Estimation of Spatial-Temporal Hawkes Models for Earthquake Occurrences
Estimation of Spatial-Temporal Hawkes Models for Earthquake Occurrences

Author: James Molyneux

Publisher:

Published: 2018

Total Pages: 92

ISBN-13:

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Point processes have long been used as an effective modeling technique in the forecasting of earthquakes. In this dissertation, we evaluate the ability of earthquake focal mechanisms to predict the locational direction of future events and the usefulness of more complicated point process models including such covariates. We also introduce a new computational method for estimating parameters of point processes models using the Stoyan-Grabarnik estimator which avoids the need to numerically compute the intractable integral term needed to compute estimates via maximum likelihood.

Estimation and Inference for Self-exciting Point Processes with Applications to Social Networks and Earthquake Seismology
Estimation and Inference for Self-exciting Point Processes with Applications to Social Networks and Earthquake Seismology

Author: Eric Warren Fox

Publisher:

Published: 2015

Total Pages: 100

ISBN-13:

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Self-exciting point processes describe random sequences of events where the occurrence of an event increases the likelihood that subsequent events occur nearby in time and space. Models for self-exciting point processes have many important applications to diverse topics such as earthquake and crime forecasting, epidemiology, invasive species, and social networks. The first part of this dissertation discusses a new application of self-exciting point processes to modeling the times when e-mails are sent by individuals in a social network. The proposed models are fit to datasets from West Point Military Academy and the Enron Corporation, and the resulting parameter estimates characterize communication behaviors and leadership roles for users in each network. We argue that the self-exciting models adequately capture major temporal clustering features in the data and perform better than traditional stationary Poisson models. The second part of this dissertation discusses the nonparametric method of Marsan and Lengline (2008) for estimating space-time Hawkes point process models of earthquake occurrences. Their method provides an estimate of a stationary background rate for mainshocks, and a histogram estimate of the triggering function for the rate of aftershocks following an earthquake. At each step of the procedure the model estimates rely on computing the probability each earthquake is a mainshock or aftershock of a previous event. We focus on improving Marsan and Lengline's method by proposing novel ways to incorporate a non-stationary background rate, and adding error bars to the histogram estimates which capture the sampling variability and bias in the estimation of the underlying seismic process. A simulation study is designed to validate and assess new methodology. An application to earthquake data from the Tohoku District in Japan is also discussed, and the results are compared to a well established parametric model of seismicity for this region.

Earthquake Occurrence
Earthquake Occurrence

Author: Rodolfo Console

Publisher: John Wiley & Sons

Published: 2017-07-17

Total Pages: 141

ISBN-13: 1119372224

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Earthquake Occurrence provides the reader with a review of algorithms applicable for modeling seismicity, such as short-term earthquake clustering and pseudo-periodic long-term behavior of major earthquakes. The concept of the likelihood ratio of a set of observations under different hypotheses is applied for comparison among various models. In short-term models, known by the term ETAS, the occurrence space and time rate density of earthquakes is modeled as the sum of two terms, one representing the independent or spontaneous events, and the other representing the activity triggered by previous earthquakes. Examples of the application of such algorithms in real cases are also reported. Dealing with long-term recurrence models, renewal time-dependent models, implying a pseudo-periodicity of earthquake occurrence, are compared with the simple time-independent Poisson model, in which every event occurs regardless of what has occurred in the past. The book also introduces a number of computer codes developed by the authors over decades of seismological research.

An Introduction to the Theory of Point Processes
An Introduction to the Theory of Point Processes

Author: D.J. Daley

Publisher: Springer Science & Business Media

Published: 2006-04-10

Total Pages: 487

ISBN-13: 0387215646

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Point processes and random measures find wide applicability in telecommunications, earthquakes, image analysis, spatial point patterns, and stereology, to name but a few areas. The authors have made a major reshaping of their work in their first edition of 1988 and now present their Introduction to the Theory of Point Processes in two volumes with sub-titles Elementary Theory and Models and General Theory and Structure. Volume One contains the introductory chapters from the first edition, together with an informal treatment of some of the later material intended to make it more accessible to readers primarily interested in models and applications. The main new material in this volume relates to marked point processes and to processes evolving in time, where the conditional intensity methodology provides a basis for model building, inference, and prediction. There are abundant examples whose purpose is both didactic and to illustrate further applications of the ideas and models that are the main substance of the text.

Earthquake Statistical Analysis through Multi-state Modeling
Earthquake Statistical Analysis through Multi-state Modeling

Author: Irene Votsi

Publisher: John Wiley & Sons

Published: 2019-04-02

Total Pages: 196

ISBN-13: 1786301504

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Earthquake occurrence modeling is a rapidly developing research area. This book deals with its critical issues, ranging from theoretical advances to practical applications. The introductory chapter outlines state-of-the-art earthquake modeling approaches based on stochastic models. Chapter 2 presents seismogenesis in association with the evolving stress field. Chapters 3 to 5 present earthquake occurrence modeling by means of hidden (semi-)Markov models and discuss associated characteristic measures and relative estimation aspects. Further comparisons, the most important results and our concluding remarks are provided in Chapters 6 and 7.

Earthquakes
Earthquakes

Author: Yan Y. Kagan

Publisher: John Wiley & Sons

Published: 2013-12-18

Total Pages: 358

ISBN-13: 1118637895

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This book is the first comprehensive and methodologically rigorous analysis of earthquake occurrence. Models based on the theory of the stochastic multidimensional point processes are employed to approximate the earthquake occurrence pattern and evaluate its parameters. The Author shows that most of these parameters have universal values. These results help explain the classical earthquake distributions: Omori's law and the Gutenberg-Richter relation. The Author derives a new negative-binomial distribution for earthquake numbers, instead of the Poisson distribution, and then determines a fractal correlation dimension for spatial distributions of earthquake hypocenters. The book also investigates the disorientation of earthquake focal mechanisms and shows that it follows the rotational Cauchy distribution. These statistical and mathematical advances make it possible to produce quantitative forecasts of earthquake occurrence. In these forecasts earthquake rate in time, space, and focal mechanism orientation is evaluated.

Predicting Pandemics in a Globally Connected World, Volume 1
Predicting Pandemics in a Globally Connected World, Volume 1

Author: Nicola Bellomo

Publisher: Springer Nature

Published: 2022-09-22

Total Pages: 314

ISBN-13: 3030965627

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This contributed volume investigates several mathematical techniques for the modeling and simulation of viral pandemics, with a special focus on COVID-19. Modeling a pandemic requires an interdisciplinary approach with other fields such as epidemiology, virology, immunology, and biology in general. Spatial dynamics and interactions are also important features to be considered, and a multiscale framework is needed at the level of individuals and the level of virus particles and the immune system. Chapters in this volume address these items, as well as offer perspectives for the future.

Statistical Methods and Modeling of Seismogenesis
Statistical Methods and Modeling of Seismogenesis

Author: Nikolaos Limnios

Publisher: John Wiley & Sons

Published: 2021-03-31

Total Pages: 336

ISBN-13: 1119825032

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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.

Some Methods of Assessing and Estimating Point Processes Models for Earthquake Occurrences
Some Methods of Assessing and Estimating Point Processes Models for Earthquake Occurrences

Author: Alejandro Veen

Publisher:

Published: 2006

Total Pages: 166

ISBN-13: 9780542901522

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The third part of this work applies the weighted K-function to assess the goodnessof-fit of a class of point process models for the spatial distribution of earthquakes in Southern California. Then, the proposed EM-type algorithm is used to estimate declustered background seismicity rates of geologically distinct regions in Southern California.