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We present the first observations of seismic waves propagating through the core of Mars. These observations, made using seismic data collected by the InSight geophysical mission, have allowed us to construct the first seismically constrained models for the elastic properties of Mars' core. We observe core-transiting seismic phase SKS from two farside seismic events detected on Mars and measure the travel times of SKS relative to mantle traversing body waves. SKS travels through the core as a compressional wave, providing information about bulk modulus and density. We perform probabilistic inversions using the core-sensitive relative travel times together with gross geophysical data and travel times from other, more proximal, seismic events to seek the equation of state parameters that best describe the liquid iron-alloy core. Our inversions provide constraints on the velocities in Mars' core and are used to develop the first seismically based estimates of its composition. We show that models informed by our SKS data favor a somewhat smaller (median core radius = 1,780 to 1,810 km) and denser (core density = 6.2 to 6.3 g/cm3) core compared to previous estimates, with a P-wave velocity of 4.9 to 5.0 km/s at the core-mantle boundary, with the composition and structure of the mantle as a dominant source of uncertainty. We infer from our models that Mars' core contains a median of 20 to 22 wt% light alloying elements when we consider sulfur, oxygen, carbon, and hydrogen. These data can be used to inform models of planetary accretion, composition, and evolution.

The most distant marsquake recorded so far by the InSight seismometer occurred at an epicentral distance of 146.3 ± 6.9o, close to the western end of Valles Marineris. On the seismogram of this event, we have identified seismic wave precursors, i.e., underside reflections off a subsurface discontinuity halfway between the marsquake and the instrument, which directly constrain the crustal structure away (about 4100-4500 km) from the InSight landing site. Here we show that the Martian crust at the bounce point between the lander and the marsquake is characterized by a discontinuity at about 20 km depth, similar to the second (deeper) intra-crustal interface seen beneath the InSight landing site. We propose that this 20-km interface, first discovered beneath the lander, is not a local geological structure but likely a regional or global feature, and is consistent with a transition from porous to non-porous Martian crustal materials.

Constraining the thermal and compositional state of the mantle is crucial for deciphering the formation and evolution of Mars. Mineral physics predicts that Mars' deep mantle is demarcated by a seismic discontinuity arising from the pressure-induced phase transformation of the mineral olivine to its higher-pressure polymorphs, making the depth of this boundary sensitive to both mantle temperature and composition. Here, we report on the seismic detection of a midmantle discontinuity using the data collected by NASA's InSight Mission to Mars that matches the expected depth and sharpness of the postolivine transition. In five teleseismic events, we observed triplicated P and S waves and constrained the depth of this discontinuity to be 1,006 [Formula: see text] 40 km by modeling the triplicated waveforms. From this depth range, we infer a mantle potential temperature of 1,605 [Formula: see text] 100 K, a result consistent with a crust that is 10 to 15 times more enriched in heat-producing elements than the underlying mantle. Our waveform fits to the data indicate a broad gradient across the boundary, implying that the Martian mantle is more enriched in iron compared to Earth. Through modeling of thermochemical evolution of Mars, we observe that only two out of the five proposed composition models are compatible with the observed boundary depth. Our geodynamic simulations suggest that the Martian mantle was relatively cold 4.5 Gyr ago (1,720 to 1,860 K) and are consistent with a present-day surface heat flow of 21 to 24 mW/m2.

Analyses of seismic data from the InSight mission have provided the first in situ constraints on the thickness of the crust of Mars. These crustal thickness constraints are currently limited to beneath the lander that is located in the northern lowlands, and we use gravity and topography data to construct global crustal thickness models that satisfy the seismic data. These models consider a range of possible mantle and core density profiles, a range of crustal densities, a low-density surface layer, and the possibility that the crustal density of the northern lowlands is greater than that of the southern highlands. Using the preferred InSight three-layer seismic model of the crust, the average crustal thickness of the planet is found to lie between 30 and 72 km. Depending on the choice of the upper mantle density, the maximum permissible density of the northern lowlands and southern highlands crust is constrained to be between 2,850 and 3,100 kg m−3. These crustal densities are lower than typical Martian basaltic materials and are consistent with a crust that is on average more felsic than the materials found at the surface. We argue that a substantial portion of the crust of Mars is a primary crust that formed during the initial differentiation of the planet. Various hypotheses for the origin of the observed intracrustal seisimic layers are assessed, with our preferred interpretation including thick volcanic deposits, ejecta from the Utopia basin, porosity closure, and differentiation products of a Borealis impact melt sheet.

Seismic anisotropy is now commonly studied on Earth and has been detected at various depths, from the crust to the top of the lower mantle, in the lowermost mantle, and in the inner core. In the mantle, observations of seismic anisotropy are often taken as an indication of past or present deformation resulting in the preferential orientation of anisotropic minerals. In the crust, it can come from stress-induced oriented cracks, compositional layering, or crystallographic preferred orientation of minerals. While many questions remain regarding the presence and interpretation of seismic anisotropy on Earth, scientists are now faced with new, exciting challenges in trying to constrain the structure of other planetary bodies. One of the goals of NASA’s InSight mission, which landed on Mars in November 2018 and includes a very broadband seismometer, is to constrain Mars interior structure. Compared to seismic studies of Earth, which benefit from the availability of a wealth of high quality data recorded on many seismic stations, difficulties with InSight stem from having only one seismic instrument and only a few high quality events. In this study, we analyzed the horizontally polarized (SH)-wave reflections generated from the shallowest crustal layer (layer 1) detected at 8 ± 2 km beneath the InSight lander site by a previous receiver function (RF) study. From Sol 105, when the first low-frequency marsquake was recorded, to Sol 1094, a total of 83 broadband and low-frequency events were detected, but only nine are rated as quality-A with constraints on both their epicentral distance and back azimuth. Of those nine events, we selected four that did not show any interference with mantle triplications generated by the olivine to the wadsleyite phase transition and that had a clear signal after the direct SH phase. A model space search approach enabled us to obtain a range of acceptable SH-wave velocities and layer thicknesses, which we then compared with the RF models of Knapmeyer-Endrun et al. (2021). We found that the acceptable SH-wave speeds are systematically lower than those from the RF study. Since this RF analysis is sensitive to vertically polarized (SV)-waves, we interpret this difference as the signature of radial anisotropy with an anisotropy coefficient ?=(???/???)2 between 0.7 and 0.9. Modeling of preferred alignment of inclusions shows that dry or fluid-filled cracks/fractures, and igneous inclusions can reproduce the observed radial anisotropy amplitude with VSV>VSH.

