Bayesian seismic AVO inversion for reservoir variables with bimodal spatial histograms
We consider seismic AVO inversion for prediction of the reservoir properties porosity and water saturation. An oil reservoir at 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 in a Bayesian framework. The prior spatial model for porosity and water saturation is specified to be a selection Gaussian random field, 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 a selection Gaussian random field. Hence, the Bayesian seismic inversion can be solved analytically and the bimodal characteristics of the water saturations can be reproduced. The methodology is defined and demonstrated on two synthetic cases inspired by real data from an oil reservoir. Compared to standard spatial Gaussian models, the improvement of the inversion results is substantial. Inversion of the real seismic AVO data along a well trace reproduces the corresponding well observations fairly precisely, and is considered very encouraging.