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

A Bayesian seismic amplitude versus offset (AVO) inversion scheme with a laterally coupled prior model for porosity, water saturation, and volume of clay is proposed. A 2-D section and a 3-D volume of an oil reservoir are studied. The oil reservoir is considered at the initial state, which entails gravitationally induced bimodality in the water saturations along vertical traces. A selection Gaussian random field (S-GRF) prior model, capable of representing this bimodality, is specified for porosity, water saturation, and volume of clay. The S-GRF is specified to have lateral correlation, which may reduce the impact of trace-unique signal errors in the seismic AVO data on the inversion results. The likelihood model is linear and Gaussian, for which the S-GRF prior model is conjugate; hence, the posterior model is also an S-GRF. The form of the posterior distribution is therefore known and its parameter values can be analytically computed. Real seismic AVO data from the 2-D section and the 3-D volume are inverted and the results appear to be reliable along validation wells and represent a geologically plausible reservoir design. Furthermore, a notable variance reduction in the laterally coupled posterior model relative to an alternative posterior model without lateral coupling is achieved