A new approach for conditioning process-based geologic models to well data

Abstract

Generating a realistic earth model that simultaneously fits data observed at multiple well locations has been a long-standing problem in petroleum geology. Two insights are offered for solving this problem in a Bayesian framework. The first is conceptual—it connects geologic inversion to the new field of probabilistic programming and shows that the usual description of a Bayesian problem in terms of a graphical model is inadequate for describing a process-based geologic model due to the dynamics of the generative algorithm. This is a paradigm shift in probabilistic modeling where stochastic generative models are represented using a syntax resembling modern programming languages. Probabilistic programming allows one to generalize this structure to include complex programming concepts, while also simplifying the process of developing new inference algorithms. The second insight is algorithmic and involves using variational inference to derive a simpler, more computationally tractable approximation to the posterior probability density function. If this surrogate distribution is close to the true posterior, it allows for very fast simulation of an arbitrary number of models that all fit the data equally well. This study focuses on the particular geologic formation known as submarine lobes: elongated pancake-like formations which are sequentially laid down, one on top of the other over geologic time, forming potential petroleum reservoirs. The location and orientation of the lobes at each time step are the variables that are optimized so that, at the final time step, all available well data are approximately fit. The methodology is illustrated on synthetic data as a proof-of-concept, and compared to several alternatives. An important conclusion is that, even though the variational approximation is crude, it produces better predictions than any point-based method, including maximum likelihood. The fact that probabilistic programming outperforms conventional Bayesian approaches in the case of lobe models offers the potential for attacking more complicated forward models where multiple geologic processes are simultaneously active.