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 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.

Parametric spatial covariance models in the ensemble Kalman filter

“…A more complete analysis would also track the sediment type composition or grain size distribution in the layer structure, and might additionally estimate changing environmental controls on the sedimentation process, such as sea level and sediment supply. Wingate et al (2016) considered an event-based geological model trading off physical verisimilitude for computational speed and convenience of conditioning, and took a probabilistic programming approach coupled with variational inference to condition this model to observations. This geological inversion task is an atypical application of the EnKF because the observations, being borehole measurements, were collected long after the sedimentation process had finished.…”

Modelling parametric uncertainty in large-scale stratigraphic simulations

“…In this context a trial-and-error manual calibration is extremely time consuming and leads to a single (deterministic) solution. Probabilistic approaches have been proposed to address these issues 10 , 11 . Recently a few studies 8 , 12 presented automatic calibration procedures for the general purpose SFM Dionisos 13 .…”

Conditioning surface-based geological models to well data using artificial neural networks

“…The difficulty in parametrizing the objects presents a limitation of the method as this could impact the computational expense and time cost of solving the inverse problem, due to the non-uniqueness and high-dimensionality of the problem. To generate multiple lobe models that fit observed data at well locations, [11] applied a variational inference method which used a stochastic gradient optimizer to determine the optimal parameters of a surrogate probability density function (PDF) that approximates the posterior PDF. The method allowed for the rapid generation of multiple conditioned samples when compared to a Markov Chain Monte Carlo (MCMC) method, although the MCMC yielded models that better fit the data.…”