 THEORY For a given angular frequency, ω, a fundamental-mode surface-wave seismogram can be written as a function of amplitude and phase (e.g. Tromp & Dahlen 1992, 1993), \begin{eqnarray*} u(\omega ) = A(\omega )\exp [i\Phi (\omega )], \end{eqnarray*} (1) where u(ω) denotes the recorded displacement at the station, and A(ω) and Φ(ω) are the amplitude and phase, respectively. For a given earthquake source and receiver location, the phase of the wave is the sum of four effects, \begin{eqnarray*} \Phi = \Phi _\text{S} + \Phi _\text{R} + \Phi _\text{C} + \Phi _\text{P}, \end{eqnarray*} (2) where ΦS is the source phase, ΦR is the receiver phase, ΦC is the phase contribution due to each ray focus, and ΦP is the propagation phase. The propagation phase is written \begin{eqnarray*} \Phi _\text{P} = \int \frac{\omega }{c(\omega )} ~\text{d}s = \int \omega p(\omega ) ~\text{d}s, \end{eqnarray*} (3) where c(ω) is the phase velocity and p(ω) is the slowness, and the integral is along the ray path. For an earthquake with a known location and focal mechanism and assuming a spherical earth model, we compute a synthetic seismogram, u0(ω), \begin{eqnarray*} u^0(\omega ) = A^0(\omega )\exp [i\Phi ^0(\omega )]. \end{eqnarray*} (4) The propagation phase of the synthetic seismogram is written \begin{eqnarray*} \Phi ^0_\text{P} (\omega ) = \frac{\omega R \Delta }{c^0} = \omega R \Delta p^0 = \omega X p^0, \end{eqnarray*} (5) where c0 and p0 are the phase velocity and slowness for the spherical Earth, Δ is the angular epicentral distance, R is the radius of the Earth, and X is the great-circle path length. We write the observed surface-wave seismogram as a perturbation with respect to the reference seismogram, \begin{eqnarray*} u(\omega ) = \left[ A^0(\omega ) + \delta A(\omega ) \right] \exp i \left[\Phi ^0 (\omega ) + \delta \Phi (\omega ) \right]. \end{eqnarray*} (6) Assuming the phase contributions due to the source, receiver, and each ray focus are accounted for, we attribute an observed phase anomaly at a given frequency, δΦ, to perturbations in the propagation phase, \begin{eqnarray*} \Phi _\text{P} = \Phi ^0_\text{P} + \delta \Phi = \frac{\omega X}{c^0 + \overline{\delta \text{c}}}, \end{eqnarray*} (7) where |$\overline{\delta \text{c}}$| is the average phase-velocity perturbation along the great circle path. Assuming ray theory, we interpret phase anomalies as having accumulated along the path between earthquake source and receiver, \begin{eqnarray*} \delta \Phi = \omega \int \delta p(\theta ,\varphi ) ~\text{d}s, \end{eqnarray*} (8) where δp(θ, φ) is the local slowness perturbation. The local phase-velocity perturbation, δc(θ, φ), is calculated from the slowness perturbation. For a weakly anisotropic Earth, azimuthal variations in surface-wave phase slowness can be described as having two- and four-fold symmetry with respect to the propagation azimuth, ζ (Smith & Dahlen 1973). The azimuthal dependence for both Love and Rayleigh wave phase slowness is written \begin{eqnarray*} \frac{\delta p (\theta ,\varphi ,\zeta )}{p^0} = A_0(\theta ,\varphi ) &+&A_1(\theta ,\varphi ) \cos (2\zeta ) + A_2(\theta ,\varphi ) \sin (2\zeta ) \\ &+&A_3(\theta ,\varphi ) \cos (4\zeta ) + A_4(\theta ,\varphi ) \sin (4\zeta ), \nonumber \end{eqnarray*} (9) where A0(θ, φ) is the azimuthally averaged term, equivalent to an isotropic phase-slowness perturbation in the case with no anisotropy, and A1(θ, φ), A2(θ, φ), A3(θ, φ), and A4(θ, φ) are laterally varying coefficients describing azimuthal variations about the average. 4 METHODS 4.1 Model parametrization We interpret our phase-anomaly measurements, δΦ, in a ray-theory framework; phase anomalies are attributed to slowness perturbations along the length of the great-circle path between earthquake source and receiver (eq. 8). Laterally varying perturbations in slowness at a given frequency, δp(θ, φ)/p0, are parametrized with a set of basis functions on the surface of a sphere, \begin{eqnarray*} \frac{\delta p(\theta ,\varphi )}{p^0} = \sum _{i=1}^{N} a_i B_i (\theta ,\varphi ), \end{eqnarray*} (10) where N is the number of basis functions, ai are the model coefficients, and Bi(θ, φ) are the basis functions. We choose to parametrize our model with 5° × 5° pixels. We invert for each of the coefficients A0(θ, φ), A1(θ, φ), A2(θ, φ), A3(θ, φ), and A4(θ, φ) in every model pixel. We select the boundaries of our model domain so that the entire length of each path is within the domain and every pixel is crossed by at least one path. As a result, we do not need to correct our phase-anomaly measurements for the effects of structure outside the model domain. To determine the azimuthally anisotropic phase slowness in each pixel, we minimize the misfit function \begin{eqnarray*} \chi ^2 = \sum _{j=1}^{N} \frac{1}{\sigma _j^2} \left( \delta \Phi _j^{\text{obs}} - \delta \Phi _j^{\text{pred}}\right)^2, \end{eqnarray*} (11) where j is the index of the observation, N is the number of observations, and σj is the observational uncertainty, which was computed by Ekström (2011) by comparison of measurements from similar paths. 4.2 Model regularization—roughness We regularize the inversion by minimizing the roughness, |$\mathcal {R}$|⁠, defined as the rms gradient of the isotropic phase-slowness variations \begin{eqnarray*} \mathcal {R}^2 = \frac{1}{4\pi }\int _{\Omega }\left(\nabla \frac{\delta p}{p^0} \right) \cdot \left(\nabla \frac{\delta p}{p^0}\right) \text{d}\Omega . \end{eqnarray*} (12) Similarly, we define the anisotropic roughness, |$\mathcal {R}_{n\zeta }$|⁠, \begin{eqnarray*} \mathcal {R}_{n\zeta }^2 = \frac{1}{4\pi }\int _{\Omega } \left[ (\nabla c_{n\zeta }) \cdot (\nabla c_{n\zeta }) + (\nabla s_{n\zeta }) \cdot (\nabla s_{n\zeta }) \right] \text{d}\Omega , \end{eqnarray*} (13) where cnζ and snζ are the laterally varying cosine and sine coefficients for 2ζ and 4ζ azimuthal anisotropy. Azimuthal anisotropy on a sphere must be described with care because directions of constant azimuth at two nearby points are not parallel directions. In particular, applying smoothness-damping constraints directly to the coefficients A1(θ, φ), A2(θ, φ), A3(θ, φ), and A4(θ, φ) leads to undesirable results at high latitudes. Ekström (2006) introduced the concept of local parallel azimuth and applied it to a global parametrization in terms of spherical splines. In this method, the ray propagation direction at a given point is referenced to the north direction at the fixed knot points of the model parametrization, rather than being referenced to geographical north at the point. In an approach similar to that employed by Ma & Masters (2015), we apply the concept of local parallel azimuth to our pixel parametrization. The correction for an azimuth at a point (θ, φ) is calculated, \begin{eqnarray*} \zeta _i (\theta ,\varphi )= \zeta (\theta ,\varphi ) - \left(\alpha _i(\theta ,\varphi ) - \beta _i(\theta ,\varphi ) - \pi \right), \end{eqnarray*} (14) where ζi(θ, φ) is the local parallel azimuth at the ith pixel, αi(θ, φ) is the azimuth from the point (θ, φ) to the ith pixel, and βi(θ, φ) is the back azimuth from the ith pixel to (θ, φ). We compute the gradient operator numerically and correct for the local parallel azimuth. The smoothness constraint is applied at each pixel by referencing the azimuths to the pixels north, south, east, and west of the centre pixel. Specifically, we calculate the squared discretized gradient of the anisotropic slowness perturbations, \begin{eqnarray*} \left[ (\nabla c) \cdot (\nabla c) + (\nabla s) \cdot (\nabla s) \right] &\approx& \left[ 4\delta p^\text{c}_\text{a} - \left( \delta p^\text{n}_\text{a} + \delta p^\text{s}_\text{a} + (1/\cos (\theta )) \right. \right. \nonumber \\ && \left. \left. \times (\delta p^\text{e}_\text{a} + \delta p^\text{w}_\text{a} )\right) \right], \end{eqnarray*} (15) where δpa is the anisotropic slowness perturbation at the centre, north, south, east, and west pixels. The factor 1/cos (θ) is necessary to account for the changing size of a degree of longitude with increasing latitude, and θ is the latitude of the centre pixel. The anisotropic slowness perturbation for the 2ζ perturbations at a given pixel is \begin{eqnarray*} \delta p_a = A_1(\theta ,\varphi ) \cos (2\zeta ) + A_2(\theta ,\varphi ) \sin (2\zeta ). \end{eqnarray*} (16) It is necessary to apply the smoothness constraint in two directions, and we choose to apply it in the north and northeast directions. In the north direction, ζ = 0, so we write the slowness perturbation, dropping the (θ, φ), as \begin{eqnarray*} \delta p^\text{c}_\text{a} = A_1. \end{eqnarray*} (17) The azimuth correction for a neighbouring pixel is \begin{eqnarray*} \zeta _i = \alpha _i - \beta _i - \pi . \end{eqnarray*} (18) The slowness perturbation at the north pixel is then \begin{eqnarray*} \delta p^n_a = A_1 \cos (2(\alpha _i - \beta _i )) + A_2 \sin (2(\alpha _i - \beta _i )). \end{eqnarray*} (19) In the northeast direction, ζ = π/4, and we recalculate the slowness perturbations for the centre and north pixels: \begin{eqnarray*} \delta p^\text{c}_\text{a} = A_2 \end{eqnarray*} (20) \begin{eqnarray*} \zeta _i = \alpha _i - \beta _i - 3\pi /4 \end{eqnarray*} (21) \begin{eqnarray*} \delta p^\text{n}_\text{a} = -A_1 \sin (2(\alpha _i - \beta _i )) + A_2 \cos (2(\alpha _i - \beta _i )) . \end{eqnarray*} (22) Similarly, we compute the 2ζ anisotropic slowness perturbations for the south, east, and west pixels and apply the discretized gradient operator to smooth the model in each direction. The gradient for the 4ζ anisotropic slowness perturbations is calculated analogously. 