Finite-Frequency SKS Splitting: Measurement and Sensitivity Kernels

Abstract

Splitting of SKS waves caused by anisotropy may be analyzed by measuring the splitting intensity, i.e., the amplitude of the transverse signal relative to the radial signal in the SKS time window. This quantity is simply related to structural parameters. Extending the widely used cross-correlation method for measuring travel-time anomalies to anisotropic problems, we propose to measure the SKSsplitting intensity by a robust cross-correlation method that can be automated to build large high-quality datasets. For weak anisotropy, the SKS-splitting intensity is retrieved by cross-correlating the radial signal with the sum of the radial and transverse signals. The cross-correlation method is validated based upon a set of Californian seismograms. We investigate the sensitivity of the SKS-splitting intensity to general anisotropy in the mantle based upon a numerical technique (the adjoint spectralelement method) considering the full physics of wave propagation. The computations reveal a sensitivity remarkably focused on a small number of elastic parameters and on a small region of the upper mantle. These fundamental properties and the practical advantages of the measurement make the cross-correlation SKS-splitting intensity particularly well adapted for finite-frequency imaging of upper-mantle anisotropy.

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

“…Analytical expressions for finite-frequency sensitivity kernels for shear wave splitting intensity were developed by Favier and Chevrot (2003) and Favier et al (2004), and these studies provided the first theoretical framework for considering full finite-frequency effects on shear wave splitting measurements. Subsequent studies have explored various aspects of incorporating finite-frequency sensitivity kernels into a tomographic framework (Chevrot 2006;) and on numerically calculating sensitivity kernels using an adjoint approach (Sieminski et al 2008) or in realistic, heterogeneous starting models .…”

“…From a measurement point of view, the splitting intensity is a more robust measurement (Chevrot 2000) that is less affected by subjective choices on the part of the analyst such as filtering or windowing (Long and van der Hilst 2005b) and also deals better with waveforms that exhibit null or near-null splitting. Finally, the splitting intensity is commutative, unlike the so-called splitting operator (Silver and Chan 1991;Silver and Savage 1994), which means that it can be summed along a ray (or throughout a sensitivity kernel volume) and can be treated similarly to a traveltime delay in traditional wavespeed tomography, as it can be linearly related to anisotropic perturbations at depth (Chevrot 2006;Sieminski et al 2008).…”

“…Splitting intensity sensitivity kernels are obtained by solving the partial differential equations (PDEs) that govern wave-equation splitting tomography; the kernel expressions can then be evaluated approximately (using single-scattering Born theory) either analytically (Chevrot 2006) or numerically , in some cases by utilizing adjoint computations (Sieminski et al 2008). An example of 2-D splitting intensity sensitivity kernels for an SKS arrival for the parameterization used by is shown in Fig.…”

“…The analysis of shear wave splitting from a wave-equation point of view also allows for better depth resolution; as demonstrated by Chevrot (2006), even perfectly vertical SKS waves can be used for tomographic imaging if finite-frequency effects are taken into account, because SKS sensitivity kernels will overlap at depth if the station spacing is small enough. The theoretical development of finite-frequency sensitivity kernels for splitting intensity measurements has progressed a great deal, and includes work on accounting for near-surface effects , benchmarking sensitivity kernel computations against spectral element waveform simulations ), computing kernels using an adjoint formulation (Sieminski et al 2008) and with respect to background models that include realistic heterogeneity derived from geodynamical models , and incorporating sensitivity kernel computations into tomographic inversions (Chevrot 2006;Long et al 2007a; Fig. 8).…”

Theory and Observations - Seismic Anisotropy

“…The concept of 'splitting intensity' (Chevrot, 2000), which does not rely on resolving a fast axis and a delay time, but keeps these two elements unresolved into one parameter for each data or each set of data having similar polarizations, has proved to be a more robust measurement (Monteiller and Chevrot, 2010) that varies more linearly with the properties of the structure traversed by the waves. It can more easily be incorporated into tomographic studies that allow multiple layers, in particular using finitefrequency kernels (Chevrot, 2006;Sieminski et al, 2008), and combined with surface-wave data in case of lateral and vertical variation of the anisotropy (Romanowicz and Yuan, 2012;Silver and Long, 2011).…”