Events

Faculty candidate Dario Grana, Stanford University, will give a talk entitled "Bayesian inversion methods for reservoir properties estimation from seismic data" as part of the Claude R. Hocott Graduate Seminar Series.

Abstract: The construction of 3D reservoir models describing the spatial distribution of petrophysical and dynamic properties is an essential step in reservoir modeling and fluid flow simulation. Generally, the only available data to condition reservoir models far away from the wells are seismic data. Rock properties can be obtained from seismic data as a solution of an inverse problem combining rock physics and seismic modeling with inverse theory and geostatistics. Deterministic methods provide local minima of the solution of the inverse problem but do not allow to quantify uncertainty. On the other hand probabilistic approaches provide the full posterior distribution of the inverse problem. In my research I focus on Bayesian inversion methods for the estimation of reservoir properties. A common assumption in probabilistic approaches is the Gaussian distribution of the model, however reservoir properties are generally multimodal. The use of Gaussian mixture models allows us to describe the multimodal behavior of reservoir properties and preserve the analytical solution of the Bayesian inverse problem. In this talk, I am going to propose a method to estimate the posterior pdf of the reservoir properties, such as porosity, clay content and fluid saturations, using a full Bayesian approach. We first calculate the conditional probabilities of elastic properties conditioned by seismic data, we then estimate the rock physics likelihood function and we compute the posterior distribution of reservoir properties. Direct sampling from this distribution or sampling through Markov chain Monte Carlo methods can be quite difficult due to the necessity of including a spatial continuity model. I then propose a statistical methodology where we combine geostatistical methods and inverse problem theory to generate realizations of the posterior distribution of a linear inverse problem under Gaussian mixture assumptions. This is achieved using sequential Gaussian mixture simulation, a new geostatistical algorithm for generating samples of a Gaussian mixture random field including a spatial continuity model. A similar Bayesian method can then be used in time-lapse studies to estimate changes of dynamic properties, particularly pressure and saturation, from differences of time-lapse surveys.