4.3 Model regularization—age dependence We have fewer crossing paths at the edges of our model domain, making it difficult to resolve, for example, velocities along the southern part of the East Pacific Rise. In order to recover realistic phase velocities in regions with poor path coverage, we implement an additional regularization scheme in which we take advantage of the previously demonstrated age dependence of oceanic phase velocity (e.g. Nishimura & Forsyth 1988, 1989) to construct an a priori model of the horizontal gradient in slowness perturbation. We damp the gradient of the isotropic model parameters towards the gradient of the age-dependent model. We model the age dependence of the slowness perturbation by assuming a half-space-cooling model for the oceanic plate. This cooling model predicts that the depth to a given temperature varies with the square root of cooling time (Turcotte & Schubert 2002). As temperature is typically the dominant control on seismic velocity perturbations within the upper mantle, we expect that isotropic shear and compressional velocities also should vary as a function of the square root of seafloor age. The age dependence of surface-wave phase velocity, however, is more complicated than a simple square root function due to the depth averaging of the sensitivity to elastic structure. In order to model the age dependence of phase velocities, we first predict oceanic geotherms at different plate ages assuming a half-space-cooling model, then we use the method of Jackson & Faul (2010) to convert these temperature profiles to upper-mantle seismic velocities. Finally, we calculate the resulting Rayleigh and Love phase velocities and find that the predicted surface-wave slowness can be described well by the function \begin{eqnarray*} p_i = c_1 T_i + c_2 \sqrt{T_i} + c_3, \end{eqnarray*} (23) where pi is the slowness and Ti is the seafloor age in Ma for the ith pixel. The seafloor age is defined as the average value of the global age model of Müller et al. (2008) within each pixel. The linear term is necessary to predict accurate phase velocities at young seafloor ages, particularly at short periods; without this term, the predicted phase velocities are too high. We confirm that the form of age dependence expressed in eq. (23) holds for observed phase velocities by modelling the age dependence of the Pacific Rayleigh and Love phase velocities in dispersion model GDM52 (Ekström 2011). Harmon et al. (2009) also found that a function of this form describes well the variation in phase velocity for young lithosphere near the East Pacific Rise. The total slowness perturbation in our inversions, (δp/p0)i, is calculated with respect to a constant initial starting model, so both the perturbation and absolute phase slowness should be described by eq. (23). We use this age relationship to model the slowness perturbation as a function of age. For any two adjacent pixels with seafloor ages Ti and Tj, we calculate the gradient between predicted age-dependent slowness perturbations, \begin{eqnarray*} \left(\nabla \frac{\delta p}{p^0}\right)^0_{ij} = \left(\frac{\delta p}{p^0}\right)^0_{i} - \left(\frac{\delta p}{p^0}\right)^0_{j}, \end{eqnarray*} (24) where |$(\delta p/p^0)^0_i$| and |$(\delta p/p^0)^0_j$| are calculated using the age model. We damp the gradient of the isotropic model parameters towards the age-dependent gradient. We define the age-dependent roughness as \begin{eqnarray*} \mathcal {R}^2_{\text{age}} = \frac{1}{4\pi }\int _{\Omega } \frac{1}{\log _{10}(N_{ij})} \left[ \left(\nabla \frac{\delta p}{p^0} \right) - \left(\nabla \frac{\delta p}{p^0} \right)^0 \right]^2 \text{d}\Omega , \end{eqnarray*} (25) where (∇δp/p0)0 is the predicted gradient in age-dependent phase-slowness perturbations, calculated as in eq. (24), and N is the average number of paths that sample any two adjacent pixels. In areas where the model is well sampled by crossing paths, we do not want the age-dependent damping scheme to have a dominant effect on the model perturbations. The weight 1/log10(Nij) ranges between 0.1 and 1.0 and is applied in order to focus this damping on the pixels that are most poorly resolved. For pixels that do not contain seafloor or for which the seafloor age is not defined, we do not apply age-dependent damping. While the strength and orientation of azimuthal anisotropy may vary with seafloor age and location relative to the spreading ridge, the form of the expected variation is not well known and we do not apply the age-dependent damping scheme to the model parameters that describe azimuthal anisotropy. For pixels on the edge of our model domain that are located on continents, rather than oceanic plates, we damp the slowness of these continental pixels towards the value given by GDM52 (Ekström 2011), \begin{eqnarray*} \mathcal {R}^2_{c} = \frac{1}{4\pi }\int _{\Omega } \left( p - p_{c} \right)^2 \text{d}\Omega , \end{eqnarray*} (26) where pc is the slowness at the centre of the continental pixel evaluated from GDM52. 4.4 Inversion scheme In a full inversion for isotropic and 2ζ and 4ζ azimuthal anisotropy, with age-dependent damping, we minimize the total misfit function \begin{eqnarray*} \chi ^{\prime 2}=\chi ^2 + \lambda \mathcal {R}^2 + \lambda _{2\zeta } \mathcal {R}_{2\zeta }^2 + \lambda _{4\zeta } \mathcal {R}_{4\zeta }^2 + \lambda _{\text{age}} \mathcal {R}_{\text{age}}^2 + \lambda _{\text{c}} \mathcal {R}_{\text{c}}^2, \end{eqnarray*} (27) where λ, λ2ζ, λ4ζ, λage, and λc are the relative weights assigned to the observations and damping schemes. We minimize the total misfit function χ′2 in an iterative least-squares inversion. The starting model for the inversion at each period is the uniform phase velocity of the PREM model (Dziewonski & Anderson 1981), but we find that our choice of starting model does not influence strongly the resulting phase-velocity maps. We choose to iterate because this allows us to use the age dependence of our inverted phase velocities as an a priori constraint on the subsequent iteration, as described in Section 4.3. For the first iteration, we assume a constant starting model without age dependence. After the first and each subsequent iteration, we solve for the best-fitting coefficients c1, c2 and c3 of eq. (23) to model the inverted slowness perturbations as a function of seafloor age. We then predict the expected horizontal slowness gradient between any two pixels. In the subsequent iteration, the starting model is taken to be the phase-velocity model from the prior iteration and we solve for the total slowness perturbation from the initial starting model. 5 RESULTS We performed inversions for isotropic Love and Rayleigh wave phase velocity and their 2ζ and 4ζ azimuthal variations at periods between 25 and 250 s. We first present the results of inversions for the isotropic terms only. Subsequently, we present the results of anisotropic inversions. In each case, we examine the trade-offs between smoothness damping, age-dependent gradient damping, and data fit by minimizing χ′2 in a series of inversions in which we vary the damping weights λ, λ2ζ, λ4ζ, and λage. We perform these tests for a reference period of 50 s and compare the normalized data misfit χ2/N, where N is the total number of observations, to the model roughness, |$\mathcal {R}^2$|⁠, in order to determine our preferred damping parameters. Once the reference damping weight, λ(f0), is selected, we calculate the weight at different periods by scaling to the reference weight such that |$\lambda (f) = \frac{f_0}{f} \lambda (f_0)$|⁠. The damping weights for isotropic and anisotropic smoothness damping and age-dependent gradient damping all are scaled by frequency in the same manner. 