Statistical Seismology

Statistical Seismology aims to bridge the gap between physics-based and statistics-based models. This volume provides a combination of reviews, methodological studies, and applications, which point to promising efforts in this field. The volume will be useful to students and professional researchers alike, who are interested in using stochastic modeling for probing the nature of earthquake phenomena, as well as an essential ingredient for earthquake forecasting.

This special issue emerged following the 2013 8th International Statistical Seismology (StatSei8) workshop in Beijing. The articles within have been collected to report on exciting new research in statistical seismology methods and applications; it contains a collection of the newest methods, techniques and results related to statistical analysis of earthquake occurrence and earthquake probability forecasting. The articles within ultimately help to define future research directions in the field. Especially, the rapid development of observation technologies has brought geophysical research into the big-data era. This includes not only non-seismicity geophysical data, such as GPS observation on surface displacement, InSAR observation of the co-seismic deformation, ionospheric observations, etc., but also extended seismological data including slow earthquakes, tremor, and VLF earthquakes. The subject of statistical seismology bridges the gap between physical and statistical models. Many significant achievements have been accomplished during the last several decades, including formulation of conditional intensity models for quantifying seismicity rates, earthquake probability forecasts, and theories related to rigorous testing of forecast models.

204 Pure app!. geophys. , P. Reasenberg demonstrated that in Cascadia earthquakes are four times more likely to be foreshocks than in California. Many speakers emphasized the regional differences in all earthquake parameters, and it was generally understood that basic models of the earthquake occurrence must be modified for regional application. The idea that the focal mechanisms of foreshocks may differ from that of background activity was advocated by Y. Chen and identified by M. Ohtake as possibly the thus far most neglected property of foreshocks, in efforts to identify them. S. Matsumura proposed that focal mechanism patterns of small earthquakes may differ character istically near locked fault segments into which fault creep is advancing. Considerable discussion was devoted to the status of the seismic gap hypothesis because M. Wyss argued that the occurrence of the M 7. 9, 1986, Andreanof Islands earthquake was a confirmation of Reid's rebound theory of earthquakes and thus of the time predictable version of the gap hypothesis, whereas Y. Kagan believed he could negate this view by presenting a list of nine earthquake pairs with M> 7. 4, moment centroid separation of less than 100 km, and time difference less than about 60% of the time he estimated it would take plate motions to restore the slip of the first event.

The Encyclopedia of Mathematical Geosciences is a complete and authoritative reference work. It provides concise explanation on each term that is related to Mathematical Geosciences. Over 300 international scientists, each expert in their specialties, have written around 350 separate articles on different topics of mathematical geosciences including contributions on Artificial Intelligence, Big Data, Compositional Data Analysis, Geomathematics, Geostatistics, Geographical Information Science, Mathematical Morphology, Mathematical Petrology, Multifractals, Multiple Point Statistics, Spatial Data Science, Spatial Statistics, and Stochastic Process Modeling. Each topic incorporates cross-referencing to related articles, and also has its own reference list to lead the reader to essential articles within the published literature. The entries are arranged alphabetically, for easy access, and the subject and author indices are comprehensive and extensive.

The study of earthquakes is a multidisciplinary field, an amalgam of geodynamics, mathematics, engineering and more. The overriding commonality between them all is the presence of natural randomness. Stochastic studies (probability, stochastic processes and statistics) can be of different types, for example, the black box approach (one state), the white box approach (multi-state), the simulation of different aspects, and so on. This book has the advantage of bringing together a group of international authors, known for their earthquake-specific approaches, to cover a wide array of these myriad aspects. A variety of topics are presented, including statistical nonparametric and parametric methods, a multi-state system approach, earthquake simulators, post-seismic activity models, time series Markov models with regression, scaling properties and multifractal approaches, selfcorrecting models, the linked stress release model, Markovian arrival models, Poisson-based detection techniques, change point detection techniques on seismicity models, and, finally, semi-Markov models for earthquake forecasting.