Coda wave interferometry and relative source location
A wide range of applications requires relative locations of sources of energy to be known accurately. Most conventional location methods are either subject to errors that depend strongly on inaccuracy in the model of propagation velocity used, or demand a well-distributed network of surrounding seismic stations in order to produce reliable results. A source location method based on coda wave interferometry (CWI) is relatively insensitive to the number of seismic stations and to the source-to-station azimuthal coverage. It therefore opens new avenues for research, for applications in areas with unfavourable recording geometries, and for applications which require a complementary method. CWI uses scattered waves in the coda of seismograms to estimate the small differences between two seismic states, and currently has three types of applications: estimating bulk velocity change of the medium, scatterer displacement, and source location perturbation. When used for source location, CWI is used to estimate the distances between pairs of sources with similar mechanism (equivalent to estimating location perturbation of the same source), which are then used jointly to determine the relative location of a cluster of sources using a probabilistic framework as an optimization problem. However, estimating source separation is a relatively new type of application of CWI. In the first part of this thesis, the performance of CWI is tested in models with varying complexities and types: from point-scatterer media as assumed in the CWI theory, to layered media as in classic Earth models, to media with combinations of point-scatters and layers, and finally to the more realistic Marmousi model. This thesis also presents the first elastic case of testing CWI to estimate source separation in synthetic experiments. The study contributes to better understand and interpret the source separation estimates and therefore relative locations using CWI. The second part of this thesis validates the location algorithm with synthetic data. When applied to real seismic data, the algorithm is found to suffer from the impact of large difference in the dominant wavelength of recordings made on different instruments. This thesis introduces a new formulation for the optimization problem to account for data from multiple station channels. In addition, it proposes a way to standardize the selection of parameters when implementing the method. The algorithm is applied to a micro-seismic dataset of mining induced events recorded in Nottinghamshire, England. The earthquake location results are highly consistent when using different individual seismometer channels, showing that it is possible to locate event clusters with a single-channel seismometer. These microseismic events have shorter distinguishable codas in recorded waveforms, and hence fewer recorded scattered waves than those that have been used to test this method previously. Thus, the potential applications of this cost-effective method are extended to seismic events over a wider range of magnitudes. Given the advantages of this location method, it has been applied only once in literature other than in this thesis. It is likely that one reason that it is not used more widely is the lack of reliable code that implements this multistage method. This thesis develops a well-commented MATLAB code called CWIcluster that does so, accompanied by a clear and thorough user manual. It implements the location method in three stages: classifying events into clusters, computing inter-source separations using CWI, and estimating their relative locations. Each stage can be implemented in an automated sense given criteria chosen by the user. It is shown that the location algorithm is able to correct bias (underestimation) in the CWI separation estimates to some extent. The third part of this thesis returns to the three basic types of applications of CWI. Standard CWI methods require an assumption that a single type of perturbation has taken place in the system (as do most other methods that measure changes in a seismic system). However, in reality more than one type of perturbation can occur simultaneously. This thesis proposes a general treatment to account for multiple types of perturbations, allowing each type to be recognized and estimated with the effects of others being compensated. The appendices include a co-authored submitted paper that examines the influence of velocity change and source location perturbation on one another in the context of a rock-physics laboratory. Overall this thesis intensively tests the relatively new method of coda wave interferometry to estimate inter-source separations in various environments, and explores its potential to detect multiple types of perturbations that have occurred simultaneously, thus extending our understanding of the set of CWI methods in general. In addition, it validates the relative location method based on CWI and provides ways to improve the original method, as well as a way to assess the quality of results when applied to real data. Finally, it presents a new freely-available code package to implement the location method, which the authors hope will introduce this method more widely in both academia and industry.