Written by: Mark Sams of Ikon Science and James Gunning of CSIRO
Seismic reflection pre-stack angle gathers can be simultaneously inverted within a joint facies and elastic inversion framework using a hierarchical Bayesian model of elastic properties and categorical classes of rock and fluid properties. The Bayesian prior implicitly supplies low-frequency information via a set of multivariate compaction trends for each rock and fluid type, combined with a Markov random field model of lithotypes, which carries abundance and continuity preferences. For the likelihood, we use a simultaneous, multi-angle, convolutional model, which quantifies the data misfit probability using wavelets and noise levels inferred from well ties. Under Gaussian likelihood and facies-conditional prior models, the posterior has a simple analytic form, and the maximum a-posteriori inversion problem boils down to a joint categorical/continuous non-convex optimization problem. To solve this, a set of alternative, increasingly comprehensive optimization strategies are described: (i) an expectation-maximization algorithm using belief propagation, (ii) globalization of method (i) using homotopy, and (iii) a discrete space approach using simulated annealing.
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