Statistical learning and inference of subsurface properties under complex geological uncertainty with seismic data
Keywords: Energy Resources Engineering.

Attempting to characterize, image or quantify the subsurface using geophysical data for exploration and development of earth resources presents interesting and unique challenges. Subsurface heterogeneities are the result of abstract paleo geological events, exhibiting variability that is spatially complex and existent across multiple scales. This leads to significantly high-dimensional inverse problems under complex geological uncertainty, which are computationally challenging to solve with conventional geophysical and statistical inference methods. In this dissertation, we discuss these challenges within the context of subsurface property estimation from seismic data. We discuss three specific seismic estimation problems and propose methods from statistical learning and inference to tackle these challenges. The first problem we address is that of incorporating constraints from geological history of a basin into seismic estimation of P-wave velocity and pore pressure. In particular, our approach relies on linking velocity models to the basin modeling outputs of porosity, mineral volume fractions, and pore pressure through rock-physics models. We account for geologic uncertainty by defining prior probability distributions uncertain basin modeling parameters. We have developed an approximate Bayesian inference framework that uses migration velocity analysis in conjunction with well and drilling data for updating velocity and pore pressure uncertainty. We apply our methodology in 2D to a real field case from the Gulf of Mexico. We demonstrate that our methodology allows for building a geologic and physical model space for velocity and pore-pressure prediction with reduced uncertainty. In the second problem, we investigate the applicability of deep learning models for conditioning reservoir facies models, parameterized by geologically realistic geostatistical models such as training-image based and object-based models, to seismic data. In our proposed approach, end-to-end discriminative learning with convolutional neural networks (CNNs) is employed to directly learn the conditional distribution of model parameters given seismic data. The training dataset for the learning problem is derived by defining and sampling prior distributions on uncertain parameters and using physical forward model simulations. We apply our methodology to a 2D synthetic example and a 3D real case study of seismic facies estimation. Our synthetic experiments indicate that CNNs are able to almost perfectly predict the complex geological features, as encapsulated in the prior model, consistently with seismic data. For real case applications, we propose a methodology of prior falsification for ensuring the consistency of specified subjective prior distributions with real data. We found modeling of additive noise, accounting for modeling imperfections and presence of noise in the data, to be useful in ensuring that a CNN, trained on synthetic simulations, makes reliable predictions on real data. In the final problem, we present a framework that enables estimation of low-dimensional sub-resolution reservoir properties directly from seismic data, without requiring the solution of a high dimensional seismic inverse problem. Our workflow is based on the Bayesian evidential learning approach and exploits learning the direct relation between seismic data and reservoir properties to efficiently estimate reservoir properties. The theoretical framework we develop allows incorporation of non-linear statistical models for seismic estimation problems. Uncertainty quantification is performed with approximate Bayesian computation. With the help of a synthetic example of estimation of reservoir net-to-gross and average fluid saturations in sub-resolution thin sand reservoir, several nuances are foregrounded regarding the applicability of unsupervised and supervised learning methods for seismic estimation problems. Finally, we demonstrate the efficacy of our approach by estimating posterior uncertainty of reservoir net-to-gross in sub-resolution thin sand reservoir from an offshore delta dataset using pre-stack seismic data