Seismic Bayesian evidential learning: estimation and uncertainty quantification of sub-resolution reservoir properties

Abstract

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 3D pre-stack seismic data.

Probabilistic Evaluation of Geoscientific Hypotheses With Geophysical Data: Application to Electrical Resistivity Imaging of a Fractured Bedrock Zone

“…(2020), Lopez‐Alvis et al. (2019), and Pradhan and Mukerji (2020) use feature extraction techniques to identify summary statistics that represent the key features in their data. If the summary statistic extracted from the data is defined by , then the posterior distribution of model parameters is then estimated via (Hermans et al., 2015; Lopez‐Alvis et al., 2019).…”

“…(2015), Lopez‐Alvis et al. (2019), and Pradhan and Mukerji (2020) to estimate posterior distributions. In these studies, with the exception of Pradhan and Mukerji (2020), the posterior density is estimated through kernel density estimation in the reduced‐dimension space (Scheidt et al., 2018).…”

“…(2019), and Pradhan and Mukerji (2020) to estimate posterior distributions. In these studies, with the exception of Pradhan and Mukerji (2020), the posterior density is estimated through kernel density estimation in the reduced‐dimension space (Scheidt et al., 2018). We extend this kernel density estimation method for cases where has a defined error distribution by calculating the conditional distribution for multiple realizations of drawn from the measurement distribution .…”

“…In this work we leverage machine learning to optimize feature selection. Machine learning has been used in a Popper‐Bayes framework before to relate geophysical data to a specific hypothesis, that is, (Enemark et al., 2020), and to directly predict reservoir properties from seismic data (Pradhan & Mukerji, 2019). We follow the work of Pradhan and Mukerji (2019) and use machine learning to update model parameters, that is, directly from geophysical data, such that where is the machine learning inverse model.…”

Ensemble-Based Electrical Resistivity Tomography with Data and Model Space Compression

“…For nonlinear problems and/or non-Gaussian assumptions, a complete characterization of the PPD is only possible through sampling, and in these contexts, Markov Chain Monte Carlo (MCMC; Sambridge & Mosegaard, 2002;Sen & Stoffa, 2013) algorithms can be used to numerically estimate the target posterior. These methods provide accurate uncertainty assessments but require a considerable computational effort to converge toward stable PPD estimations, especially in large-dimensional model spaces and for expensive forward model evaluations (Aleardi & Salusti, 2020;Aleardi et al, 2017Pradhan & Mukerji, 2020;Sajeva et al, 2014).…”