https://earth.usc.edu/~becker/preprints/lb10.pdf

Mantle dynamics and seismic anisotropy

Measurements of the splitting or birefringence of seismic shear waves that have passed through the Earth’s mantle yield constraints on the strength and geometry of elastic anisotropy in various regions, including the upper mantle, the transition zone, and the D″ layer. In turn, information about the occurrence and character of seismic anisotropy allows us to make inferences about the style and geometry of mantle flow because anisotropy is a direct consequence of deformational processes. While shear wave splitting is an unambiguous indicator of anisotropy, the fact that it is typically a near-vertical path-integrated measurement means that splitting measurements generally lack depth resolution. Because shear wave splitting yields some of the most direct constraints we have on mantle flow, however, understanding how to make and interpret splitting measurements correctly and how to relate them properly to mantle flow is of paramount importance to the study of mantle dynamics. In this paper, we review the state of the art and recent developments in the measurement and interpretation of shear wave splitting—including new measurement methodologies and forward and inverse modeling techniques,—provide an overview of data sets from different tectonic settings, show how they help us relate mantle flow to surface tectonics, and discuss new directions that should help to advance the shear wave splitting field.

https://link.springer.com/content/pdf/10.1007%2Fs10712-009-9075-1.pdf

Shear Wave Splitting and Mantle Anisotropy: Measurements, Interpretations, and New Directions

Seismic anisotropy beneath stable continental interiors

Seismic tomography: a window into deep Earth

We present a review of the application of the spectral-element method to regional and global seismology. This technique is a high-order variational method that allows one to compute accurate synthetic seismograms in three-dimensional heterogeneous Earth models with deformed geometry. We first recall the strong and weak forms of the seismic wave equation with a particular emphasis set on fluid regions. We then discuss in detail how the conditions that hold on the boundaries, including coupling boundaries, are honored. We briefly outline the spectral-element discretization procedure and present the time-marching algorithm that makes use of the diagonal structure of the mass matrix. We show examples that illustrate the capabilities of the method and its interest in the context of the computation of three-dimensional synthetic seismograms.

Spectral Element Analysis in Seismology

SUMMARY

Shear wave splitting observations are often used to constrain upper-mantle anisotropy. However, their interpretation, which is still controversial, always implicitly relies on geometric ray theory. This high-frequency approximation does not take the finite frequency of the shear wavefield into account. In this paper, the effects of transverse isotropic perturbations of the elastic parameters on shear wave splitting are investigated. The theory, based on the first-order Born approximation, allows the derivation of 2-D and 3-D Frechet or sensitivity kernels for a new seismic observable called the splitting intensity. It is shown that the splitting intensity measured at the surface can be written to first order as a weighted average of two anisotropic perturbation parameters γc and γs related to the anisotropic parameter γ introduced by Mensch & Rasolofosaon. We also demonstrate, using a stationary-phase approximation, that the volume integral of the sensitivity kernels for a homogeneous transverse isotropic medium leads to the ray theoretical prediction for the splitting intensity. A numerical experiment on a two-block model demonstrates that lateral variations of anisotropy in the upper mantle introduce complicated and counterintuitive effects on shear wave splitting observed at the surface.

/pdf/sensitivity-kernels-for-shear-wave-splitting-in-transverse-351vn0auym.pdf

Sensitivity kernels for shear wave splitting in transverse isotropic media

Three dimensional sensitivity kernels for shear wave splitting in transverse isotropic media and their validation

SUMMARY Splitting intensity, a new seismic observable that characterizes seismic anisotropy, can be ex- pressed as linear combinations of elastic perturbations involving 3-D sensitivity (or Frechet) kernels. We conduct a numerical study of elastic wave propagation in weakly anisotropic het- erogeneous media in order to investigate the validity of the different assumptions made in the derivation of these kernels. For characteristic periods larger than 6 s, the splitting parame- ters obtained from the analysis of synthetic seismograms calculated using a spectral-element method (SEM) are in excellent agreement with predictions based upon the 3-D kernels. This suggests that the kernels fully capture the complexity of shear wave splitting in heterogeneous anisotropic media and can be used for tomography. In addition, they can be used to calculate synthetic splitting parameters in 3-D anisotropic media, which represents a very small amount of computation compared with finite-difference or finite-element modelling. 3-D kernels dis- tribute sensitivity off of the reference ray given by the laws of geometrical optics. This has important consequences for the interpretation of apparent splitting parameters, which usually relies on ray theory. Apparent splitting parameters estimated at the surface can differ signif- icantly from the anisotropic properties in the underlying medium wherever heterogeneities occur with a characteristic wavelength smaller than approximately 0.75 times the width of the first Fresnel zone √ λz, with λ the wavelength and z the depth.

/pdf/shear-wave-splitting-in-three-dimensional-anisotropic-media-4qpsaugl04.pdf

Shear wave splitting in three-dimensional anisotropic media

SUMMARY

In the last few years, Frechet (or sensitivity) kernels for seismic traveltimes have become important tools for mantle tomography. Sensitivity kernels for splitting intensity have been introduced recently for a better interpretation of shear wave splitting measurements. All ray-based sensitivity kernels studies relied so far on a far-field approximation of the Green's tensor. Under this approximation, the sensitivity kernels for splitting intensity do not accurately describe shear wave splitting at shallow depth. Here, we investigate the influence of near-field terms of the Green's tensor on the sensitivity kernels for both splitting intensity and traveltimes. Using the Born approximation, we derive analytical expressions for the complete sensitivity kernels. In contrast to the kernels obtained from the far-field Green's tensor, the sensitivity kernels based upon the complete Green's tensor are no longer zero on the ray path and show a complicated structure near the receiver. The results show that the near-field terms are needed to get accurate kernels at shallow depth. Using the complete Green's tensor, we define the normalized depth interval where near-field terms are important.

/pdf/near-field-influence-on-shear-wave-splitting-and-traveltime-2qe94fgpi0.pdf

Noémie Favier

Papers

Sensitivity kernels for shear wave splitting in transverse isotropic media

Three dimensional sensitivity kernels for shear wave splitting in transverse isotropic media and their validation

Shear wave splitting in three-dimensional anisotropic media

Near-field influence on shear wave splitting and traveltime sensitivity kernels