Non-linear Bayesian inversion of seismic reflection amplitudes

Abstract

Seismic amplitudes can be used to assess subsurface information beyond a structural image through an amplitude-versus-angle (AVA) inversion. It is an application with challenging pre-processing and a difficult inversion due to an ill-posed forward model. In this thesis two inversion method tailored for AVA inversion are presented. They share a common basis in a hierarchical Bayesian model. Model parameters and noise priors are assumed multivariate, normally distributed with the important covariance matrices. Both methods handle non-linear forward models and have a built-in regularization. One algorithm uses sampling to explore the posterior distribution and hence the uncertainties. The other algorithm searches for only the maximum a posteriori solution. While the first method is very computer intensive, the second is a very fast algorithm. Both methods are tested on inversion of synthetic AVA data with only PP and joint PP and PS, in combination with both linear and nonlinear forward models. The last part of the thesis is AVA inversion of the top Utsira Sand reflector at the CO2 injection site, Sleipner, North Sea, Norway. Focus here is on three topics. First a detailed postmigration workflow for creating reflection amplitudes is presented. Key steps are extraction of amplitudes, offset-to-angle conversion and scaling to reflection amplitudes. It is followed by the inversion with both the inversion methods presented in this thesis. The forward models are linear and quadratic, but only PP data is available. The third and last point is a fluid substitution in order to verify the inversion results.