5.1 Isotropic phase-velocity maps Results of the isotropic inversions at several periods are shown in Fig. 2 for Rayleigh waves and in Fig. 3 for Love waves. As expected, phase velocities of both Love and Rayleigh waves at all periods exhibit slow velocities beneath the East Pacific Rise; the area of low velocities beneath the ridge is narrow at short periods and broadens with increasing period. We observe the fastest phase velocities in the northwest Pacific. Figure 2. View largeDownload slide Rayleigh wave phase-velocity perturbations at four periods from isotropic inversion. Perturbations are shown as percent deviation from PREM at each period. Figure 2. View largeDownload slide Rayleigh wave phase-velocity perturbations at four periods from isotropic inversion. Perturbations are shown as percent deviation from PREM at each period. Figure 3. View largeDownload slide Love wave phase-velocity perturbations at four periods from isotropic inversion. Perturbations are shown as percent deviation from PREM at each period. Figure 3. View largeDownload slide Love wave phase-velocity perturbations at four periods from isotropic inversion. Perturbations are shown as percent deviation from PREM at each period. We assess the performance of the age-dependent damping scheme by performing an inversion without this damping for comparison. Fig. 4 shows the phase-velocity maps for 50-s Rayleigh waves with and without the age-dependent damping applied. For this comparison, we choose the damping weights such that the resulting model roughness is similar between the two maps. The largest difference between the models occurs along the southern boundary of the model domain, where the mid-ocean ridge is made slower by damping the phase velocity towards the gradient for young seafloor ages. Aside from this region in the southern part of the model where the path coverage is relatively weak, differences between the maps generally are less than |$\pm 1\hbox{ per cent}$| and they occur primarily along the mid-ocean ridges, where we model slower phase velocities, and seaward of continents, where we model slightly faster phase velocities when age-dependent damping is applied. At longer periods, the differences between the two models are smaller. At shorter periods, the differences are larger, reaching |$\pm 2\hbox{ per cent}$| for 25-s Rayleigh waves, but the patterns remain the same. Figure 4. View largeDownload slide Phase-velocity maps for 50-s Rayleigh waves, shown as percent deviation from PREM, (a) with the gradient damped towards the age-dependent model, (b) without the age-dependent damping, and (c) the difference between the two models. Note the different colour scale for (c). Figure 4. View largeDownload slide Phase-velocity maps for 50-s Rayleigh waves, shown as percent deviation from PREM, (a) with the gradient damped towards the age-dependent model, (b) without the age-dependent damping, and (c) the difference between the two models. Note the different colour scale for (c). Applying the age-dependent gradient damping in regions near mid-ocean ridges has a significant effect because the gradient of phase velocity with age is largest for young seafloor, and because the ridge that forms the southern boundary of the Pacific is less well covered by crossing paths than other areas of the model (Fig. 1). Velocities also change rapidly across subduction margins, where the downgoing plate consists of old seafloor and the upper plate consists of young seafloor or continental or arc material. A larger weight for the traditional smoothness damping, λ, is required for the inversion where no age-dependent damping is applied, and the smoothing leads to unreasonably high velocities at the ridge and slow velocities adjacent to subduction margins. In the inversion where we apply age-dependent gradient damping, we are able to decrease λ and recover low velocities at the ridge that are more realistic and slightly faster phase velocities for the oceanic pixels at the subduction margins that are likely closer to their true values. This behaviour indicates that the age-dependent damping achieves the desired result of minimal influence in well-sampled regions and a realistic constraint in poorly sampled seafloor regions and areas where rapid lateral variations are expected. For all other phase-velocity results presented in this paper, we have performed the inversions with the age-dependent damping scheme. We examine the age dependence of phase velocity in our isotropic maps by comparing the total phase-velocity perturbation from the starting model to the best-fitting age model (eq. 23). Figs 5(a)–(d) shows phase-velocity perturbations as a function of seafloor age and maps of the differences between the perturbations and the best-fitting age model for the isotropic-only inversions for Rayleigh and Love waves at 50 s. The simple, age-dependent model fits the data well overall, but with some scatter. A subset of model pixels in the western equatorial Pacific with seafloor ages older than 120 Ma exhibit phase velocities uniformly slower than the best-fitting age model. These model pixels are slow for both Rayleigh and Love waves at all periods, with the largest perturbation at short periods (Figs 2 and 3). The slow phase-velocity perturbation in this region is the largest deviation from a simple age model in the Pacific and corresponds to the region of thickened oceanic crust in the Ontong Java Plateau (Hussong et al.1979; Gladczenko et al.1997). Figure 5. View largeDownload slide Left column shows the total isotropic phase-velocity perturbation from the starting model (PREM) as a function of seafloor age for (a) 50-s Love waves and (c) 50-s Rayleigh waves from the isotropic inversions, and (e) 50-s Rayleigh waves from the inversion including 2ζ azimuthal terms. Grey points show phase-velocity perturbations associated with pixels located on the Nazca or Cocos plates. Black line shows the best-fitting age model. Right column shows the difference between the total phase-velocity perturbation and the best-fitting age model. Figure 5. View largeDownload slide Left column shows the total isotropic phase-velocity perturbation from the starting model (PREM) as a function of seafloor age for (a) 50-s Love waves and (c) 50-s Rayleigh waves from the isotropic inversions, and (e) 50-s Rayleigh waves from the inversion including 2ζ azimuthal terms. Grey points show phase-velocity perturbations associated with pixels located on the Nazca or Cocos plates. Black line shows the best-fitting age model. Right column shows the difference between the total phase-velocity perturbation and the best-fitting age model. Around 15° S, a broad, linear feature of relatively slow phase velocity compared to the best-fitting age model extends from the East Pacific Rise to the northern part of the Tonga-Fiji subduction zone. We observe this feature for both Rayleigh and Love waves and at all periods examined in this study. This low-velocity anomaly coincides with the location of several hotspots and the proposed South Pacific superswell (McNutt & Fischer 1987). An elongated low-velocity anomaly is also observed in the region of the Hawaiian islands; this region of slow velocities has been previously observed and is associated with the Hawaiian hotspot and plume (e.g. Zhao 2001; Wolfe et al.2009). Damping the slowness of continental pixels towards GDM52, as described in Section 4.3, leads to more realistic continental velocities; without this regularization applied, the smoothness damping leads to modelled continental phase velocities that are too fast and some oceanic phase-velocities that are likely too slow. When we invert with the norm damping for the continental pixels, the data are fit equally well and we recover slightly faster phase velocities in the western Pacific and Nazca and Cocos plates. This damping scheme allows us to resolve the phase velocity of the oceanic plate better without sacrificing data fit. 5.2 Anisotropic phase-velocity maps We investigate the anisotropic structure of the Pacific by performing inversions for Rayleigh and Love wave phase velocities including 2ζ and 4ζ azimuthal variations. The improvement in fit to the data resulting from the inclusion of the azimuthal terms is given in Table 3. While the data fit is always improved with the addition of anisotropic parameters, the largest misfit reduction occurs when including the sensitivity to 2ζ Rayleigh wave anisotropy; data fit is improved by |$8.8\hbox{ per cent}$| at 250 s, |$27\hbox{ per cent}$| at 125 s and |$51\hbox{ per cent}$| at 45 s. Including sensitivity to 4ζ Rayleigh wave anisotropy or 2ζ and 4ζ Love wave anisotropy makes little difference to the overall data misfit; the data fit for Love waves is improved by only |$6-16\hbox{ per cent}$| with the addition of 2ζ anisotropy and by |$10\text{-}23\hbox{ per cent}$| when the sensitivity to both 2ζ and 4ζ terms is included. This implies that the strength of the Love wave anisotropic terms is small and less well resolved than the 2ζ Rayleigh wave terms. Table 3. Goodness of fit, χ2/N, for isotropic (0) and anisotropic (2ζ, 4ζ) inversions. Love Rayleigh Period (s) 0 0, 2ζ 0, 4ζ 0, 2ζ, 4ζ 0 0, 2ζ 0, 4ζ 0, 2ζ, 4ζ 25 2.414 2.086 2.094 1.944 2.337 1.510 1.894 1.414 27 2.786 2.377 2.398 2.200 2.716 1.675 2.166 1.566 30 2.995 2.529 2.549 2.320 3.041 1.753 2.378 1.635 32 2.455 2.172 2.175 2.003 2.322 1.350 1.807 1.266 35 3.204 2.846 2.854 2.632 2.589 1.412 1.974 1.318 40 3.537 3.124 3.157 2.899 2.899 1.482 