Search

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.

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.

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.

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 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.