SUMMARY: The Earth's mantle transition zone (MTZ) plays a key role in the thermal and compositional interactions between the upper and lower mantle. Seismic anisotropy provides useful information about mantle deformation and dynamics across the MTZ. However, seismic anisotropy in the MTZ is difficult to constrain from surface wave or shear wave splitting measurements. Here, we investigate the sensitivity to anisotropy of a body wave method, SS precursors, through 3-D synthetic modelling and apply it to real data. Our study shows that the SS precursors can distinguish the anisotropy originating from three depths: shallow upper mantle (80–220 km), deep upper mantle above 410 km, and MTZ (410–660 km). Synthetic resolution tests indicate that SS precursors can resolve $\ge $3 per cent azimuthal anisotropy where data have an average signal-to-noise ratio (SNR = 7) and sufficient azimuthal coverage. To investigate regional sensitivity, we apply the stacking and inversion methods to two densely sampled areas: the Japan subduction zone and a central Pacific region around the Hawaiian hotspot. We find evidence for significant VS anisotropy (15.3 ± 9.2 per cent) with a trench-perpendicular fast direction (93° ± 5°) in the MTZ near the Japan subduction zone. We attribute the azimuthal anisotropy to the grain-scale shape-preferred orientation of basaltic materials induced by the shear deformation within the subducting slab beneath NE China. In the central Pacific study region, there is a non-detection of MTZ anisotropy, although modelling suggests the data coverage should allow us to resolve at least 3 per cent anisotropy. Therefore, the Hawaiian mantle plume has not produced detectable azimuthal anisotropy in the MTZ.

SUMMARY: We investigated the likelihood of radial anisotropy in the shallow and deep upper mantle, including the mantle transition zone (MTZ) under the Indian Ocean. Seismic anisotropy can be an indicator of mantle deformation through lattice preferred orientation of anisotropic crystals in the mantle. It has thus the potential to illuminate Earth’s dynamic interior, but previous seismic tomography studies have not achieved consensus on the existence of radial anisotropy below ∼250 km depth. We developed a fully nonlinear transdimensional hierarchical Bayesian Markov Chain Monte Carlo approach to invert fundamental and higher mode surface wave dispersion data and applied it to a subset of a global Love and Rayleigh wave data set. We obtained posterior model parameter distributions for shear wave velocity (VS) and radial anisotropy ξ under the Indian Ocean. These posterior model distributions were used to calculate the probability of having radial anisotropy at different depths. We demonstrated that separate inversions of Love and Rayleigh waves yield models compatible with the results of joint inversions within uncertainties. The obtained pattern of VS anomalies agrees with most previous studies. They display negative anomalies along ridges in the uppermost mantle, but those are stronger than for regularized inversions. The Central Indian Ridge and the Southeastern Indian Ridge present velocity anomalies that extend to ∼200 km depth, whereas the Southwestern Indian Ridge seems to have a shallower origin. Weaker, laterally variable velocity perturbations were found at larger depths. The anisotropy models differ more strongly from regularized inversion results and their uncertainties were rather large. We found that anisotropy models from regularized inversions also depend on the chosen parametrization, which is consistent with the existence of a large model null-space. Apart from a fast horizontally polarized shear wave signal in the top 100 km, likely reflecting the horizontal plate motion due to asthenospheric deformation, no clear relation to surface geology was detected in the anisotropy models. We found that, although the anisotropy model uncertainties are rather large, and lateral variations are present, the data generally prefer at least 1 per cent anisotropy in the MTZ with fast vertically polarized shear waves, within errors. Incorporating group velocity data did not help better constrain deep structure by reducing parameter trade-offs. We also tested the effect of prior constraints on the 410- and 660-km topography and found that the undulations of these discontinuities had little effect on the resulting models in our study region.

SEIS, the seismometer of the InSight mission, which landed on Mars on 26 November 2018, is monitoring the seismic activity of the planet. The goal of the Mars Structure Service (MSS) is to provide, as a mission product, the first average 1-D velocity model of Mars from the recorded InSight data. Prior to the mission, methodologies have been developed and tested to allow the location of the seismic events and estimation of the radial structure, using surface waves and body waves arrival times, and receiver functions. The paper describes these validation tests and compares the performance of the different algorithms to constrain the velocity model below the InSight station and estimate the 1-D average model over the great circle path between source and receiver. These tests were performed in the frame of a blind test, during which synthetic data were inverted. In order to propagate the data uncertainties on the output model distribution, Bayesian inversion techniques are mainly used. The limitations and strengths of the methods are assessed. The results show the potential of the MSS approach to retrieve the structure of the crust and underlying mantle. However, at this time, large quakes with clear surface waves have not yet been recorded by SEIS, which makes the estimation of the 1-D average seismic velocity model challenging. Additional locatable events, especially at large epicentral distances, and development of new techniques to fully investigate the data, will ultimately provide more constraints on the crust and mantle of Mars.

