Bayesian seismic amplitude variation with offset inversion for reservoir variables with bimodal spatial histograms

Abstract

We consider seismic amplitude variation with offset (AVO) inversion for prediction of the reservoir properties porosity and water saturation. An oil reservoir at the initial state is studied; hence, gravitational effects dominate and keep hydrocarbons from mixing with water. Histograms of observations of water saturation along wells are consequently clearly bimodal, which is challenging to model. The seismic AVO inversion is cast into a Bayesian framework. The prior spatial model for porosity and water saturation is specified to be a selection Gaussian random field (S-GRF), which is capable of representing spatial variables with multimodal histograms. By using linear models for the seismic and rock-physics likelihoods, the posterior model is also an S-GRF. Hence, the Bayesian seismic inversion can be solved analytically, and the bimodal characteristics of water saturation can be reproduced. The methodology is defined and demonstrated on two synthetic cases inspired by real data from an oil reservoir, and thereafter applied to the real case. The well observations are fairly accurately reproduced and the inversion results are considered to be substantial improvements compared to standard spatial Gaussian models.