2.181 1.377 45 3.500 3.075 3.107 2.850 3.155 1.546 2.360 1.431 50 2.414 2.188 2.189 2.055 2.146 1.135 1.639 1.066 60 2.481 2.249 2.233 2.102 2.410 1.241 1.848 1.168 75 2.680 2.433 2.411 2.280 2.648 1.376 2.077 1.297 100 2.349 2.138 2.140 2.035 2.340 1.431 1.972 1.373 125 1.821 1.670 1.695 1.615 1.999 1.462 1.789 1.421 150 2.769 2.491 2.526 2.339 2.374 1.776 2.030 1.682 200 1.456 1.368 1.361 1.304 2.290 1.998 2.090 1.922 250 2.040 1.912 1.939 1.846 2.043 1.863 1.919 1.811 Love Rayleigh Period (s) 0 0, 2ζ 0, 4ζ 0, 2ζ, 4ζ 0 0, 2ζ 0, 4ζ 0, 2ζ, 4ζ 25 2.414 2.086 2.094 1.944 2.337 1.510 1.894 1.414 27 2.786 2.377 2.398 2.200 2.716 1.675 2.166 1.566 30 2.995 2.529 2.549 2.320 3.041 1.753 2.378 1.635 32 2.455 2.172 2.175 2.003 2.322 1.350 1.807 1.266 35 3.204 2.846 2.854 2.632 2.589 1.412 1.974 1.318 40 3.537 3.124 3.157 2.899 2.899 1.482 2.181 1.377 45 3.500 3.075 3.107 2.850 3.155 1.546 2.360 1.431 50 2.414 2.188 2.189 2.055 2.146 1.135 1.639 1.066 60 2.481 2.249 2.233 2.102 2.410 1.241 1.848 1.168 75 2.680 2.433 2.411 2.280 2.648 1.376 2.077 1.297 100 2.349 2.138 2.140 2.035 2.340 1.431 1.972 1.373 125 1.821 1.670 1.695 1.615 1.999 1.462 1.789 1.421 150 2.769 2.491 2.526 2.339 2.374 1.776 2.030 1.682 200 1.456 1.368 1.361 1.304 2.290 1.998 2.090 1.922 250 2.040 1.912 1.939 1.846 2.043 1.863 1.919 1.811 View Large Table 3. Goodness of fit, χ2/N, for isotropic (0) and anisotropic (2ζ, 4ζ) inversions. Love Rayleigh Period (s) 0 0, 2ζ 0, 4ζ 0, 2ζ, 4ζ 0 0, 2ζ 0, 4ζ 0, 2ζ, 4ζ 25 2.414 2.086 2.094 1.944 2.337 1.510 1.894 1.414 27 2.786 2.377 2.398 2.200 2.716 1.675 2.166 1.566 30 2.995 2.529 2.549 2.320 3.041 1.753 2.378 1.635 32 2.455 2.172 2.175 2.003 2.322 1.350 1.807 1.266 35 3.204 2.846 2.854 2.632 2.589 1.412 1.974 1.318 40 3.537 3.124 3.157 2.899 2.899 1.482 2.181 1.377 45 3.500 3.075 3.107 2.850 3.155 1.546 2.360 1.431 50 2.414 2.188 2.189 2.055 2.146 1.135 1.639 1.066 60 2.481 2.249 2.233 2.102 2.410 1.241 1.848 1.168 75 2.680 2.433 2.411 2.280 2.648 1.376 2.077 1.297 100 2.349 2.138 2.140 2.035 2.340 1.431 1.972 1.373 125 1.821 1.670 1.695 1.615 1.999 1.462 1.789 1.421 150 2.769 2.491 2.526 2.339 2.374 1.776 2.030 1.682 200 1.456 1.368 1.361 1.304 2.290 1.998 2.090 1.922 250 2.040 1.912 1.939 1.846 2.043 1.863 1.919 1.811 Love Rayleigh Period (s) 0 0, 2ζ 0, 4ζ 0, 2ζ, 4ζ 0 0, 2ζ 0, 4ζ 0, 2ζ, 4ζ 25 2.414 2.086 2.094 1.944 2.337 1.510 1.894 1.414 27 2.786 2.377 2.398 2.200 2.716 1.675 2.166 1.566 30 2.995 2.529 2.549 2.320 3.041 1.753 2.378 1.635 32 2.455 2.172 2.175 2.003 2.322 1.350 1.807 1.266 35 3.204 2.846 2.854 2.632 2.589 1.412 1.974 1.318 40 3.537 3.124 3.157 2.899 2.899 1.482 2.181 1.377 45 3.500 3.075 3.107 2.850 3.155 1.546 2.360 1.431 50 2.414 2.188 2.189 2.055 2.146 1.135 1.639 1.066 60 2.481 2.249 2.233 2.102 2.410 1.241 1.848 1.168 75 2.680 2.433 2.411 2.280 2.648 1.376 2.077 1.297 100 2.349 2.138 2.140 2.035 2.340 1.431 1.972 1.373 125 1.821 1.670 1.695 1.615 1.999 1.462 1.789 1.421 150 2.769 2.491 2.526 2.339 2.374 1.776 2.030 1.682 200 1.456 1.368 1.361 1.304 2.290 1.998 2.090 1.922 250 2.040 1.912 1.939 1.846 2.043 1.863 1.919 1.811 View Large To assess our resolution of azimuthal anisotropy across the Pacific, we compute a measure of local resolution for our phase-anomaly data set (Figs 1 c and d). For each model pixel, we define the local resolution to be the logarithm of the ratio between the maximum and minimum eigenvalues of the inner-product matrix that contains the sensitivity to perturbations to average phase velocity and 2ζ and 4ζ azimuthal variations within the pixel. A low value of this ratio, known as the condition number, requires several paths crossing each pixel in multiple directions and indicates that the inversion is well constrained. By this metric, resolution of azimuthal anisotropy is good across most of the central Pacific for Rayleigh waves and worse for Love waves. At the edges of the model domain, there are few crossing paths and the local resolution is weak, so we avoid interpreting azimuthal anisotropy in these areas. Due to the relatively poor resolution of Love wave azimuthal anisotropy and the small improvement in misfit when anisotropic terms are included in the inversion (Table 3), we select the isotropic model as our preferred Love wave phase-velocity model. For Rayleigh waves, including the 4ζ terms in the inversion leads to a relatively small reduction in misfit of |$3\text{-}7\hbox{ per cent}$| compared to the improvement from including only the 2ζ terms, so we select as our preferred Rayleigh wave phase-velocity model the inversion that includes only the isotropic and 2ζ anisotropic velocity variations. Fig. 6 shows Rayleigh wave phase velocity and its 2ζ azimuthal variations at four periods. At all periods, the magnitude of the isotropic velocity variations is reduced when including sensitivity to azimuthal variations, but we still observe strong age dependence. The strength of the azimuthal anisotropy is largest at short periods, and decreases with increasing period. At short periods, there are large lateral variations in the orientation of the anisotropy fast axis. At long periods, the variations are smoother. Figure 6. View largeDownload slide Anisotropic Rayleigh wave phase-velocity perturbations at four periods. Perturbations are shown as percent deviation from PREM at each period. The orientations of the black lines represent the fast azimuth direction for 2ζ anisotropy and the length of the bar is scaled to the anisotropy strength. Peak anisotropy strength is (a) |$2.9\hbox{ per cent}$| at 25 s, (b) |$2.5\hbox{ per cent}$| at 50 s, (c) |$2.1\hbox{ per cent}$| at 75 s and (d) |$1.5\hbox{ per cent}$| at 125 s. Figure 6. View largeDownload slide Anisotropic Rayleigh wave phase-velocity perturbations at four periods. Perturbations are shown as percent deviation from PREM at each period. The orientations of the black lines represent the fast azimuth direction for 2ζ anisotropy and the length of the bar is scaled to the anisotropy strength. Peak anisotropy strength is (a) |$2.9\hbox{ per cent}$| at 25 s, (b) |$2.5\hbox{ per cent}$| at 50 s, (c) |$2.1\hbox{ per cent}$| at 75 s and (d) |$1.5\hbox{ per cent}$| at 125 s. For Rayleigh waves, including sensitivity to azimuthal anisotropy in our inversions leads to isotropic oceanic phase velocities that are closer to a simple age-dependent model (Figs 5 e and f), a result that holds both when we apply the age-dependent gradient damping scheme in the inversions and when we do not. The magnitude of the phase-velocity differences from the age-dependent model is smaller in the anisotropic phase-velocity maps than in the isotropic-only maps. Phase velocities in the Nazca plate and northeast Pacific plate are slower, while velocities in the southern Pacific are faster. Including sensitivity to Love wave azimuthal anisotropy does not reduce the variation in isotropic phase velocities about an age-dependent model, further suggesting that our observations do not require Love wave azimuthal anisotropy. 5.3 Prediction of NoMelt phase anomalies Using our preferred phase-velocity models, we predict the surface-wave dispersion for the paths recorded on the NoMelt network that are |$90\hbox{ per cent}$| within the Pacific. Because there are very few NoMelt paths relative to our phase-anomaly data set (Table 2), including these data in the inversion does not improve significantly the lateral resolution of our model. Instead of using these data as an additional constraint, we choose to use predictions of these phase-anomaly data to help validate our models. Table 4 shows the variance reduction, |$1-\sum _{j=1}^{N} (\delta \Phi _j^{\text{obs}} - \delta \Phi _j^{\text{pred}})^2/\sum _{j=1}^{N}(\delta \Phi _j^{\text{obs}})^2$|⁠, for the NoMelt phase-anomaly observations. The variance reduction describes the improvement in data misfit relative to our starting model, the uniform phase velocity predicted by PREM. Our preferred phase-velocity models explain a significant fraction of the phase-anomaly variance; variance reduction is greater than |$81\hbox{ per cent}$| for Love waves and |$97\hbox{ per cent}$| for Rayleigh waves between 25 and 45 s. At long periods, the variance reduction is lower: |$59\hbox{ per cent}$| for the 125-s Love wave data and |$50\hbox{ per cent}$| for 125-s Rayleigh wave data. Similarly to the full phase-anomaly data set (Table 5), the variance reduction is greatest at short periods because the data variance is larger. At long periods, the uniform starting model does a relatively good job explaining the data, so the reduction in variance from our preferred models is lower. This effect is larger for Rayleigh waves than for Love waves because Rayleigh waves have relatively deeper sensitivity to elastic structure. The velocity at depths where long-period Rayleigh waves have the greatest sensitivity has less lateral variation than the shallower velocity structure, to which Love waves are more sensitive. Table 