It is strongly debated whether the interface between the lithosphere and underlying as- thenosphere is a temperature-dependent rheological transition, as expected in a thermal convection system, or additionally affected by the presence of melts and/or fluids. Pre- vious surface wave studies of Pacific oceanic lithosphere have found that shear velocity and azimuthal anisotropy vary with seafloor crustal age as expected for a thermal control; however radial anisotropy does not. Various thermo-mechanical models have been pro- posed to explain this disparate behaviour. Nonetheless, it is unclear how robust the surface wave constraints are, and this is what we test in this study. We apply a Bayesian model space search approach to three published Pacific surface-wave dispersion datasets, two phase-velocity and one combined phase- and group-velocity set, and determine various proxies for the depth of the lithosphere-asthenosphere boundary (LAB) and their uncer- tainties based on the velocity and radial anisotropy model distributions obtained. In their overall character and pattern with age, the velocity models from different datasets are consistent with each other, although they differ in their values of LAB depths. Uncertainties are substantial (as much as 20 km on LAB depths) and the addition of group-velocity data does not reduce them. Radial anisotropy structures differ even in pattern and display no obvious age dependence. However, given the uncertainties, we cannot exclude that radial anisotropy, azimuthal anisotropy, and velocity models actually reflect compatible, age-dependent, LAB depth estimates. The velocity LAB trends are most like those ex- pected for half-space cooling, because velocity differences persist at old ages, below the depth of common plate cooling models. Any direct signature of sub-ridge melt would be too small-scale to be resolved by these data. However, the velocity-increasing effects of dehydration and depletion due to melting below the ridge could explain why LAB proxy depths tend to a minimum of ∼60 km below young ocean floor.

We present a new mantle model (YB14SHani) of azimuthal anisotropy for horizontally polarized shear waves (SH) in parallel with our previously published vertically polarized shear wave (SV) anisotropy model (YB13SVani). YB14SHani was obtained from higher mode Love wave phase velocity maps with sensitivity to anisotropy down to ~1200 km depth. SH anisotropy is present down to the mantle transition zone (MTZ) with an average amplitude of ~2% in the upper 250 km and ~1% in the MTZ, consistent with YB13SVani. Changes in SV and SH anisotropy were found at the top of the MTZ where olivine transforms into wadsleyite, which might indicate that MTZ anisotropy is due to the lattice-preferred orientation of anisotropic material. Beneath oceanic plates, SV fast axes become subparallel to the absolute plate motion (APM) at a depth that marks the location of a thermally controlled lithosphere-asthenosphere boundary (LAB). In contrast, SH anisotropy does not systematically depend on ocean age. Moreover, while upper mantle SV anisotropy is anomalously high in the middle of the Pacific, as seen in radial anisotropy models, SH anisotropy amplitude remains close to the average for other oceans. Based on the depth at which SV fast axes and the APM direction begin to align, we also found that the average thickness of cratonic roots is ~ 250 km, consistent with Yuan and Romanowicz (2010) for North America. Here we add new constraints on the nature of the cratonic LAB and show that it is characterized by changes in both SV and SH anisotropy.

We develop a three-dimensional model of shear wave velocity and anisotropy for the Mexico subduction zone using Rayleigh wave phase velocity dispersion measurements. This region is characterized by both steep and flat subduction and a volcanic arc that appears to be oblique to the trench. We give a new interpretation of the volcanic arc obliqueness and the location of the Tzitzio gap in volcanism based on the subduction morphology. We employ the two-station method to measure Rayleigh phase velocity dispersion curves between periods of 16 s to 171 s. The results are then inverted to obtain azimuthally anisotropic phase velocity maps and to model 3-D variations in upper mantle velocity and anisotropy. Our maps reveal lateral variations in phase velocity at all periods, consistent with the presence of flat and steep subduction. We also find that the data are consistent with two layers of anisotropy beneath Mexico: a crustal layer, with the fast directions parallel to the North American absolute plate motion, and a deeper layer that includes the mantle lithosphere and the asthenosphere, with the fast direction interpreted in terms of toroidal mantle flow around the slab edges. Our combined azimuthal anisotropy and velocity model enables us to analyze the transition from flat to steep subduction and to determine whether the transition involves a tear resulting in a gap between segments or is a continuous deformation caused by a lithospheric flexure. Our anisotropy results favor a tear, which is also consistent with the geometry of the volcanic belt.

The boundary between the lithosphere and asthenosphere is associated with a plate-wide high seismic velocity “lid” overlying lowered velocities, consistent with thermal models. Seismic body waves also intermittently detect a sharp velocity reduction at similar depths, the Gutenberg (G) discontinuity, which cannot be explained by temperature alone. We compared an anisotropic tomography model with detections of the G to evaluate their context and relation to the lithosphere-asthenosphere boundary (LAB). We find that the G is primarily associated with vertical changes in azimuthal anisotropy and lies above a thermally controlled LAB, implying the two are not equivalent interfaces. The origin of the G is a result of frozen-in lithospheric structures, regional compositional variations of the mantle, or dynamically perturbed LAB.

