Variational Bayesian Inversion of Seismic Attributes Jointly for Geological Facies and Petrophysical Rock Properties

Seismic attributes (derived quantities) such as P-wave and S-wave impedances and P-wave to S-wave velocity ratios may be used to classify subsurface volume of rock into geological facies (distinct lithology-fluid classes) using pattern recognition methods. Seismic attributes may also be used to estimate subsurface petrophysical rock properties such as porosity, mineral composition and pore-fluid saturations. Both of these estimation processes are conventionally carried out independent of each other and involve considerable uncertainties, which may be reduced significantly by a joint estimation process. We present an efficient probabilistic inversion method for joint estimation of geological facies and petrophysical rock properties. Seismic attributes and petrophysical properties are jointly modeled using a Gaussian mixture (GM) distribution whose parameters are initialized by unsupervised learning using well-log data. Rock physics models may be used in our method to augment the training data if the existing well data are limited, however this is not required if sufficient well data are available. The inverse problem is solved using the Bayesian paradigm that models uncertainties in the form of probability distributions. Probabilistic inference is performed using variational optimization which is a computationally efficient deterministic alternative to the commonly used sampling based stochastic inference methods. With the help of a real data application from the North Sea we show that our method is computationally efficient, honors expected spatial correlations of geological facies, allows reliable detection of convergence, and provides full probabilistic results without stochastic sampling of the posterior distribution.