MSAT: a New Matlab Toolbox for the Analysis and Modelling of Seismic Anisotropy

Studies of seismic anisotropy rarely end with measurements of shear-wave splitting - instead an explanation of the physical origin of the anisotropy is sought in order to yield useful geological or geophysical information. We describe a new Matlab toolbox designed to aid the modelling needed for this interpretative step of the analysis of seismic anisotropy. Provision of key building blocks for modelling in this modern integrated development environment allows the rapid development and prototyping of explanations for measured anisotropy. The Matlab graphical environment also permits plotting of key anisotropic parameters. Furthermore, this work complements the SplitLab toolbox used for measuring shear wave splitting and the MTEX toolbox used for the analysis of textures in rocks. MSAT (the Matlab Seismic Anisotropy Toolbox) includes a wide range of functions which can be used to rapidly build models of seismic anisotropy. Available functions include: the determination of phase velocities as a function of wave propagation direction, the analysis of multi-layer splitting, a novel interpolation scheme for elastic constants tensors, the estimation of the anisotropy caused by the presence of aligned inclusions and the measurement of the degree of anisotropy exhibited by an elastic material. We include a database of elastic properties of rocks and minerals and functions to plot seismic anisotropy as a function of wave propagation direction in the form of pole figures or as three-dimensional plots. The toolbox includes extensive documentation and example applications which integrate with the Matlab documentation system alongside automated test cases for all functions. All code is open source and available freely to all. We encourage users to feed back any changes they may need to make. Key examples of the use of this software include: (1) Calculation of the pattern of backazimuthal variation of shear wave splitting caused by the interaction of two dipping layers of partially-aligned olivine. This shows the variation of splitting parameters with the strength of anisotropy and the dip and thickness of the anisotropic layers. (2) Analysis of the effect of the change in the elastic constants of clinopyroxenes with pressure as calculated using density functional theory. This shows that despite the overall anisotropy decreasing with increasing pressure, the measured shear wave splitting for particular wave propagation directions is expected to dramatically increase. (3) Calculation and simplification of the seismic anisotropy derived from polycrystalline modelling of texture development in the lowermost mantle. By combining MTEX with our toolbox we are able to take the output of visco-plastic self-consistent calculations, calculate the elastic anisotropy without imposing any particular symmetry, and estimate how well this can be explained as a layer exhibiting vertical transverse isotropy.