A comparison of seismic velocity inversion methods for layered acoustics

Abstract

In seismic imaging, one tries to infer the medium properties of the subsurface from seismic reflection data. These data are the result of an active source experiment, where an explosive source and an array of receivers are placed at the surface. Due to the absence of low frequencies in the data, the corresponding inverse problem is strongly non-linear in the slowly varying component of the velocity. The least-squares misfit functional typically exhibits local minima and has a small basin of attraction. The usual approach of fitting the data in a least-squares sense by employing a gradient-based optimisation method will therefore most likely result in a wrong velocity model. In the geophysical community, this problem has long been recognised and alternative formulations of the inverse problem have been developed. We review several of these formulations and analyse the sensitivity to the error in the smooth velocity component. This analysis is carried out for laterally homogeneous velocities using an asymptotic solution of the wave equation. The analysis suggests that formulations which are geared towards fitting the phases of the data, rather than the amplitudes, have smooth corresponding misfit functionals with a large basin of attraction.