We present fundamental-mode Rayleigh-wave azimuthally anisotropic phase velocity maps obtained for the Great Basin region at periods between 16 s and 102 s. These maps offer the first depth constraints on the origin of the semi-circular shear-wave splitting pattern observed in central Nevada, around a weak azimuthal anisotropy zone. A variety of explanations have been proposed to explain this signal, including an upwelling, toroidal mantle flow around a slab, lithospheric drip, and a megadetachment, but no consensus has been reached. Our phase velocity study helps constrain the three-dimensional anisotropic structure of the upper mantle in this region and contributes to a better understanding of the deformation mechanisms taking place beneath the western United States. The dispersion measurements were made using data from the USArray Transportable Array. At periods of 16 s and 18 s, which mostly sample the crust, we find a region of low anisotropy in central Nevada coinciding with locally reduced phase velocities, and surrounded by a semi-circular pattern of fast seismic directions. Away from central Nevada the fast directions are ∼ N–S in the eastern Great Basin, NW–SE in the Walker Lane region, and they transition from E–W to N–S in the northwestern Great Basin. Our short-period phase velocity maps, combined with recent crustal receiver function results, are consistent with the presence of a semi-circular anisotropy signal in the lithosphere in the vicinity of a locally thick crust. At longer periods (28–102 s), which sample the uppermost mantle, isotropic phase velocities are significantly reduced across the study region, and fast directions are more uniform with an ∼ E–W fast axis. The transition in phase velocities and anisotropy can be attributed to the lithosphere–asthenosphere boundary at depths of ∼ 60 km. We interpret the fast seismic directions observed at longer periods in terms of present-day asthenospheric flow-driven deformation, possibly related to a combination of Juan de Fuca slab rollback and eastward-driven mantle flow from the Pacific asthenosphere. Our results also provide context to regional SKS splitting observations. We find that our short-period phase velocity anisotropy can only explain ∼ 30% of the SKS splitting times, despite similar patterns in fast directions. This implies that the origin of the regional shear-wave splitting signal is complex and must also have a significant sublithospheric component.

The presence of radial anisotropy in the upper mantle, transition zone and top of the lower mantle is investigated by applying a model space search technique to Rayleigh and Love wave phase velocity models. Probability density functions are obtained independently for S-wave anisotropy, P-wave anisotropy, intermediate parameter η, Vp, Vs and density anomalies. The likelihoods for P-wave and S-wave anisotropy beneath continents cannot be explained by a dry olivine-rich upper mantle at depths larger than 220 km. Indeed, while shear-wave anisotropy tends to disappear below 220 km depth in continental areas, P-wave anisotropy is still present but its sign changes compared to the uppermost mantle. This could be due to an increase with depth of the amount of pyroxene relative to olivine in these regions, although the presence of water, partial melt or a change in the deformation mechanism cannot be ruled out as yet. A similar observation is made for old oceans, but not for young ones where VSH>VSV appears likely down to 670 km depth and VPH>VPV down to 400 km depth. The change of sign in P-wave anisotropy seems to be qualitatively correlated with the presence of the Lehmann discontinuity, generally observed beneath continents and some oceans but not beneath ridges. Parameter η shows a similar age-related depth pattern as shear-wave anisotropy in the uppermost mantle and it undergoes the same change of sign as P-wave anisotropy at 220 km depth. The ratio between dlnVs and dlnVp suggests that a chemical component is needed to explain the anomalies in most places at depths greater than 220 km. More tests are needed to infer the robustness of the results for density, but they do not affect the results for anisotropy.

Radial seismic anisotropy models are traditionally obtained using empirical constraints based on laboratory experiments and petrological considerations. We tested the hypothesis that such petrological constraints affect the uppermost mantle models of S wave anisotropy using a statistical approach. In addition, we were able to determine which model features are constrained by the data and which are dominated by the prior. We focused on large-scale models and found that the most likely models obtained in both cases are highly correlated. This demonstrates that for the best data-fitting solution, the geometry of uppermost mantle radial anisotropy is not strongly affected by prior petrological constraints. The amplitude of the anomalies, however, can change significantly: The best data-fitting model obtained without petrological constraints displays stronger amplitudes than the one obtained with prior. This could become an issue when quantitatively interpreting seismic anisotropy models, and thus emphasizes the importance of accurately accounting for parameter uncertainties and trade-offs, and of understanding whether the seismic data or the prior constraints the model. We showed that model uncertainties are strongly affected by the prior as the relative RMS uncertainties were reduced by a factor of 2. In addition, we showed that while the model distributions are not necessarily Gaussian a priori, imposing petrological constraints can force the distributions to be narrower and more Gaussian-like, as expected from inverse theory. Finally, we demonstrated that the age dependence of seismic wave velocities is robust and independent of prior constraints. A similar age signal exists for anisotropy, but with larger uncertainties without prior constraints.

The mantle transition zone is believed to play an important role in the thermochemical evolution of our planet and in its deep water cycle. Constraining mantle flow at these depths can help elucidate its nature and better understand mantle dynamics and the history of plate tectonics. Seismic anisotropy, i.e., the directional dependence of seismic wave velocity, provides us with the most direct constraints on mantle deformation. Its detection below ∼250km depth is challenging, and it is often assumed that the deep upper mantle is seismically isotropic due to a change in mantle deformation mechanism. Here, we present a global model of azimuthal anisotropy for the top 1000 km of the mantle. We used a dataset composed of fundamental and higher mode Rayleigh wave phase velocity maps, which provides resolution of azimuthal anisotropy to much greater depths than in previous studies. Our model unravels the presence of significant anisotropy in the transition zone, challenging common views of mantle deformation mechanisms, and reveals a striking correlation between changes in anisotropy amplitudes and in the fast direction of wave propagation where upper mantle phase transitions occur. The newly found relation between anisotropy changes and phase transformations gives new insight on the nature of the MTZ and suggests that the anisotropy originates from the lattice preferred orientation of anisotropic material. While the interpretation of our results in terms of mantle deformation is not straightforward due to many possible scenarios, possible explanations for our findings include recrystallization during phase transformations, or changes in the slip system across the MTZ boundaries, which in turn could be explained by changes in the water content of mantle material, consistent with the idea that the transition zone acts as a water filter.

