Developing Training Image-Based Priors for Inversion of Subsurface Geophysical and Flow Data

Abstract:

Forecasting in subsurface formations, whether for groundwater, storage or oil & gas production, can rely on a wealth of geological information. Currently, most of this information remains underused in both the theory and practice of forecasting based on inverse models which heavily relies on spatial covariances and multi-Gaussian theory. By means of real field studies, I will provide an outline of how such geological information can be accounted through the construction and validation of a large set of training images and the generation of model realizations with MPS (multiple-point geostatistics). Often most critical in solving such inverse problems is the development of prior models that are later used for posterior sampling or stochastic search. I propose therefore a two-stage approach where the first stage consists of a validation of the training image-based prior with the geophysical and flow data. This stage will require only the generation of a few (100s) geological models and the forward modeling of the data response on these models. For geophysical data, the validation consists of comparing histograms of multi-scale wavelet transforms between the forward models and the field data. For flow data, the validation is based on a reduction of dimensionality of the forward response and the data using multi-dimensional scaling. The outcome of this validation is an estimate of the prior probability assigned to each training image, with several training images getting assigned zero probability (incompatible with field data). These prior probabilities are used in the second stage to actually invert for the data using stochastic search. In such stochastic search, I avoid parameterizing the model space and present methods that efficiently perform a direct search in the space of the validated training image-based prior model realizations.