Electromagnetic Imaging of the Earth's Subsurface using Advanced Galerkin Methods

Objective:

IMAGEARTH Project is focused on the development of advanced numerical methods for the proper simulation and inversion of geophysical electromagnetic (EM) measurements. Both on-surface data (magnetotellurics, and controlled source electromagnetics) and borehole measurements (acquired with the most advanced laterolog, logging-while-drilling, and geosteering tools) will be considered in this project. For the inverse simulations, we will investigate functionality and performance of two popular approaches, gradient-based and Bayesian, and evaluate the potential for combining those approaches in hybrid methods. The use of Bayesian methods will also allow us to produce more reliable uncertainty estimates that go beyond a simple linearization of the cost functional around a local minima. For the forward simulations, we will focus on a novel dimensionally adaptive method that efficiently enables to combine subdomains of different spatial dimensionality coupled via a traditional Galerkin formulation. To speed up computations for problems with a large number of right hand sides (sources) such as those naturally appearing in geophysical EM imaging, we will consider solver based discretizations, which we have recently shown to provide fast simulations. We will also apply non-fitting grids, which may not only expedite and simplify the implementation of such methods, but also facilitate simulations associated to inverse problems with varying resistivity distributions (material properties) between two subsequent iterations. To control the discretization error, we will employ an adaptive method recently developed in our group based on using unconventional error representations. While most studies will be performed on the frequency domain, we will also analyze the case of time domain methods, which are vital for simulation of some most recent borehole EM measurement acquisition systems. The numerical methods developed in this Project will be implemented in an HPC software that will employ library PETSc and exploit several levels of parallelism, including: (a) based on multiple frequencies, (b) based on a domain decomposition approach, (c) in terms of transmitter/receiver combinations, and (d) in terms of multiple Earth model configurations for the case of the Bayesian inversion. We will apply the resulting methods, algorithms, and software for various imaging applications, including: hydrocarbon exploration, CO2 sequestration, earthquake hazard assessment, and optimal placement of geothermal heat pumps.