Automated objective identification of seismic phases

Abstract

We have developed two types of statistical models to characterize long-term spatiotemporal seismic activity. The first type treats the times of earthquake occurrences as continuous data, while the second type discretises (bins) the occurrence times.

We applied the first type of models to earthquake data (1973-2015) from the Middle America Trench (MAT) and Northern California (NCA). The models were able to discriminate between different types of clustering behaviour. Background activity, mainshocks and aftershocks were identifiable in both the MAT and NCA studies, allowing the transitions between and activity within these phases to be quantified. At the MAT, some precursory activity was found, with implications for better earthquake forecasting. In NCA, however, any such activity was obscured by the different character of the data, which consisted of fewer, but longer, sequences, leading to aftershock behaviour being emphasised. The spatial model again exhibited background and aftershock activity, and two types of possibly precursory activity, one akin to traditional foreshocks, and the other to long-distance triggering.

We applied the second type of models to non-volcanic tremors in Japan, and identified distinct segments of tremor source regions and the spatiotemporal migration pattern among these segments. The second type of models have much lower computational cost that the first type.

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Technical Abstract

We developed two new types of continuous-time hidden Markov model, Markov modulated Hawkes process with marks (MMHPM) and spatiotemporal MMHPM, to investigate long-term seismicity rate holistically, using the entire earthquake record in a selected region to identify patterns correlated with subsequent large earthquakes, rather than the traditional way of hunting for individual foreshocks. We derived a hybrid estimation procedure for the parameters of the models by combining the Expectation Maximization algorithm and direction maximization of the log likelihood. We applied these models to earthquake catalogues from two regions in different tectonic environments, the Middle America Trench (MAT) and Northern California (NCA), and compared the features of the seismicity captured by the models for the two catalogues. The results from the data analysis suggest that the MMHPMs perform better than the original temporal MMHP in capturing the occurrence patterns of earthquakes. This means that the magnitudes carry information beyond that expressed simply by the greater number of triggered events used as a signal by our earlier work. The new model with magnitudes as marks is particularly effective in capturing the behaviour of several of the major earthquakes and their immediate offspring. The states discriminate between different types of clustering behaviour. Background activity, mainshocks and aftershocks all have identifiable states in both the MAT and NCA studies, allowing the transitions between, and activity within them to be quantified. At the MAT, a precursory state was visible, but in NCA, the additional states represent a second longer aftershock period and a composite foreshock/minor mainshock/major aftershock state. The spatial model naturally suffers from reduced temporal resolution compared to the purely temporal model. We again saw a background and aftershock state, but the remaining three states in the preferred model formed a sub-system with preferential transitions among themselves. Two of the three states exhibited some precursory character, one concentrated in time and space, the other much more diffuse. The former corresponds more to traditional foreshock activity, and the latter to static triggering.

We also developed a type of discrete hidden Markov models (HMMs) to investigate the spatiotemporal migration of non-volcanic tremors, where each state represents a distinct segment of tremor sources. A mixture distribution of a Bernoulli variable and a continuous variable is introduced into the HMM to solve the problem that tremor clusters are very sparse in time. We applied our model to the tremor data from the Tokai region in Japan to identify distinct segments of tremor source regions and the results reveal the spatiotemporal migration pattern among these segments.