Joint Facies and Anisotropy AVO/AVAZ Inversion Using the EM Algorithm

AVO/AVAZ inversion for fracture and anisotropy parameters is a very under-determined problem with general anisotropy representations. Inferences are vulnerable to missing low-frequency information, and anisotropy parameters often leak or smear across lithology boundaries. Significant leverage against this problem can be gained by inverting simultaneously for facies and elastic parameters, and associating facies with reduced-freedom anisotropy models like TTI or HTI. These reduced-dimensionality models have more comparable degrees of freedom (4 to 5) to those evident in joint AVO and AVAZ reflection amplitudes. Availability of facies variables enables jointly constraining to facies-specific multivariate depth-trends and reflectivity models.

We use a hierarchical Bayesian framework, where the elastic parameters in the prior are conditional on the facies variable, and the facies labels are modelled using a Markov random field. In the likelihood (data misfit), the facies labels couple to the anisotropic reflectivity model. This makes the inversion problem a mixed discrete/continuous optimisation problem. We use the Expectation-Maximisation algorithm, which requires alternating large-scale reweighted-least-squares optimisation for elastic parameters, and belief-propagation/message-passing for facies labels inference. Test cases in inverting for fracture angles in HTI media are encouraging.