4. Variance reduction, |$1-\sum _{j=1}^{N} (\delta \Phi _j^{\text{obs}} - \delta \Phi _j^{\text{pred}})^2/\sum _{j=1}^{N}(\delta \Phi _j^{\text{obs}})^2$|⁠, of NoMelt phase-anomaly observations assuming our preferred model. Period (s) Love Rayleigh 25 0.999 0.980 27 0.999 0.986 30 0.998 0.989 32 0.875 0.986 35 0.819 0.982 40 0.897 0.978 45 0.976 0.976 50 0.979 0.959 60 0.983 0.940 75 0.971 0.923 100 0.960 0.828 125 0.587 0.495 Period (s) Love Rayleigh 25 0.999 0.980 27 0.999 0.986 30 0.998 0.989 32 0.875 0.986 35 0.819 0.982 40 0.897 0.978 45 0.976 0.976 50 0.979 0.959 60 0.983 0.940 75 0.971 0.923 100 0.960 0.828 125 0.587 0.495 View Large Table 4. Variance reduction, |$1-\sum _{j=1}^{N} (\delta \Phi _j^{\text{obs}} - \delta \Phi _j^{\text{pred}})^2/\sum _{j=1}^{N}(\delta \Phi _j^{\text{obs}})^2$|⁠, of NoMelt phase-anomaly observations assuming our preferred model. Period (s) Love Rayleigh 25 0.999 0.980 27 0.999 0.986 30 0.998 0.989 32 0.875 0.986 35 0.819 0.982 40 0.897 0.978 45 0.976 0.976 50 0.979 0.959 60 0.983 0.940 75 0.971 0.923 100 0.960 0.828 125 0.587 0.495 Period (s) Love Rayleigh 25 0.999 0.980 27 0.999 0.986 30 0.998 0.989 32 0.875 0.986 35 0.819 0.982 40 0.897 0.978 45 0.976 0.976 50 0.979 0.959 60 0.983 0.940 75 0.971 0.923 100 0.960 0.828 125 0.587 0.495 View Large Table 5. Variance reduction, |$1-\sum _{j=1}^{N} (\delta \Phi _j^{\text{obs}} - \delta \Phi _j^{\text{pred}})^2/\sum _{j=1}^{N}(\delta \Phi _j^{\text{obs}})^2$|⁠, of the phase-anomaly data set assuming the preferred phase-velocity model and the 1-D age-dependent model described by eq. (23) at each period. Love Rayleigh Period (s) Best model Age model Best model Age model 25 0.981 0.969 0.988 0.966 27 0.985 0.972 0.991 0.967 30 0.986 0.970 0.991 0.965 32 0.983 0.964 0.988 0.959 35 0.980 0.957 0.987 0.955 40 0.976 0.944 0.985 0.945 45 0.971 0.931 0.982 0.933 50 0.950 0.906 0.962 0.900 60 0.938 0.882 0.949 0.859 75 0.908 0.828 0.919 0.768 100 0.863 0.764 0.818 0.554 125 0.817 0.713 0.699 0.384 150 0.787 0.635 0.688 0.405 200 0.685 0.558 0.616 0.388 250 0.516 0.398 0.363 0.204 Love Rayleigh Period (s) Best model Age model Best model Age model 25 0.981 0.969 0.988 0.966 27 0.985 0.972 0.991 0.967 30 0.986 0.970 0.991 0.965 32 0.983 0.964 0.988 0.959 35 0.980 0.957 0.987 0.955 40 0.976 0.944 0.985 0.945 45 0.971 0.931 0.982 0.933 50 0.950 0.906 0.962 0.900 60 0.938 0.882 0.949 0.859 75 0.908 0.828 0.919 0.768 100 0.863 0.764 0.818 0.554 125 0.817 0.713 0.699 0.384 150 0.787 0.635 0.688 0.405 200 0.685 0.558 0.616 0.388 250 0.516 0.398 0.363 0.204 View Large Table 5. Variance reduction, |$1-\sum _{j=1}^{N} (\delta \Phi _j^{\text{obs}} - \delta \Phi _j^{\text{pred}})^2/\sum _{j=1}^{N}(\delta \Phi _j^{\text{obs}})^2$|⁠, of the phase-anomaly data set assuming the preferred phase-velocity model and the 1-D age-dependent model described by eq. (23) at each period. Love Rayleigh Period (s) Best model Age model Best model Age model 25 0.981 0.969 0.988 0.966 27 0.985 0.972 0.991 0.967 30 0.986 0.970 0.991 0.965 32 0.983 0.964 0.988 0.959 35 0.980 0.957 0.987 0.955 40 0.976 0.944 0.985 0.945 45 0.971 0.931 0.982 0.933 50 0.950 0.906 0.962 0.900 60 0.938 0.882 0.949 0.859 75 0.908 0.828 0.919 0.768 100 0.863 0.764 0.818 0.554 125 0.817 0.713 0.699 0.384 150 0.787 0.635 0.688 0.405 200 0.685 0.558 0.616 0.388 250 0.516 0.398 0.363 0.204 Love Rayleigh Period (s) Best model Age model Best model Age model 25 0.981 0.969 0.988 0.966 27 0.985 0.972 0.991 0.967 30 0.986 0.970 0.991 0.965 32 0.983 0.964 0.988 0.959 35 0.980 0.957 0.987 0.955 40 0.976 0.944 0.985 0.945 45 0.971 0.931 0.982 0.933 50 0.950 0.906 0.962 0.900 60 0.938 0.882 0.949 0.859 75 0.908 0.828 0.919 0.768 100 0.863 0.764 0.818 0.554 125 0.817 0.713 0.699 0.384 150 0.787 0.635 0.688 0.405 200 0.685 0.558 0.616 0.388 250 0.516 0.398 0.363 0.204 View Large In addition to providing a test of our model, our ability to predict the NoMelt phase-anomaly observations well indicates that the measurements are accurate. This is the first time the measurement technique of Ekström et al. (1997) has been applied to data collected on ocean-bottom instruments, though phase-velocity measurements have been obtained from such data previously using other techniques. Our result supports the argument for inclusion of such data in plate- and global-scale models, in addition to the focused studies for which the instruments are typically deployed. 6 DISCUSSION Our preferred phase-velocity models are isotropic for Love waves and include 2ζ azimuthal variations for Rayleigh waves. Although we invert for models that include the full sensitivity to 2ζ and 4ζ azimuthal variations, we find that the improvement in data fit is small with the addition of the 4ζ term for Rayleigh waves and of either or both terms for Love waves (Table 3). Our observations are consistent with modelling of the elasticity tensor of olivine that suggests that the dominant anisotropy terms are 2ζ for Rayleigh wave anisotropy and 4ζ for Love wave anisotropy, with the Love wave anisotropy predicted to be quite small (Montagner & Nataf 1986). Inverting for only the 4ζ azimuthal terms for Love waves leads to models that fit the data as well as models with only 2ζ azimuthal anisotropy, suggesting that any existing Love wave anisotropy is too weak for our data to resolve. Models including only the 4ζ azimuthal terms for Rayleigh waves fit the data worse than models including only the 2ζ azimuthal terms, confirming that the dominant Rayleigh wave azimuthal anisotropy has a 2ζ pattern. In the discussion that follows, we refer to our preferred set of maps, which are shown in Fig. 3 for Love waves and Fig. 6 for Rayleigh waves. 6.1 Age dependence of phase velocity Our surface-wave phase-velocity maps show a clear age dependence. Fig. 7 shows the median dispersion for our preferred Rayleigh and Love wave models in several age bins. We compute the median isotropic phase velocity in each bin from all pixels in the model domain that have an average seafloor age within the range of that age bin. For both Rayleigh and Love waves, the youngest seafloor is the slowest, and at long periods the oldest seafloor is the fastest. For short-period Rayleigh waves, there is a reversal in this trend for the oldest seafloor; the median phase velocity at 25 s for seafloor with ages greater than 110 Ma is slightly slower than for seafloor with ages between 52 and 110 Ma. Forward modelling of phase velocities indicates that changes in seafloor depth, water-layer thickness, and sediment thickness likely explain this pattern, a result consistent with the findings of Nishimura & Forsyth (1989) and Ma & Dalton (2017). In particular, we find that the greater seafloor depth and corresponding water-layer thickness for the oldest seafloor in crustal model CRUST2.0 (Bassin et al.2000) explain the average behaviour of relatively slow short-period Rayleigh wave velocities. Figure 7. View largeDownload slide Median dispersion in oceanic pixels for (a and c) Rayleigh and (b and d) Love waves in several age bins. Solid lines show our preferred model, and dashed lines show the regionalized phase velocities of (a) Nishimura & Forsyth (1988), (b) Nishimura & Forsyth (1985) and (c and d) Nishimura & Forsyth (1989). X symbols show the predicted phase velocity at age 0 Ma from the best-fitting age model at each period (eq. 23). Note that the age bins are different in (b) to facilitate comparison with Nishimura & Forsyth (1985). Figure 7. View largeDownload slide Median dispersion in oceanic pixels for (a and c) Rayleigh and (b and d) Love waves in several age bins. Solid lines show our preferred model, and dashed lines show the regionalized phase velocities of (a) Nishimura & Forsyth (1988), (b) Nishimura & Forsyth (1985) and (c and d) Nishimura & Forsyth (1989). X symbols show the predicted phase velocity at age 0 Ma from the best-fitting age model at each period (eq. 23). Note that the age bins are different in (b) to facilitate comparison with Nishimura & Forsyth (1985). We compare our median dispersion to the pure-path regionalization of Pacific phase velocities of Nishimura & Forsyth (1985, 1988, 1989; Fig. 7). The phase-velocity models of Nishimura & Forsyth (1989) were corrected to account for probable reheating events associated with anomalously shallow seafloor. Those models provide an estimate of phase velocity for the unperturbed seafloor of the Pacific. The dispersion curves we present here represent the existing structure, which includes any alteration of the lithosphere and crust that has occurred since the seafloor was created, so the most direct comparison can be made between our modelled phase velocities and the Love (Nishimura & Forsyth 1985) and Rayleigh wave (Nishimura & Forsyth 1988) pure-path phase-velocity models that do not contain corrections for reheating associated with anomalously shallow regions. Overall, the character of our age-binned, median dispersion