Multiscale and upscaling methods for geophysical electromagnetic forward modeling

Abstract

Accurate and efficient simulation of electromagnetic responses in realistic geophysical settings is crucial to the exploration, imaging, and characterization of buried natural resources, such as mineral and hydrocarbon deposits. However, in practice, these simulations are computationally expensive. The geophysical settings consider highly heterogeneous media and features at multiple spatial scales that require a very large mesh to be accurately represented. This results in a system of equations to be solved that often exceeds the limits of average computers. Thus, the key is to reduce the problem size but retain the accuracy of the electromagnetic responses. Upscaling and multiscale techniques have been successfully applied to the problem of simulating fluid flow through heterogeneous porous media, where they are able to drastically reduce the size of the resulting fine-mesh system by casting it into a coarse-mesh system that is much cheaper to solve, while achieving a level of accuracy similar to that obtained with conventional discretization schemes. Recognizing the success that such techniques have had in fluid flow applications, this dissertation extends their use for application to electromagnetic modeling. In this dissertation, two new parallel simulation methods for the quasi-static Maxwell’s equations in the frequency domain are proposed, an upscaling framework for the electrical conductivity, and a multiscale finite volume with oversampling method. Both methods are combined with an adaptive mesh refinement technique (OcTree) to boost their computational performance. The performance of these methods is demonstrated by using field-inspired and synthetic examples that include a large electrical conductivity contrast. This investigation shows that both proposed methods are feasible to tackle geophysical electromagnetic problems, where being able to reduce the size of the problem can be particularly advantageous when extended domains are considered or when the mesh must capture the spatial distribution of the media heterogeneity outside the region where the electromagnetic responses are measured. Furthermore, both methods are new contributions to the literature in the field of computational methods in geophysical electromagnetics. Finally, both methods increase the current predictive and analytic capabilities by making the simulation of electromagnetic responses in larger and more complex geophysical settings more feasible than currently is possible.