Abstract:
In this thesis, we study inverse problems arising in geothermal reservoir engineering
from a Bayesian perspective. These problems are challenging; the forward problem
captures complex physical processes, which frequently results in long run-times and
model failures, and the data that is available is typically sparse and noisy. Exact sampling methods for solving Bayesian inverse problems, such as Markov chain
Monte Carlo, are challenging to apply to these problems; instead, computationally
efficient approximations are generally required. Ensemble methods form a class of
efficient, derivative-free algorithms that have been used to approximate the solutions
to Bayesian inverse problems arising in a variety of settings; their use in a geothermal context, however, has remained largely unexplored. In this thesis, we investigate
the potential of ensemble methods for solving geothermal inverse problems. We first
review several widely-used ensemble methods and evaluate their performance when
applied to a simplified geophysical problem with a reference posterior computed
using Markov chain Monte Carlo. The results of this comparison suggest that ensemble methods are capable of providing approximations to the posterior that are of
comparable quality to those computed using conventional, derivative-based methods
for approximate Bayesian inference. We then demonstrate the application of ensemble methods to two high-dimensional, synthetic geothermal case studies. Finally,
we explore the use of ensemble methods for large-scale geophysical optimal experimental design problems, and show how these methods can be used with a variety
of potential design criteria. Throughout our numerical experiments, we illustrate
how ensemble methods can be combined with flexible geometric and hierarchical
model parametrisation schemes. Our results suggest that ensemble methods have
the potential to provide accurate, computationally inexpensive approximations of
the solutions to inverse problems and optimal experimental design problems arising
in geothermal reservoir engineering.