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 a priori model for the elastic parameters, assumingisotropic medium. The model incorporates spatial dependence in inline-crossline and traveltimedimensions. Previous attempts at solving this problem in high dimension has largelyinvolved linear models with stationary structure. In this paper we study inversion methodsusing a non-linear, quadratic approximation for the reflectivity model. The methods incorporatenon-stationary prior and likelihood error models. In particular, we compare results for thelinear and quadratic model without and with the stationary assumption. The computationalroutines required for the non-linear inversion scheme are based on ideas from numerical linearalgebra. These are thoroughly investigated here, in our context of seismic amplitude versusangle inversion, defining starting positions that avoid unphysical optima and pre-conditionersrequired for large scale inversion. A parameter sweep over different noise level reveals whereit may be advantageous to use a non-linear inversion.©The Authors 2013.