Sambridges Neighborhood Algorithm was applied to normal mode and surface wave phase velocity data to determine the likelihood of radial anisotropy in mantle reference models. This full model space search technique provides probability density functions for each model parameter and therefore reliable estimates of resolution and uncertainty, without having to introduce unnecessary regularization on the model space. Our results for shear wave anisotropy (described by parameter ξ) show a fast decrease with depth with no significant deviation from Preliminary Reference Earth Model (PREM) at any depth. The data do not require strong deviations from PREM for P wave anisotropy either, except between 220 and 400 km depth and in the D″ layer. The intermediate parameter η might depart from PREM between 220 and 670 km depth. This implies a likely deeper P wave anisotropy and η anisotropy than S wave anisotropy. The sign change in the anisotropic parameters across the 670-km discontinuity found by other authors is not warranted by our data set, which is far more extensive than in previous studies. We found that density needs to be well resolved because we observe a high dependence of the results for P wave-related parameters on the presence or absence of density in the parameterization. S wave anisotropy and η are less affected by density. A well-resolved negative density anomaly was found in the uppermost mantle, and a density excess was observed in the transition zone and the lowermost mantle which might be a seismic signature of the recently identified postperovskite phase.

We determine the 3-D shear wave speed variations in the crust and upper mantle in the southeastern borderland of the Tibetan Plateau, SW China, with data from 25 temporary broad-band stations and one permanent station. Interstation Rayleigh wave (phase velocity) dispersion curves were obtained at periods from 10 to 50 s from empirical Greens function (EGF) derived from (ambient noise) interferometry and from 20 to 150 s from traditional two-station (TS) analysis. Here, we use these measurements to construct phase velocity maps (from 10 to 150 s, using the average interstation dispersion from the EGF and TS methods between 20 and 50 s) and estimate from them (with the Neighbourhood Algorithm) the 3-D wave speed variations and their uncertainty. The crust structure, parametrized in three layers, can be well resolved with a horizontal resolution about of 100 km or less. Because of the possible effect of mechanically weak layers on regional deformation, of particular interest is the existence and geometry of low (shear) velocity layers (LVLs). In some regions prominent LVLs occur in the middle crust, in others they may appear in the lower crust. In some cases the lateral transition of shear wave speed coincides with major fault zones. The spatial variation in strength and depth of crustal LVLs suggests that the 3-D geometry of weak layers is complex and that unhindered crustal flow over large regions may not occur. Consideration of such complexity may be the key to a better understanding of relative block motion and patterns of seismicity.

Traditionally P- and S-wave tomography has been based on the inversion of data that are sensitive to the desired Earth structure, and model covariance is estimated from imperfect resolution and data error propagation. This analysis ignores the usually large null-spaces, and hence the significant non-uniqueness of the solution encountered in seismic tomography problems. Here we perform a model space search for P- and S-velocity structure to find acceptable fits to recent normal-mode splitting and fundamental-mode phase velocity data.The survey of the model space employs the neighbourhood algorithm of Sambridge, which preferentially samples the good data-fitting regions. A Bayesian approach is used subsequently to extract robust information from the ensemble of models.We particularly focus on posterior marginal probability density functions and covariances for the various model parameters. The covariance matrix obtained is very useful in providing insights into the trade-offs between the different variables and the uncertainties associated with them. We stay within the framework of perturbation theory, meaning that our emphasis is on the null-space of the linear inverse problem rather than the neglected non-linearity. The whole model space (including the nullspace) is sampled within reasonable parameter bounds, and hence the error bars are determined by all fitting models rather than subjective prior information. We estimated P and S models for spherical harmonic degree two only. The uncertainties are quite large and corresponding relative errors can exceed 100 per cent in the mid-mantle for Vp. We find a good correlation of our most likely S model with previous models but some small changes in amplitude. Our most likely P model differs quite strongly from the recent P model SB10L18 and the correlation between our most likely P and S models is small. Among all the good data-fitting models, there are, however, many that have a significant Vp −Vs correlation. We compute dlnVs/dlnVp from the models that correlate significantly.We find an increase with depth in the top 1500 km. Deeper in the mantle, normal-mode data prefer modest values compared with traveltime data.

