Group Sparsity Regularization for Calibration of SubsurfaceFlow Models under Geologic Uncertainty

Abstract:

Subsurface flow model calibration inverse problems typically involve inference of high-
dimensional aquifer properties from limited monitoring and performance data. To find plausible

solutions, the dynamic flow and pressure data are augmented with prior geological information

about the unknown properties. Specifically, geologic continuity that exhibits itself as strong

spatial correlation in heterogeneous rock properties has motivated various regularization and

parameterization techniques for solving ill-posed model calibration inverse problems. However,

complex geologic formations, such as fluvial facies distribution, are not amenable to generic

regularization techniques; hence, more specific prior models about the shape and connectivity

of the underlying geologic patterns are necessary for constraining the solution properly. Inspired

by recent advances in signal processing, sparsity regularization uses effective basis functions to

compactly represent complex geologic patterns for efficient model calibration. Here, we present

a novel group-sparsity regularization that can discriminate between alternative plausible prior

models based on the dynamic response data. This regularization property is used to select

prior models that better reconstruct the complex geo-spatial connectivity during calibration. With

group sparsity, the dominant spatial connectivity patterns are encoded into several parameter

groups where each group is tuned to represent certain types of geologic patterns. In the model

calibration process, dynamic flow and pressure data are used to select a small subset of

groups to estimate aquifer properties. We demonstrate the effectiveness of the group sparsity

regularization for solving ill-posed model calibration inverse problems.