Spatio-temporal modelling of earthquakes and earthquake clustering
Bayliss, Kirsty L.
Individual earthquakes cannot be predicted reliably at present. However, earthquake occurrence is not totally random, being characterised by clustering of events in both time and space. Understanding such clustering is vital for the development of more robust forecasting methodologies, for example during seismicity swarms, aftershock sequences, or for applications investigating induced seismicity. This thesis explores the spatio-temporal occurrence of earthquakes using Bayesian probabilistic approaches to characterise the evolution of seismicity and its clustering in time and space. Specifically, it examines spatio-temporal clustering of earthquakes, and explores a potential new approach to modelling the spatio-temporal evolution of seismicity which may be useful for future forecasting applications. The style of earthquake clustering can only be categorised in retrospect. A ‘mainshock-aftershock’ sequence has a large mainshock, followed by a decaying sequence of smaller events, and may include smaller ‘foreshocks’ before the largest event. In contrast, a ‘swarm’ is composed of smaller, similar magnitude events without an obvious mainshock. Diagnostic mapping of the style of clustering would allow parameters in seismic hazard models to reflect this, and by extrapolation forecast the likelihoods of future events. However, despite this widely recognised and studied clustering behaviour, there are currently no robust diagnostic methods for identifying cluster style in the analysis of such sequences. In this thesis, I develop a new probabilistic method for the identification of linked events for characterising cluster style, based on a nearest-neighbour algorithm that identifies the closest events in a multidimensional space-time-magnitude sense. Once events are linked to their most likely parent, aWeibull mixture model is fitted to the bimodal nearest-neighbour distance distribution using the Markov-Chain Monte-Carlo method. The resulting distributions establish the probability that a candidate event pair belongs to the clustered or background component of the mixture distribution. The chain of potentially causally-related events can then be expressed as a probability tree. A stochastic ‘thinning’ is applied to quantify uncertainty within the tree structure, allowing the formal construction of probabilistic earthquake cluster networks. This allows the consideration of the uncertainty that exists in links between events. There is significant uncertainty in resulting metrics when a probabilistic approach is used, due to the stochastic thinning of sequence links. This makes metrics like the average leaf depth extremely variable over many realisations, and the level of associated uncertainty in the metric is potentially more useful than the metric itself. The resulting network structure is also sensitive to key parameters such as magnitude cutoff, with changes in magnitude cutoff affecting the metrics and their uncertainty. The uncertainties within cluster sequences create inherent difficulties in categorising clustering. Swarms of smaller magnitude events can be particularly difficult to study due to increased uncertainty in the links between events and the small magnitudes involved which make them particularly sensitive to changes in magnitude cutoff. An understanding of link and metric uncertainties is necessary for the construction of a robust cluster classification system. Metrics such as the number of events before the largest magnitude event in a sequence and the length of the longest linear chain of events are potentially most useful of the metrics studied, especially when contrasted with the number of direct offspring of the largest event. The definition of earthquake clusters remains somewhat nebulous and the results of different methods for identifying clusters are not necessarily comparable. I demonstrate this by comparing a waveform based clustering algorithm with the probabilistic clustering algorithm developed here, and highlight the differences in identified clusters. Such methods can be combined to provide better understanding of the spatio-temporal evolution of cluster sequences relative to underlying fault motion. Ideally, hybrid models that combine different data could be constructed to account for the observed spatio-temporal variation in seismicity. The Integrated Nested Laplace Approximation (INLA) method is a computationally-efficient method of building spatial and spatio-temporal models that works particularly well with point process data. The INLA approach allows the straightforward creation of models containing different combinations of spatially-varying data such that multiple models can be easily compared. I conclude by presenting the foundations of how INLA can be applied to analyse seismicity, and explore the suitability of such a method using synthetic and real data, including its first application to data from Southern California. Synthetic data demonstrates the potential of the INLA method for improving spatial models of seismicity, and the results with real data demonstrate that the INLA approach can reproduce results from the literature and provide a potential framework for rapid model construction and comparison.