We applied Sambridges Neighbourhood Algorithm (NA) to degree-8 fundamental mode Love and Rayleigh wave phase velocity maps between 40 and 150 s to find models of radial anisotropy in the upper 220 km of the mantle. The NA is a powerful tool to explore a multidimensional model space and retrieve an ensemble of models from which statistical inferences (posterior probability density functions (PPDFs) and trade-offs) can be made. We sought solutions for density anomalies and perturbations in the five elastic coefficients that describe transverse isotropy and obtained independent probability density functions for S-wave anisotropy, P-wave anisotropy, intermediate parameter η, Vp, Vs and density anomalies. We find robust departures from PREM in S-wave anisotropy (ξ) under cratons and oceans alike, with a clear change of sign in the anomalies with respect to the reference model at approximately 100 km depth. No significant difference is observed between cratons and oceans, both in the amplitude and depth variation of ξ. The signal within continents is clearly age related, with platforms and tectonically active regions characterized by a rapid decrease in ξ with depth, while cratons display a more constant signal. A similar age dependence in S-wave anisotropy is also observed beneath oceans: a strong and rapidly decreasing anisotropy for young oceans and a more constant anisotropy for older oceans. Perturbations in P-wave anisotropy (φ) are small and limited to the shallowest part of the continents. A small age-dependent signal for φ is observed beneath oceans. Anomalies in intermediate parameter η are similar to those in φ (but not globally correlated), but the deviation from PREM is stronger for η than for φ. Cratons appear to be devoid of any η anisotropy in the top 100 km. There is no obvious global correlation between deviations in φ and deviations in ξ, and the ratio between dη and dξ is clearly regionally variable, which cautions against the use of commonly used proportionality factors between these variables in inversions. In all regions, we found a good correlation between the equivalent isotropic P- and S-wave velocity anomalies, with a ratio d ln Vs/d ln Vp close to 1. Density anomalies were not sufficiently well resolved with fundamental mode data alone, but do not influence the results for anisotropy.

We investigate whether the coupling of normal mode (NM) multiplets can help us constrain mantle anisotropy.We first derive explicit expressions of the generalized structure coefficients of coupled modes in terms of elastic coefficients, including the Love parameters describing radial anisotropy and the parameters describing azimuthal anisotropy (Jc, Js, Kc, Ks, Mc, Ms, Bc, Bs, Gc, Gs, Ec, Es, Hc, Hs, Dc and Ds ). We detail the selection rules that describe which modes can couple together and which elastic parameters govern their coupling. We then focus on modes of type 0Sl − 0T l+1 and determine whether they can be used to constrain mantle anisotropy. We show that they are sensitive to six elastic parameters describing azimuthal anisotropy, in addition to the two shear-wave elastic parameters L and N (i.e. VSV and VSH ).We find that neither isotropic nor radially anisotropic mantle models can fully explain the observed degree two signal. We show that the NM signal that remains after correction for the effect of the crust and mantle radial anisotropy can be explained by the presence of azimuthal anisotropy in the upper mantle. Although the data favour locating azimuthal anisotropy below 400 km, its depth extent and distribution is still not well constrained by the data. Consideration of NM coupling can thus help constrain azimuthal anisotropy in the mantle, but joint analyses with surface-wave phase velocities is needed to reduce the parameter trade-offs and improve our constraints on the individual elastic parameters and the depth location of the azimuthal anisotropy

A technique for searching full model space that was applied to measurements of anomalously split normal modes showed a robust pattern of P-wave and S-wave anisotropy in the inner core. The parameter describing P-wave anisotropy changes sign around a radius of 400 kilometers, whereas S-wave anisotropy is small in the upper two-thirds of the inner core and becomes negative at greater depths. Our results agree with observed travel-time anomalies of rays traveling at epicentral distances varying from 150° to 180°. The models may be explained by progressively tilted hexagonal close-packed iron in the upper half of the inner core and could suggest a different iron phase in the center.

We present a new mantle model (YB14SHani) of azimuthal anisotropy for horizontally polarized shear waves (SH) in parallel with our previously published vertically polarized shear wave (SV) anisotropy model (YB13SVani). YB14SHani was obtained from higher mode Love wave phase velocity maps with sensitivity to anisotropy down to ∼1200 km depth. SH anisotropy is present down to the mantle transition zone (MTZ) with an average amplitude of ∼2% in the upper 250 km and ∼1% in the MTZ, consistent with YB13SVani. Changes in SV and SH anisotropy were found at the top of the MTZ where olivine transforms into wadsleyite, which might indicate that MTZ anisotropy is due to the lattice-preferred orientation of anisotropic material. Beneath oceanic plates, SV fast axes become subparallel to the absolute plate motion (APM) at a depth that marks the location of a thermally controlled lithosphere-asthenosphere boundary (LAB). In contrast, SH anisotropy does not systematically depend on ocean age. Moreover, while upper mantle SV anisotropy is anomalously high in the middle of the Pacific, as seen in radial anisotropy models, SH anisotropy amplitude remains close to the average for other oceans. Based on the depth at which SV fast axes and the APM direction begin to align, we also found that the average thickness of cratonic roots is ∼ 250 km, consistent with Yuan and Romanowicz (2010) for North America. Here we add new constraints on the nature of the cratonic LAB and show that it is characterized by changes in both SV and SH anisotropy. ©2014. American Geophysical Union. All Rights Reserved.

The boundary between the lithosphere and asthenosphere is associated with a platewide high-seismic velocity "lid" overlying lowered velocities, consistent with thermal models. Seismic body waves also intermittently detect a sharp velocity reduction at similar depths, the Gutenberg (G) discontinuity, which cannot be explained by temperature alone. We compared an anisotropic tomography model with detections of the G to evaluate their context and relation to the lithosphere-asthenosphere boundary (LAB). We find that the G is primarily associated with vertical changes in azimuthal anisotropy and lies above a thermally controlled LAB, implying that the two are not equivalent interfaces. The origin of the G is a result of frozen-in lithospheric structures, regional compositional variations of the mantle, or dynamically perturbed LAB.

