Summary
It is natural to use a branching process to describe occurrence patterns of earthquakes, which are apparently clustered in both space and time. The clustering features of earthquakes are important for seismological studies.
Based on some empirical laws in seismicity studies, several point-process models have been proposed in literature, classifying seismicity into two components, background seismicity and clustering seismicity, where each earthquake event, no matter it is a background event or generated by another event, produces (triggers) its own offspring (aftershocks) according to some branching rules. There are further ideas on probability separation of background seismicity from the clustering seismicity assuming a constant background occurrence rate throughout the whole studied region and other authors proposed a stochastic declustering method and made the probability based declustering method practical.
In this paper, we show some useful graphical diagnostic methods for improving model formulation.
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Zhuang, J., Ogata, Y., Vere-Jones, D. (2006). Diagnostic Analysis of Space-Time Branching Processes for Earthquakes. In: Baddeley, A., Gregori, P., Mateu, J., Stoica, R., Stoyan, D. (eds) Case Studies in Spatial Point Process Modeling. Lecture Notes in Statistics, vol 185. Springer, New York, NY. https://doi.org/10.1007/0-387-31144-0_15
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DOI: https://doi.org/10.1007/0-387-31144-0_15
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