High-Performance Computing Methods for Electromagnetic Well Logging Inverse Problems

Understanding the earth model from real-world measurements is critical in geophysical explorations. When the physical process of generating measurements is described as a nonlinear model, iterative processes are needed to determine the earth model parameters from the measurements, and the process is known as geophysical inversion. As the detection techniques improve, the measurements contain more information about the earth model, resulting in a growth in the earth model dimension. Meanwhile, a more advanced detection technique usually means a more complicated physical process of generating measurements, which corresponds to a forward model with higher nonlinearity. Both factors have placed more requirements on the inverse algorithms. Traditional gradient-based algorithms can solve the inverse problem in a relatively short time, however, they only find local minimums without uncertainty quantification. If uncertainty quantification is desired, Bayesian inference methods have emerged as a viable option. However, Bayesian inference methods are slower than gradient-based algorithms since they usually require sampling. Therefore, efficient Bayesian inference methods are necessary for robust geophysical inversion with uncertainty quantification. This dissertation focuses on efficient Bayesian inference methods for solving geophysical inverse problems using high-performance computing techniques. In this dissertation, two efficient Markov chain Monte Carlo (MCMC) sampling methods with parallel computing techniques, as well as one MCMC method taking into account varying problem dimensions are proposed. It also demonstrates a bi-fidelity deterministic inversion method, in which a smooth surrogate model is used to assist the inversion. The proposed methods are assessed using the electromagnetic (EM) well-logging inverse problem, which infers the earth model through measurements taken from subsurface sensors during the high-angle and horizontal well drilling. Besides the inversion algorithms, two HPC techniques are investigated and tested in this dissertation, and they show promise of solving geophysical inverse problems efficiently.