A Bayesian Forward Simulation Approach to Establishing a Realistic Prior Model for Complex Geometrical Objects

Geology is a descriptive science making itself hard to provide quantification. We develop a Bayesian forward simulation approach to formulate a realistic prior model for geological images using the Approximate Bayesian computation (ABC) method. In other words, our approach aims to select a set of representative images from a larger list of complex geometrical objects and provide a probability distribution on it. This allows geologists to start contributing their perspectives to the specification of a realistic prior model. We examine the proposed ABC approach on an experimental Delta dataset and show that, on the basis of selected representative images, the nature of the variability of the Delta can be statistically reproduced by means of the IQSIM, a state-of-the-art multiple-point geostatistical (MPS) simulation algorithm. The results demonstrate that the proposed approach may have a broader spectrum of application. In addition, two different choices for the size of the prior, i.e., the number of representative images are compared and discussed.