Three-dimensional non-stationary and non-linear isotropic AVA inversion

Abstract

Inversion of seismic data to elastic parameters is a known problem in the geophysics literature. We focus on the situation with a Gaussian <it>a priori</it> model for the elastic parameters, assuming isotropic medium. The model incorporates spatial dependence in inline–crossline and traveltime dimensions. Previous attempts at solving this problem in high dimension has largely involved linear models with stationary structure. In this paper we study inversion methods using a non-linear, quadratic approximation for the reflectivity model. The methods incorporate non-stationary prior and likelihood error models. In particular, we compare results for the linear and quadratic model without and with the stationary assumption. The computational routines required for the non-linear inversion scheme are based on ideas from numerical linear algebra. These are thoroughly investigated here, in our context of seismic amplitude versus angle inversion, defining starting positions that avoid unphysical optima and pre-conditioners required for large scale inversion. A parameter sweep over different noise level reveals where it may be advantageous to use a non-linear inversion.