Exemplar-based synthesis of geology using kernel discrepancies and generative neural networks

Exemplar-based synthesis of geology using kernel discrepancies and generative neural networks Shing Chan and Ahmed H. Elsheikh Heriot-Watt University, United Kingdom School of Energy, Geoscience, Infrastructure and Society September 24, 2018 Abstract We propose a framework for synthesis of geological images based on an exemplar image (a.k.a. We synthesize new realizations such that the discrepancy in the patch distribution between the realizations and the exemplar image is minimized. Such discrepancy is quantified using a kernel method for two-sample test called maximum mean discrepancy. To enable fast synthesis, we train a generative neural network in an offline phase to sample realizations efficiently during deployment, while also providing a parametrization of the synthesis process. We assess the framework on a classical binary image representing channelized subsurface reservoirs, finding that the method reproduces the visual patterns and spatial statistics (image histogram and two-point probability functions) of the exemplar image. 1 Introduction A challenge in subsurface flow simulations is to obtain a complete and accurate image of subsurface properties, such as permeability and porosity, that are crucial for accurate flow predictions. Since it is virtually impossible to obtain direct measurements at every point of the domain under study, engineers can only rely on indirect estimations of the subsurface properties, e.g. from seismic images and sparse measurements obtained from wells. Traditionally, the properties are modeled based on their two-point statistics; however, this tends to produce images of the subsurface that are far from realistic. In many scenarios, such as in channelized systems where the properties follow an almost binary distribution and contain strong spatial correlations, two-point statistics are not enough to describe the distribution of the properties. This shortcoming led to the development of alternative algorithmic approaches to synthesize subsuface images that can capture multipoint statistics. These methods start from an exemplar image (also called training image in the geology literature) that is deemed representative of the subsurface under study, meaning that the spatial statistics in this image is believed to be similar to that of the subsurface.