Kinematic inversion of seismic waves in an arbitrary anisotropic background medium

Abstract

Traditional kinematic inversion of seismic body waves in anisotropic media uses the "weak anisotropy" assumption and the eigenvectors of the Christoffel equation. This gives rise to a linearised inversion approach which may encounter a singularity problem with the two quasi-shear waves. This paper presents a new iterative, nonlinear kinematic inversion scheme, which does not make such an assumption, and avoids the singularity problem. It is applicable to arbitrary media, specifically those having dipping symmetry axes, a strong anisotropic background (or reference medium), and heterogeneous structure. For the forward modelling, we describe an anisotropic model with the gridded values of the five independent elastic moduli and the orientation angle of the symmetry axis, and apply a robust ray tracing method to compute the raypaths and traveltimes for all three wave modes (qP, qS1, qS2). For the inversion, we develop a simple analytic method to approximate the Jacobian matrix without the eigenvectors and perform an iterative nonlinear inversion to reconstruct all of the elastic moduli for imaging the subsurface. Using the new scheme, we have conducted several 2D synthetic imaging experiments for VSP, cross-hole and full illumination recording geometries. This involved determination of the distribution of elastic moduli from traveltime data for each of the three wave modes (qP, qSV, qSH). From these experiments, one can see the superiority of the new scheme and the capability of crosshole seismic anisotropic tomographic imaging. The differences in quality of each elastic moduli image are due to the limitations of the raypath coverage and the differing sensitivities of the various wave mode data.