Interpolation and Inversion – New Features in the Matlab Sesimic Anisotropy Toolbox

Abstract:

A key step in studies of seismic anisotropy in the mantle is often the creation of models designed to explain its physical origin. We previously released MSAT (the Matlab Seismic Anisotropy Toolbox), which includes a range of functions that can be used together to build these models and provide geological or geophysical insight given measurements of, for example, shear-wave splitting. Here we describe some of the new features of MSAT that will be included in a new release timed to coincide with the 2015 Fall Meeting.

A critical step in testing models of the origin of seismic anisotropy is the determination of the misfit between shear-wave splitting parameters predicted from a model and measured from seismic observations. Is a model that correctly reproduces the delay time "better" than a model that correctly reproduces the fast polarization? We have introduced several new methods that use both parameters to calculate the misfit in a meaningful way and these can be used as part of an inversion scheme in order to find a model that best matches measured shear wave splitting. Our preferred approach involves the creation, "splitting", and "unsplitting" of a test wavelet. A measure of the misfit is then provided by the normalized second eigenvalue of the covariance matrix of particle motion for the two wavelets in a way similar to that used to find splitting parameters from data. This can be used as part of an inverse scheme to find a model that can reproduce a set of shear-wave splitting observations.

A second challenge is the interpolation of elastic constants between two known points. Naive element-by-element interpolation can result in anomalous seismic velocities from the interpolated tensor. We introduce an interpolation technique involving both the orientation (defined in terms of the eigenvectors of the dilatational or Voigt stiffness tensor) and magnitude of the two end-member elastic tensors. This permits changes in symmetry between the end-members and removes anomalous intermediate velocity distributions.