Bayesian source inversion of microseismic events

Rapid stress release at the source of an earthquake produces seismic waves. Observations of the particle motions from such waves are used in source inversion to characterise the dynamic behaviour of the source and to help in understanding the driving processes. Earthquakes either occur naturally, such as in volcanic eruptions and natural geothermal fields, or are linked to anthropogenic activities including hydrofracture of gas and oil reservoirs, mining events and extraction of geothermal fluids. Source inversion is very sensitive to uncertainties in both the model and the data, especially for low magnitude, namely microseismic, events. Many of the uncertainties can be poorly quantified, and are often not included in source inversion. This thesis proposes a Bayesian framework enabling a complete inclusion of uncertainties in the resultant probability distribution using Bayesian marginalisation. This approach is developed for polarity and amplitude ratio data, although it is possible to use any data type, provided the noise model can be estimated. The resultant posterior probability distributions are easily visualised on different plots for orientation and source-type. Several different algorithms can be used to search the source space, including Monte Carlo random sampling and Markov chain Monte Carlo sampling. Relative information between co-located events may be used as an extension to the framework, improving the constraint on the source. The double-couple source is the commonly assumed source model for many earthquakes, corresponding to slip on a fault plane. Two methods for estimating the posterior model probability of the double-couple source type are explored, one using the Bayesian evidence, the other using trans-dimensional Markov chain Monte Carlo sampling. Results from both methods are consistent with each other, producing good estimates of the probability given sufficient samples. These provide estimates of the probability of the source being a double-couple source or not, which is very useful when trying to understand the processes causing the earthquake. Uncertainty on the polarity estimation is often hard to characterise, so an alternative approach for determining the polarity and its associated uncertainty is proposed. This uses a Bayesian estimate of the polarity probability and includes both the background noise and the arrival time pick uncertainty, resulting in a more quantitative estimate of the polarity uncertainty. Moreover, this automated approach can easily be included in automatic event detection and location workflows. The inversion approach is discussed in detail and then applied to both synthetic events generated using a finite-difference code, and to real events acquired from a temporary seismometer network deployed around the Askja and Krafla Volcanoes, Iceland.