Randomising in and over Seismology

Abstract

This thesis presents a collection of works centered on computational statistics in Bayesian seismology. Bayesian seismology interprets inverse problems in seismology as questions of inference, striving not to produce a single answer to an inverse problem, but to ascribe a probability to all possible solutions. To avoid evaluating every potential solution, or scenario, algorithms from computational statistics are necessary. However, the selection of appropriate algorithms is non-trivial, often demanding a deep understanding of the inverse problem at hand and knowledge of the potential algorithms available. This work focuses on the use of a specific algorithm, Hamiltonian Monte Carlo (HMC), and related variants. Its application to Bayesian seismology is studied from various perspectives. Firstly, a general case study for appraising a computationally demanding inverse prob- lem in seismology with HMC is presented. It is demonstrated that the use of the HMC algorithm enables successful consideration of Full-Waveform Inversion within a Bayesian inference framework, unlocking inference on parameters such as density, which have traditionally been poorly resolved. This is followed by an effort to quantify the performance of algorithms on a given class of inverse problems. The collection of No-Free-Lunch algorithms precludes any single algorithm from being universally efficient, guiding the investigation into whether HMC and related algorithms might be optimal for a reduced set of relevant problems. While this is confirmed, the attempt is restricted by the curse of dimensionality, confining the analysis to inverse problems of limited dimensionality. The expertise gained on these appraisal algorithms is subsequently distilled into an accessible and well-documented collection of open-source codes called HMCLab. This collection includes numerous didactic materials aimed at showcasing HMC and its variants to the general geophysicist. It covers various inverse problems and their Bayesian treatment, along with instructions on implementing inverse problems posed by the user. Next, two approaches to writing efficient wavefield simulation codes are proposed. The first, an open-source package named psvWave, is a C++ written and Python accessible software designed to simulate 2D wavefields in parallel. The second approach demonstrates how to leverage modern unified chips using the Metal Shading Language to accelerate existing C++. Its ease of use is demonstrated on the psvWave package. Efficient wavefield modeling is integral to Bayesian seismology, as reducing computational costs can enable more extensive evaluations of wavefield-based inverse problems. The thesis concludes with a report on multiple seismological field campaigns that are extensively documented using aerial and ground-based photogrammetry. In the three field campaigns, Structure-from-Motion methods were innovatively used to digitise the field sites. It is shown that these methods are accessible with limited resources and consumer electronics. The digitisation employing remotely operated drones enables safe surveying of hazardous fields and the ability to rapidly create meshes of structures and topography for wavefield simulations, while ground-based imagery offers a low-cost, low-risk alternative.