curves is very similar to the regionalized phase velocities of Nishimura & Forsyth (1985, 1988). Our results confirm that these pure-path models, carefully constructed three decades ago, provide a very good representation of the average age progression of Pacific phase velocities, with the limitation that they are regionalized, so no lateral variation or evolution of velocity within an age bin is allowed. The correction made by Nishimura & Forsyth (1989) to account for reheating in regions of anomalously shallow seafloor has the largest effect on phase velocities for the oldest seafloor. Our median dispersion for seafloor within the oldest age bin agrees more closely with the uncorrected pure-path models of Nishimura & Forsyth (1985, 1988) than the corrected model of Nishimura & Forsyth (1989). For Rayleigh waves in seafloor older than 110 Ma, our observed phase velocities are only |$0.7\hbox{ per cent}$| slower at 100 s than Nishimura & Forsyth (1988; Fig. 7a), but are |$1.1\hbox{ per cent}$| slower at 75 s than Nishimura & Forsyth (1989; Fig. 7c). For Love waves in the oldest seafloor age bin, median phase velocities reach only |$0.6\hbox{ per cent}$| slower than Nishimura & Forsyth (1985) at 125 s (Fig. 7b) but are up to |$2.4\hbox{ per cent}$| slower at 32 s than Nishimura & Forsyth (1989; Fig. 7d). Our observed phase velocities for seafloor of intermediate ages are very similar to those of Nishimura & Forsyth (1985, 1988), and are systematically slightly slower than the phase velocities of Nishimura & Forsyth (1989) for all ages greater than 4 Ma. These differences are all consistent with Nishimura & Forsyth (1989) representing Pacific seafloor that has not been reheated, and our models representing all Pacific lithosphere, which includes reheating and alteration signals that have the effect of decreasing phase velocities. The largest difference between our observed surface-wave dispersion and the models of Nishimura & Forsyth (1985, 1988, 1989) occurs for the youngest seafloor. For seafloor of age 0–4 Ma, we find faster velocities than Nishimura & Forsyth (1989); median phase velocities are up to |$3.8\hbox{ per cent}$| faster for 25-s Rayleigh waves and |$3.5\hbox{ per cent}$| faster for 35-s Love waves. Our overall sensitivity to the phase velocity of the youngest seafloor is low due to the 5° pixel size we use and the relatively small area of seafloor with ages 0–4 Ma. Only 15 pixels, or less than |$3\hbox{ per cent}$| of the total number of pixels in our model, fall within this youngest age bin. In addition, seafloor older than 4 Ma is included in most pixels because the ridge is not always centred in the middle of the pixel and spreading rates vary. Consequently, the values in these pixels are shifted towards higher phase velocities than if they included only the youngest seafloor. The median curves in our 0–4 Ma age bin are thus biased high. Conversely, many of the paths sampling the youngest seafloor in the model of Nishimura & Forsyth (1989) travel approximately parallel to the ridge; these waves may be focused towards the lowest-velocity regions along the ridge, in a waveguide effect (e.g. Dunn & Forsyth 2002), leading to a 0–4 Ma average that may be biased towards the lower velocities along the ridge. If we use our best-fitting age model at each period (eq. 23) to predict the phase velocities at age 0 Ma (Fig. 7), we find that the predicted velocity agrees well with the youngest age bin of Nishimura & Forsyth (1989), especially for the data with shallow sensitivity (Love waves and shorter-period Rayleigh waves). This agreement provides an additional indication that the age-dependent models represent the evolution of phase velocity with seafloor age well. Recent studies of Rayleigh wave phase velocity in the Atlantic ocean (James et al.2014) and Indian ocean (Godfrey et al.2017; Ma & Dalton 2017) have also observed phase velocities for the youngest seafloor that are faster than the phase velocities of Nishimura & Forsyth (1989). In the Atlantic, the oldest seafloor is relatively slow compared to the model of Nishimura & Forsyth (1989), but in the Indian ocean the phase velocities in the oldest seafloor are more similar, perhaps suggesting that the lithosphere in the Indian ocean has undergone less alteration and reheating than in the Pacific and Atlantic. We also compare our median observed phase velocities to those of global dispersion model GDM52 (Ekström 2011) and find that they agree very well. Although our data set is a subset of the data used to construct GDM52, modelling choices including different parametrization and damping schemes could lead to differences between the two models. However, the agreement between the two suggests that the results are independent of these modelling choices. Fig. 5 shows that most of the phase-velocity perturbation at an individual period can be explained by a simple model consistent with half-space cooling. In order to assess how much of the variance in our observed phase anomalies can be explained by plate cooling, we compute the data variance reduction, |$1-\sum _{j=1}^{N} (\delta \Phi _j^{\text{obs}} - \delta \Phi _j^{\text{pred}})^2/\sum _{j=1}^{N}(\delta \Phi _j^{\text{obs}})^2$|⁠, assuming the 1-D age-dependent model given by eq. (23) at each period, and compare it to the variance reduction from our preferred 2-D maps (Table 5). For 50-s Rayleigh waves, for example, |$90\hbox{ per cent}$| of the variance of the data can be explained by a model that depends only on seafloor age. Our preferred phase-velocity model, including lateral variations and anisotropy, explains |$96\hbox{ per cent}$| of the variance of the data. For both Rayleigh and Love waves at short periods, the variance reduction for the simple 1-D age model is high, indicating that the cooling of oceanic lithosphere explains much of the structure in the oceanic upper mantle. At longer periods (>75 s), the variance reduction is lower. At 125 s, the variance reduction for the age-dependent model is |$71\hbox{ per cent}$| for Love waves and only |$38\hbox{ per cent}$| for Rayleigh waves, compared with variance reductions for our preferred phase-velocity models of |$82\hbox{ per cent}$| for Love waves and |$70\hbox{ per cent}$| for Rayleigh waves. At 250 s, the variance reduction for the age-dependent model is |$40\hbox{ per cent}$| for Love waves and |$20\hbox{ per cent}$| for Rayleigh waves compared with |$52\hbox{ per cent}$| and |$36\hbox{ per cent}$| for our best-fitting Love and Rayleigh wave models. The fraction of variance reduction that the age-dependent model explains is greatest for short-period waves and lowest for long-period waves. For Love waves, the fraction of explained variance reduction ranges from 0.77 at 250 s to 0.99 at 25 s. For Rayleigh waves, this fraction ranges from 0.56 at 250 s to 0.98 at 25 s. Surface-wave phase velocity is sensitive to an integral of the intrinsic shear velocity over a depth range that depends on the wave’s period. The peak in sensitivity for longer-period waves occurs deeper than for short-period waves, and the plate-cooling signal is stronger in the shallow upper mantle. The depth of peak Rayleigh wave sensitivity also occurs deeper than the peak depth for Love waves; this explains why the fraction of variance reduction explained by the age-dependent model is significantly lower for long-period Rayleigh waves than for Love waves. We also observe that seafloor with ages older than ∼100 Ma shows more scatter in phase-velocity perturbations about the average age model than younger seafloor, with an increase in the strength of slow-velocity anomalies (Fig. 5). This observation is consistent with reheating of older oceanic lithosphere, possibly due to the influence of plumes or thermal-boundary-layer instabilities leading to small-scale convection in the asthenosphere. Ritzwoller et al. (2004) modelled upper-mantle shear velocities using Rayleigh waves and also found evidence for the reheating of oceanic lithosphere in the Pacific, and suggested that a large reheating event occurred from 70–100 Ma. Maggi et al. (2006b) also conducted a shear-velocity inversion based on Rayleigh waves but did not find any evidence for reheating of the Pacific lithosphere. Our observations suggest some thermal alteration of older portions of the Pacific lithosphere, but do not support a single reheating event, as the deviations do not show a sudden onset at a particular seafloor age. Although much of the data variance is explained by a simple age-dependent model, there is a significant improvement in variance reduction for phase-velocity models that include lateral variations in isotropic phase velocity and 2ζ anisotropy. The difference between the full phase-velocity perturbation and the best-fitting age model highlights the locations where the oceanic upper mantle is affected by processes other than plate cooling (Fig. 5f). Several areas stand out, including a