The mantle transition zone is believed to play an important role in the thermochemical evolution of our planet and in its deep water cycle. Constraining mantle flow at these depths can help elucidate its nature and better understand mantle dynamics and the history of plate tectonics. Seismic anisotropy, i.e., the directional dependence of seismic wave velocity, provides us with the most direct constraints on mantle deformation. Its detection below ~250 km depth is challenging, and it is often assumed that the deep upper mantle is seismically isotropic due to a change in mantle deformation mechanism. Here, we present a global model of azimuthal anisotropy for the top 1000. km of the mantle. We used a dataset composed of fundamental and higher mode Rayleigh wave phase velocity maps, which provides resolution of azimuthal anisotropy to much greater depths than in previous studies. Our model unravels the presence of significant anisotropy in the transition zone, challenging common views of mantle deformation mechanisms, and reveals a striking correlation between changes in anisotropy amplitudes and in the fast direction of wave propagation where upper mantle phase transitions occur. The newly found relation between anisotropy changes and phase transformations gives new insight on the nature of the MTZ and suggests that the anisotropy originates from the lattice preferred orientation of anisotropic material. While the interpretation of our results in terms of mantle deformation is not straightforward due to many possible scenarios, possible explanations for our findings include recrystallization during phase transformations, or changes in the slip system across the MTZ boundaries, which in turn could be explained by changes in the water content of mantle material, consistent with the idea that the transition zone acts as a water filter. © 2013.

We present fundamental-mode Rayleigh-wave azimuthally anisotropic phase velocity maps obtained for the Great Basin region at periods between 16 s and 102 s. These maps offer the first depth constraints on the origin of the semi-circular shear-wave splitting pattern observed in central Nevada, around a weak azimuthal anisotropy zone. A variety of explanations have been proposed to explain this signal, including an upwelling, toroidal mantle flow around a slab, lithospheric drip, and a megadetachment, but no consensus has been reached. Our phase velocity study helps constrain the three-dimensional anisotropic structure of the upper mantle in this region and contributes to a better understanding of the deformation mechanisms taking place beneath the western United States. The dispersion measurements were made using data from the USArray Transportable Array. At periods of 16 s and 18 s, which mostly sample the crust, we find a region of low anisotropy in central Nevada coinciding with locally reduced phase velocities, and surrounded by a semi-circular pattern of fast seismic directions. Away from central Nevada the fast directions are ∼ N-S in the eastern Great Basin, NW-SE in the Walker Lane region, and they transition from E-W to N-S in the northwestern Great Basin. Our short-period phase velocity maps, combined with recent crustal receiver function results, are consistent with the presence of a semi-circular anisotropy signal in the lithosphere in the vicinity of a locally thick crust. At longer periods (28-102 s), which sample the uppermost mantle, isotropic phase velocities are significantly reduced across the study region, and fast directions are more uniform with an ∼ E-W fast axis. The transition in phase velocities and anisotropy can be attributed to the lithosphere-asthenosphere boundary at depths of ∼ 60 km. We interpret the fast seismic directions observed at longer periods in terms of present-day asthenospheric flow-driven deformation, possibly related to a combination of Juan de Fuca slab rollback and eastward-driven mantle flow from the Pacific asthenosphere. Our results also provide context to regional SKS splitting observations. We find that our short-period phase velocity anisotropy can only explain ∼ 30% of the SKS splitting times, despite similar patterns in fast directions. This implies that the origin of the regional shear-wave splitting signal is complex and must also have a significant sublithospheric component. © 2009 Elsevier B.V. All rights reserved.

We investigate whether the coupling of normal mode (NM) multiplets can help us constrain mantle anisotropy. We first derive explicit expressions of the generalized structure coefficients of coupled modes in terms of elastic coefficients, including the Love parameters describing radial anisotropy and the parameters describing azimuthal anisotropy (Jc, Js, Kc, Ks, Mc, Ms, Bc, Bs, Gc, Gs, Ec, Es, Hc, Hs, Dc and Ds). We detail the selection rules that describe which modes can couple together and which elastic parameters govern their coupling. We then focus on modes of type 0Sl-0Tl+1 and determine whether they can be used to constrain mantle anisotropy. We show that they are sensitive to six elastic parameters describing azimuthal anisotropy, in addition to the two shear-wave elastic parameters L and N (i.e. VSV and VSH). We find that neither isotropic nor radially anisotropic mantle models can fully explain the observed degree two signal. We show that the NM signal that remains after correction for the effect of the crust and mantle radial anisotropy can be explained by the presence of azimuthal anisotropy in the upper mantle. Although the data favour locating azimuthal anisotropy below 400km, its depth extent and distribution is still not well constrained by the data. Consideration of NM coupling can thus help constrain azimuthal anisotropy in the mantle, but joint analyses with surface-wave phase velocities is needed to reduce the parameter trade-offs and improve our constraints on the individual elastic parameters and the depth location of the azimuthal anisotropy. © 2008 The Authors Journal compilation © 2008 RAS.

We determine the 3-D shear wave speed variations in the crust and upper mantle in the southeastern borderland of the Tibetan Plateau, SW China, with data from 25 temporary broad-band stations and one permanent station. Interstation Rayleigh wave (phase velocity) dispersion curves were obtained at periods from 10 to 50 s from empirical Green's function (EGF) derived from (ambient noise) interferometry and from 20 to 150 s from traditional two-station (TS) analysis. Here, we use these measurements to construct phase velocity maps (from 10 to 150 s, using the average interstation dispersion from the EGF and TS methods between 20 and 50 s) and estimate from them (with the Neighbourhood Algorithm) the 3-D wave speed variations and their uncertainty. The crust structure, parametrized in three layers, can be well resolved with a horizontal resolution about of 100 km or less. Because of the possible effect of mechanically weak layers on regional deformation, of particular interest is the existence and geometry of low (shear) velocity layers (LVLs). In some regions prominent LVLs occur in the middle crust, in others they may appear in the lower crust. In some cases the lateral transition of shear wave speed coincides with major fault zones. The spatial variation in strength and depth of crustal LVLs suggests that the 3-D geometry of weak layers is complex and that unhindered crustal flow over large regions may not occur. Consideration of such complexity may be the key to a better understanding of relative block motion and patterns of seismicity. © Journal compilation © 2008 RAS.

