Some Newer Algorithms in Joint Categorical and Continuous Inversion Problems around Seismic Data

To the statistically minded, the subsurface presents a complex, spatially correlated ”mixture” distribution of rock properties to our remote sensing tools, where the mixture originates from different rock types. The information we collect from seismic, EM and production data is often dominated by the geometrical boundaries separating lithologies in the subsurface, yet many standard geophysical inversion tools use purely continuous optimization techniques that model rock properties as if they come from some common population. Newer hierarchical Bayesian approaches that embed a discrete aspect via discrete Markov random fields, coupled with conditional prior distributions that embed rock–physics relationships, offer a more convincing way to represent the categorical aspects of geology. Some published studies on these models, using seismic data, indicate the posterior distribution can be modestly sharp, though the sampling MCMC algorithms are naturally challenging. This renews interest in the maximum aposteriori model, and this talk focuses on some of the newer algorithms for seeking maximum aposteriori models in joint discrete/continuous problems. In particular, recent algorithmic work in computer vision and graph cutting techniques has made these MRF-based estimation problems much more computationally feasible. We discuss some of these ideas in the context of joint lithology/elastic inversion.