Direct Probabilistic Inversion for Facies Using Zoeppritz Reflectivity Model

Probabilistic one-step (or direct) inversion methods are now being used frequently in the industry to infuse geophysical and geological spatial information into the inverse problem with the added benefit/complexity of solving for probabilities of the variables of interest. The inherent ambiguity of the inverse problem can be addressed by solving for probability density functions, and the Bayesian method is the natural framework for assimilating data, modelling and prior soft or hard knowledge/information. The approximate local likelihood method is a fast method that can solve direct probabilistic inversion problems taking spatial information accurately into account. The method is very flexible and has few limitations wrt spatial models and RP models which can be analytical or rule based models. However all applications so far has used the linear Aki-Richards reflectivity model which simplifies the problem. In the study we will use an extension of the method to solve the nonlinear Zoeppritz reflectivity model and apply it to a challenging AVO problem of coals where the Zoeppritz equation would be more appropriate since the small contrast assumption of the Aki-Richards equation no longer holds.