We applied Sambridge's Neighbourhood Algorithm (NA) to degree-8 fundamental mode Love and Rayleigh wave phase velocity maps between 40 and 150 s to find models of radial anisotropy in the upper 220 km of the mantle. The NA is a powerful tool to explore a multidimensional model space and retrieve an ensemble of models from which statistical inferences (posterior probability density functions (PPDFs) and trade-offs) can be made. We sought solutions for density anomalies and perturbations in the five elastic coefficients that describe transverse isotropy and obtained independent probability density functions for S-wave anisotropy, P-wave anisotropy, intermediate parameter η, Vp, Vs and density anomalies. We find robust departures from PREM in S-wave anisotropy (ξ) under cratons and oceans alike, with a clear change of sign in the anomalies with respect to the reference model at approximately 100 km depth. No significant difference is observed between cratons and oceans, both in the amplitude and depth variation of ξ. The signal within continents is clearly age related, with platforms and tectonically active regions characterized by a rapid decrease in ξ with depth, while cratons display a more constant signal. A similar age dependence in S-wave anisotropy is also observed beneath oceans: a strong and rapidly decreasing anisotropy for young oceans and a more constant anisotropy for older oceans. Perturbations in P-wave anisotropy (φ) are small and limited to the shallowest part of the continents. A small age-dependent signal for φ is observed beneath oceans. Anomalies in intermediate parameter η are similar to those in φ (but not globally correlated), but the deviation from PREM is stronger for η than for φ. Cratons appear to be devoid of any η anisotropy in the top 100 km. There is no obvious global correlation between deviations in φ and deviations in ξ, and the ratio between dη and dξ is clearly regionally variable, which cautions against the use of commonly used proportionality factors between these variables in inversions. In all regions, we found a good correlation between the equivalent isotropic P- and S-wave velocity anomalies, with a ratio d In V s/d In Vp close to 1. Density anomalies were not sufficiently well resolved with fundamental mode data alone, but do not influence the results for anisotropy. © 2004 RAS.

The presence of radial anisotropy in the upper mantle, transition zone and top of the lower mantle is investigated by applying a model space search technique to Rayleigh and Love wave phase velocity models. Probability density functions are obtained independently for S-wave anisotropy, P-wave anisotropy, intermediate parameter η, Vp, Vs and density anomalies. The likelihoods for P-wave and S-wave anisotropy beneath continents cannot be explained by a dry olivine-rich upper mantle at depths larger than 220 km. Indeed, while shear-wave anisotropy tends to disappear below 220 km depth in continental areas, P-wave anisotropy is still present but its sign changes compared to the uppermost mantle. This could be due to an increase with depth of the amount of pyroxene relative to olivine in these regions, although the presence of water, partial melt or a change in the deformation mechanism cannot be ruled out as yet. A similar observation is made for old oceans, but not for young ones where VSH VSV appears likely down to 670 km depth and VPH VPV down to 400 km depth. The change of sign in P-wave anisotropy seems to be qualitatively correlated with the presence of the Lehmann discontinuity, generally observed beneath continents and some oceans but not beneath ridges. Parameter η shows a similar age-related depth pattern as shear-wave anisotropy in the uppermost mantle and it undergoes the same change of sign as P-wave anisotropy at 220 km depth. The ratio between dln Vs and dln Vp suggests that a chemical component is needed to explain the anomalies in most places at depths greater than 220 km. More tests are needed to infer the robustness of the results for density, but they do not affect the results for anisotropy. © 2003 Elsevier B.V. All rights reserved.

Traditionally P- and S-wave tomography has been based on the inversion of data that are sensitive to the desired Earth structure, and model covariance is estimated from imperfect resolution and data error propagation. This analysis ignores the usually large null-spaces, and hence the significant non-uniqueness of the solution encountered in seismic tomography problems. Here we perform a model space search for P- and S-velocity structure to find acceptable fits to recent normal-mode splitting and fundamental-mode phase velocity data. The survey of the model space employs the neighbourhood algorithm of Sambridge, which preferentially samples the good data-fitting regions. A Bayesian approach is used subsequently to extract robust information from the ensemble of models. We particularly focus on posterior marginal probability density functions and covariances for the various model parameters. The covariance matrix obtained is very useful in providing insights into the trade-offs between the different variables and the uncertainties associated with them. We stay within the framework of perturbation theory, meaning that our emphasis is on the null-space of the linear inverse problem rather than the neglected non-linearity. The whole model space (including the null-space) is sampled within reasonable parameter bounds, and hence the error bars are determined by all fitting models rather than subjective prior information. We estimated P and S models for spherical harmonic degree two only. The uncertainties are quite large and corresponding relative errors can exceed 100 per cent in the mid-mantle for Vp. We find a good correlation of our most likely S model with previous models but some small changes in amplitude. Our most likely P model differs quite strongly from the recent P model SB10L 18 and the correlation between our most likely P and S models is small. Among all the good data-fitting models, there are, however, many that have a significant Vp - Vs correlation. We compute d In Vs/d In Vp from the models that correlate significantly. We find an increase with depth in the top 1500 km. Deeper in the mantle, normal-mode data prefer modest values compared with traveltime data.