Hierarchical Bayesian Inversion for the Point Source Moment Tensor: Method and Applications

Abstract

One of the most important aspects of seismology is explaining the generation of seismic waves during earthquakes. The first mathematical models of earthquakes involved shear faulting, where deformation of rocks surrounding the fault increases the stress level, causes rock fracturing and results in radiation of elastic waves. Over the years, a large number of earthquakes that cannot be explained only with shear faulting have been observed. Hence, the mathematical model of seismic sources evolved into a seismic moment tensor (MT), which also includes isotropic and compensated linear vector dipole components. Although uncertainties in MT inversions are important for estimating solution robustness, they are rarely available. Furthermore, noise in the data can alter the waveform and cause spurious non-double-couple components.

In this thesis, I address these issues using Bayesian hierarchical inversion, a relatively novel technique in seismology. Its probabilistic approach gives an ensemble of solutions instead of just one best-fit solution, thus, it can be used to estimate MT uncertainties. The algorithm developed as a part of this thesis uses waveform data of regional earthquakes and explosions with moderate magnitudes to compute the centroid location and the seismic moment tensor. The algorithm includes a sophisticated treatment of data noise utilising an empirical noise covariance matrix, and including the level of noise as an unknown in the inversion. As a result, the model complexity is determined by the data themselves.

There are two major groups of events for which the Bayesian approach can be of great importance, and to which the algorithm has been applied. The first one is seismic events in complex geological environments, such as volcanic and geothermal areas. A significant number of these events are expected to have source processes that require the full MT. The second group is explosions, where the algorithm can be valuable for nuclear proliferation. The feasibility of the approach is initially demonstrated on synthetic data contaminated with noise. It is shown that the empirical covariance matrix improves the location estimate. This is followed by application to a well-studied earthquake from Long Valley caldera, a volcanic environment in California, where a statistically significant isotropic component of the source is confirmed.

The method was further improved to include multiple noise parameters that determine the fit on each record, and in turn weight the stations' contribution in the inversion. Subsequently, I have analysed several earthquakes from a geothermal field in California, The Geysers. The double-couple components of the sources agree well with the regional stress field, but the non-double-couple components show a variety of values.

Finally, the method is applied to the 2013 Democratic People's Republic of Korea nuclear explosion. Since the paths to the recording stations in the region traverse significantly different crustal structures, a linear inversion was initially conducted to create a composite structural model that better explained the oceanic raypaths. The Bayesian inversion shows exceptionally low uncertainties in the moment tensor solution for this event, characterising it as a crack mechanism, which explains the non-isotropic radiation as a result of material damage.