Equivalent Heterogeneity Analysis as a Tool for Understanding the Resolving Power of Anisotropic Travel‐Time Tomography

Abstract

Abstract We investigate whether 2D anisotropic travel‐time tomography can uniquely determine both the spatially varying isotropic and anisotropic components of the seismic velocity field. This issue was first studied by Mochizuki (1997) for the special case of Radon’s problem (tomography with infinitely long rays), who found it to be nonunique. Our analysis extends this result to all array geometries and demonstrates that all such tomographic inversions are nonunique. Any travel‐time dataset can be fit by a model that is either purely isotropic, purely anisotropic, or some combination of the two. However, a pair of purely isotropic and purely anisotropic velocity models that predict the same travel times are very different in other respects, including spatial scale. Thus, prior information can be used to select among equivalent solutions to achieve a unique solution embodying a given set of prior expectations about model properties. We extend the notion of a resolution test, used in traditional isotropic tomography, to the anisotropic case. Our equivalent heterogeneity analysis focuses on the anisotropic heterogeneity equivalent to a point isotropic heterogeneity, and vice versa. We demonstrate that it provides insights into the structure of an anisotropic tomography problem that facilitates both the selection of appropriate prior information and the interpretation of results. We recommend that it be routinely applied to all surface‐wave inversions where the presence of anisotropy is suspected, including those based on noise correlation.