low-velocity feature extending between the East Pacific Rise and Tonga-Fiji subduction zone around 15° S that may be related to a series of hotspots associated with the South Pacific superswell, including the Easter Island, Pitcairn, Macdonald, Society and Samoa hotspots (Isse et al.2006; Suetsugu et al.2009; Isse et al.2016). This region has anomalously shallow seafloor and shows evidence for a relatively thin elastic plate, consistent with elevated mantle temperatures in the region (McNutt & Fischer 1987). Near Hawaii, there is a region of anomalously slow Rayleigh wave velocities that is elongated in the orientation of the island chain; this feature is related to the Hawaiian plume and associated hotspot track. Previous modelling of the structure local to the East Pacific Rise found an asymmetry of seismic velocities across the ridge, with faster velocities on the eastern side of the ridge (Forsyth et al.1998; The MELT Seismic Team 1998; Toomey et al.2002; Hammond & Toomey 2003; Harmon et al.2009). In the area of the MELT experiment, located across the East Pacific Rise around 17° S, we find the seafloor to the west of the ridge to be slightly slower than seafloor to the east (Figs 5 d and f). At a larger scale, when we model only isotropic phase-velocity perturbations, we find a weak asymmetry on average, with Rayleigh wave velocity faster in the Nazca plate than the Pacific plate (Fig. 5c). However, when we also invert for 2ζ azimuthal anisotropy, as in our preferred model, this observed difference disappears (Fig. 5e). The grey dots in Figs 5(c) and (e) show the phase-velocity perturbations for pixels located on the Nazca and Cocos plates. Accounting for the azimuthal anisotropy of Rayleigh waves leads to isotropic phase velocities that follow a simple age dependence more closely. When we allow the east and west sides of the East Pacific Rise to follow independent age models, we find that our data are consistent with more rapidly increasing velocities on the east side of the ridge, but do not require this structure. For these models, variance reduction improves by less than |$0.3\hbox{ per cent}$|⁠. The asymmetry observed by previous workers has a length scale of several hundred kilometres, approximately the same size as one pixel in our model. Consequently, we are not able to resolve asymmetry local to the East Pacific Rise. We find that our data do not require asymmetry across the ridge on a larger scale, suggesting that asymmetry with a length scale larger than ∼500 km is weak. 6.2 Age dependence of azimuthal anisotropy We observe that, like the isotropic phase velocities, the strength of Rayleigh wave azimuthal anisotropy depends on age (Fig. 8). For all periods, the median strength of Rayleigh wave 2ζ anisotropy is largest for young seafloor ages and gradually becomes smaller for ages greater than 70 Ma. We observe the lowest anisotropy strength for seafloor from 130–180 Ma. The median azimuthal anisotropy strength for 75-s Rayleigh waves, for example, decreases from an average of |$1.1\hbox{ per cent}$| for seafloor of ages between 0 and 60 Ma to an average of |$0.4\hbox{ per cent}$| for 120–180 Ma seafloor. This finding agrees with previous work suggesting that the magnitude of surface-wave anisotropy decreases as a function of seafloor age (Nishimura & Forsyth 1988; Smith et al.2004; Debayle & Ricard 2013). One possible explanation is a decrease in the absolute strength of anisotropy in older seafloor, perhaps as a result of reheating or other alteration of the lithosphere that leads to a disruption in anisotropic fabric. However, some authors (e.g. Smith et al.2004) have proposed that variations in the strength of anisotropy with age may be due to the differences of anisotropy orientation in the lithosphere and asthenosphere at older ages. Figure 8. View largeDownload slide Median magnitude of Rayleigh wave 2ζ anisotropy in 10-Myr age bins at eight periods. Figure 8. View largeDownload slide Median magnitude of Rayleigh wave 2ζ anisotropy in 10-Myr age bins at eight periods. According to the simplest model of the formation of A-type olivine fabric anisotropy in oceanic lithosphere and asthenosphere, the orientation of anisotropy in the lithosphere should reflect the direction of mantle flow at the time the plate stopped deforming ductilely, while the orientation in the asthenosphere should reflect the orientation of recent mantle flow. For young seafloor in the Pacific, spreading direction and absolute plate motion tend to be aligned with one another, so it is also likely that the orientation of azimuthal anisotropy is similar between the lithosphere and asthenosphere. For older seafloor, palaeospreading and absolute-plate-motion directions are more likely to diverge, so the anisotropy orientation between lithosphere and asthenosphere may also be different. Because surface waves are sensitive to structure over a range of depths, they will be influenced by anisotropy in both the lithosphere and asthenosphere. For surface waves sampling regions of the mantle with layers of near-perpendicular anisotropy orientations, this could lead to weak surface-wave azimuthal anisotropy even if there is strong anisotropy at depth. However, we observe the same decrease in azimuthal anisotropy strength with age for seafloor where the palaeospreading and absolute-plate-motion directions are aligned. When we only consider seafloor where the palaeospreading and absolute-plate-motion directions differ by <20°, we find that the median strength for 75-s Rayleigh wave 2ζ anisotropy decreases from an average of |$1.0\hbox{ per cent}$| for 0–60 Ma seafloor to an average of |$0.4\hbox{ per cent}$| for 120–180 Ma seafloor. This suggests that the decrease in surface-wave anisotropy magnitude with seafloor age is not primarily due to large changes in anisotropy orientation with depth, but to a decrease in the absolute strength of anisotropy in older seafloor. We observe the largest azimuthal anisotropy at the shortest periods and the weakest azimuthal anisotropy at the longest periods, suggesting that azimuthal anisotropy is strongest in the shallow upper mantle and weaker at greater depths. 6.3 Comparison with absolute plate motion and palaeospreading directions In Figs 9 and 10, we compare the orientations of the Rayleigh wave 2ζ anisotropy fast axes to palaeospreading directions and absolute-plate-motion directions across the Pacific basin. We use absolute-plate-motion directions from NUVEL-1A, in a no-net-rotation reference frame (DeMets et al.1994). We have also compared our model to the absolute plate motions of HS3 (Gripp & Gordon 2002) and find similar results for both absolute-plate-motion models; here we present only the comparison with NUVEL-1A. Palaeospreading directions were estimated as the direction normal to magnetic isochrons. Although it is simpler to interpret comparisons with 3-D models, this leads to a significant increase in complexity due to the additional parametrization and regularization choices that are required when modelling 3-D anisotropic structure. Comparison between palaeospreading and absolute-plate-motion directions and our 2-D anisotropic phase-velocity models allows us to assess several aspects of the dynamics of the Pacific plate, with a minimum of a priori constraints on the model. Figure 9. View largeDownload slide Top row shows comparison between palaeospreading direction and the 2ζ Rayleigh wave anisotropy at (a) 25 s and (b) 125 s. Yellow bars show the palaeospreading direction and blue bars show the fast-axis azimuth from our preferred anisotropic model. Background shading shows the angular misfit between the two, where white indicates perfect alignment and black indicates that the directions are perpendicular. Bottom row shows comparison between absolute-plate-motion direction and the 2ζ Rayleigh wave anisotropy at (c) 25 s and (d) 125 s. Yellow bars show the absolute-plate-motion direction and blue bars show the fast-axis azimuth from our preferred anisotropic model. Figure 9. View largeDownload slide Top row shows comparison between palaeospreading direction and the 2ζ Rayleigh wave anisotropy at (a) 25 s and (b) 125 s. Yellow bars show the palaeospreading direction and blue bars show the fast-axis azimuth from our preferred anisotropic model. Background shading shows the angular misfit between the two, where white indicates perfect alignment and black indicates that the directions are perpendicular. Bottom row shows comparison between absolute-plate-motion direction and the 2ζ Rayleigh wave anisotropy at (c) 25 s and (d) 125 s. Yellow bars show the absolute-plate-motion direction and blue bars show the fast-axis azimuth from our preferred anisotropic model. Figure 10. View largeDownload slide Median angular misfit in 10-Myr age bins between the fast azimuth of 2ζ Rayleigh wave anisotropy and (a) the palaeospreading direction (PS) and (b) the absolute-plate-motion direction (APM) at eight periods. Figure 10. View largeDownload slide Median angular misfit in 10-Myr age bins between the fast azimuth of 2ζ Rayleigh wave anisotropy and (a) the palaeospreading direction (PS) and (b) the absolute-plate-motion direction (APM) at eight periods. Fig. 9 shows a comparison for Rayleigh waves at 25 and 125 s. We observe significant angular misfit between the modelled anisotropy fast axis and both the palaeospreading and absolute-plate-motion directions at every period. However, some patterns are visible. For shorter periods, which are sensitive to shallow structure, we find a region in the northeast Pacific within which the anisotropy is very well aligned with palaeospreading direction but not aligned with absolute plate motion. This is consistent with the short-period waves being sensitive to the frozen-in alignment of olivine crystals within the oceanic lithosphere. The best overall agreement occurs between long-period anisotropy fast-axis orientation and absolute plate motion, with large areas of the Pacific basin showing relatively good agreement between the two directions. This is consistent with longer-period waves having greater sensitivity to anisotropy within the asthenosphere that is being formed by present-day shear between the oceanic plate and underlying mantle. These observations are also consistent with the results of Smith et al. (2004), who compared the azimuthal anisotropy of Rayleigh wave group velocity across the Pacific with plate motion and fossil spreading directions. The overall patterns also are similar to those of several recent 3-D models of azimuthal anisotropy (Debayle & Ricard 2013; Burgos et al.2014; Schaeffer et al.2016), although at smaller scales there are significant differences between these models. Fig. 10 shows the median angular misfit between the Rayleigh wave 2ζ anisotropy fast axes and palaeospreading and absolute-plate-motion directions at several periods as a function of seafloor age. The lowest overall misfit with absolute-plate-motion directions occurs for long-period Rayleigh wave anisotropy directions (Fig. 10b). At 125 s, 36 per cent of the pixels have a misfit less than 15° and 75 per cent of the pixels have a misfit less than 40°, with an overall median angular misfit of 20°. At 200 s, the overall median angular misfit is 19°. At 250 s, however, the angular misfit with absolute-plate-motion directions is larger; the overall median angular misfit increases to 32° and only 24 per cent and 61 per cent of pixels have misfits less than 15° and 40°, respectively. At 25 s, only 19 per cent and 55 per cent of pixels have misfits less than 15° and 40°, respectively, and the overall median angular misfit is 36°. The larger angular misfit for short periods indicates that the shallower structure aligns less well with absolute plate motion. The increase in misfit at 250 s may be explained by a greater depth of peak sensitivity; if the region of alignment with absolute-plate-motion direction is confined to the asthenosphere below the base of the plate (e.g. Debayle & Ricard 2013; Becker et al.2014; Debayle et al.2016), surface waves with long enough periods may start to be sensitive to structure beneath this layer. Median angular misfit with absolute-plate-motion direction increases gradually with seafloor age until about 100 Ma, after which the misfit generally decreases. However, the number of pixels that fall within the oldest age bins is very small, so this result must be interpreted with caution. The angular misfit with palaeospreading direction depends on period less strongly; at 25 s, 35 per cent of pixels have misfits less than 15° and 75 per cent of pixels have misfits less than 40°. At 125 s, 37 per cent and 76 per cent of pixels have misfits less than 15° and 40°. The median angular misfit with palaeospreading direction also increases as a function of seafloor age; the youngest seafloor has anisotropy orientations that align most closely with spreading directions and the alignment is worst for the oldest seafloor. Uncertainties in estimated palaeospreading direction likely increase with seafloor age and the palaeospreading direction is more different from absolute plate motion for older seafloor, both of which are likely to influence the overall misfit with our observed seismic anisotropy. In a general sense, the misfit patterns we observe are consistent with formation of LPO anisotropy in the cooling oceanic plate and deforming asthenosphere. However, we observe significant regional differences between observed anisotropy and the orientation we expect based on the palaeospreading and absolute-plate-motion directions. In the western Pacific, the angular misfit tends to be much larger than the median value. Several factors likely contribute to the worse misfit in this location: the western Pacific has some of the oldest seafloor in the Pacific, so it has a longer history of potential alteration by reheating events and associated deformation. In addition, the orientation of the fast axis of anisotropy appears to change over shorter distances in the western Pacific compared with the eastern Pacific. It is difficult to resolve smaller-scale changes in fast-axis orientation because we are using relatively long-period surface waves with long paths and are damping towards smooth models. In the central part of the Pacific plate, there are large areas with a small but consistent offset of 10°–20° between the orientation of the anisotropy fast axis and the absolute-plate-motion direction. This result suggests that there may be shear in the asthenosphere with an orientation different from the absolute plate motion of the Pacific plate. Becker et al. (2014) suggested that additional mantle flow beneath the base of the plate was required to match observed anisotropy, and our models support that conclusion. Small-scale convection may also play a role in disrupting simple anisotropy patterns and leading to a misalignment between observed seismic anisotropy and absolute-plate-motion directions (Coltice et al.2017); this would lead to small-scale variations in anisotropy orientations that we do not observe, but that may exist at length scales shorter than our resolution limit. 7 CONCLUSIONS We present new anisotropic phase-velocity maps for Rayleigh and Love waves in the Pacific between 25 and 250 s. We find that our data require azimuthal anisotropy for Rayleigh waves but not for Love waves. Both Rayleigh and Love wave phase velocity have a strong dependence on seafloor age; phase velocity almost uniformly increases as a function of plate age and simple 1-D age-dependent models explain a significant fraction of our data variance reduction. However, exceptions to this previously observed strong age dependence include slow velocity anomalies for older seafloor in the western Pacific and low velocities in the region of the Pacific superswell and the Hawaiian hotspot. When binned in comparable age ranges, our modelled phase velocities are similar to the pure-path regionalization results of Nishimura & Forsyth (1985, 1988, 1989) except for the youngest seafloor ages. We find evidence for reheating of the lithosphere at older plate ages, but the phase velocities do not support a single reheating event at a particular time. We find that azimuthal anisotropy is strongest for short-period Rayleigh waves, and that anisotropy is weaker for older seafloor. This decrease in the strength of anisotropy occurs even for seafloor where palaeospreading and absolute-plate-motion directions agree, suggesting a decrease in the absolute strength of anisotropy with seafloor age. At long periods, the orientation of the anisotropy fast axis tends to agree with absolute plate motion. However, there are large areas where our observed anisotropy orientations do not agree with either palaeospreading or absolute-plate-motion directions, suggesting the presence of shear in the asthenosphere that is not aligned with the absolute-plate-motion direction. We find that modelling Rayleigh wave anisotropy leads to better agreement between phase velocities and age-dependent models consistent with half-space cooling. When we model both isotropic and anisotropic structure, our data do not require asymmetry across the East Pacific Rise at scales larger than ∼500 km. Further work to evaluate the age dependence of both the isotropic and anisotropic signals, the layered structure of the Pacific upper mantle, and the relation to possible reheating events and reorganization of mantle flow, requires 3-D modelling. 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TI - Age dependence and anisotropy of surface-wave phase velocities in the Pacific
JF - Geophysical Journal International
DO - 10.1093/gji/ggy438
DA - 2019-01-01
UR - https://www.deepdyve.com/lp/oxford-university-press/age-dependence-and-anisotropy-of-surface-wave-phase-velocities-in-the-bWEGVGMbBw
SP - 640
VL - 216
IS - 1
DP - DeepDyve
ER -