Incorporating Physics-Based Patterns into Geophysical and Geostatistical Estimation Algorithms

Geophysical imaging systems are inherently non-linear and plagued with the challenge of limited data. These drawbacks make the solution non-unique and sensitive to small data perturbations; hence, regularization is performed to stabilize the solution. Regularization involves the application of a priori specification of the target to modify the solution space in order to make it tractable. However, the traditionally applied regularization model constraints are independent of the physical mechanisms driving the spatiotemporal evolution of the target parameters. To address this limitation, we introduce an innovative inversion scheme, basis-constrained inversion, which seeks to leverage advances in mechanistic modeling of physical phenomena to mimic the physics of the target process, to be incorporated into the regularization of hydrogeophysical and geostatistical estimation algorithms, for improved subsurface characterization. The fundamental protocol of the approach involves the construction of basis vectors from training images, which are then utilized to constrain the optimization problem. The training dataset is generated via Monte Carlo simulations to mimic the perceived physics of the processes prevailing within the system of interest. Two statistical techniques for constructing optimal basis functions, Proper Orthogonal Decomposition (POD) and Maximum Covariance Analysis (MCA), are employed leading to two inversion schemes. While POD is a static imaging technique, MCA is a dynamic inversion strategy. The efficacies of the proposed methodologies are demonstrated based on hypothetical and lab-scale flow and transport experiments