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.

Time Series Analysis in Seismology: Practical Applications provides technical assistance and coverage of available methods to professionals working in the field of seismology. Beginning with a thorough review of open problems in geophysics, including tectonic plate dynamics, localization of solitons, and forecasting, the book goes on to describe the various types of time series or punctual processes obtained from those systems. Additionally, the book describes a variety of methods and techniques relating to seismology and includes a discussion of future developments and improvements. Time Series Analysis in Seismology offers a concise presentation of the most recent advances in the analysis of geophysical data, particularly with regard to seismology, making it a valuable tool for researchers and students working in seismology and geophysics. Presents the necessary tools for time series analysis as it relates to seismology in a compact and consistent manner Includes a discussion of technical resources that can be applied to time series data analysis across multiple disciplines Describes the methods and techniques available for solving problems related to the analysis of complex data sets Provides exercises at the end of each chapter to enhance comprehension

Introduction to Petroleum Seismology, second edition (SEG Investigations in Geophysics Series No. 12) provides the theoretical and practical foundation for tackling present and future challenges of petroleum seismology especially those related to seismic survey designs, seismic data acquisition, seismic and EM modeling, seismic imaging, microseismicity, and reservoir characterization and monitoring. All of the chapters from the first edition have been improved and/or expanded. In addition, twelve new chapters have been added. These new chapters expand topics which were only alluded to in the first edition: sparsity representation, sparsity and nonlinear optimization, near-simultaneous multiple-shooting acquisition and processing, nonuniform wavefield sampling, automated modeling, elastic-electromagnetic mathematical equivalences, and microseismicity in the context of hydraulic fracturing. Another major modification in this edition is that each chapter contains analytical problems as well as computational problems. These problems include MatLab codes, which may help readers improve their understanding of and intuition about these materials. The comprehensiveness of this book makes it a suitable text for undergraduate and graduate courses that target geophysicists and engineers as well as a guide and reference work for researchers and professionals in academia and in the petroleum industry.

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.

This book presents 10 specific actions to be undertaken in order to provide results of practical relevance in seismology. From the statistical analysis of earthquakes, we can estimate the earthquake mean recurrence time and the probability of occurrence of the next earthquake. In addition, through statistical analysis, we can identify correlated foreshocks and estimate the occurrence time of the main shock. As the book shows, the general state of seismicity of a given seismic region can be assessed by statistical means, in particular the earthquake entropy. From measurements of the seismic waves on the Earth’s surface, we can deduce the tensor of the seismic moment, the earthquake’s energy and magnitude, as well as the orientation of the fault, the fault slip, the focal volume and the duration of the seismic activity.

Complexity of Seismic Time Series: Measurement and Application applies the tools of nonlinear dynamics to seismic analysis, allowing for the revelation of new details in micro-seismicity, new perspectives in seismic noise, and new tools for prediction of seismic events. The book summarizes both advances and applications in the field, thus meeting the needs of both fundamental and practical seismology. Merging the needs of the classical field and the very modern terms of complexity science, this book covers theory and its application to advanced nonlinear time series tools to investigate Earth's vibrations, making it a valuable tool for seismologists, hazard managers and engineers. - Covers the topic of Earth's vibrations involving many different aspects of theoretical and observational seismology - Identifies applications of advanced nonlinear time series tools for the characterization of these Earth's signals - Merges the needs of geophysics with the applications of complexity theory - Describes different methodologies to analyze problems, not only in the context of geosciences, but also those associated with different complex systems across disciplines

The book offers a comprehensive physical theory of the earthquakes. The presentation level is rather mathematical, but thorough physical explanations are provided everywhere.We do not know where and when and how great an earthquake occurs. The seismic events have a statistical character. Statistical Seismology is discussed extensively in this book, centered on the famous Gutenberg-Richter, Omori and Bath statistical laws. The earthquakes may be correlated, foreshocks may herald a main shock, aftershocks may follow a main shock. The pattern of such correlations, their extension in time and magnitude are discussed in this book. The earthquakes are produced by forces acting for a short time in a localized focal region placed inside the Earth. These forces give rise to elastic deformations and elastic waves, which arrive at Earth' surface as earthquakes. The nature of these forces and their effects are discussed in this book. Any earthquake begins by a feeble tremor, the so-called P and S seismic waves, followed by a large, main shock, which looks like a wall with a long tail. This book explains why it is so. We cannot predict the occurrence of the earthquakes. But we can know something about them. For instance, there exist seismographs, a sort of pendulums, which record the ground displacement. There exist agencies which tell us the earthquake magnitude, its energy, location, fault slip, by reading the seismograms. We may wish to get such information by ourselves, almost in real time, knowing the seismograph recordings, to be independent of the seismological agencies. This book teaches us how to do that. The book describes the accumulation of the seismic energy in the focal region, its release, the shape and strength of the ground displacement. It is shown that the seismic faults may give rise to rather complicated tensorial forces, which account both for the static deformations of the Earth's surface and for the seismic waves produced in an earthquake. A model of energy accumulation in the earthquake focus is formulated and used to derive the statistical Gutenberg-Richter laws. These laws are used to analize the statistics of the seismic events in Vrancea, Romania, as an example. A special emphasis is given to the short-term seismic activity. The book introduces the point tensorial force of the seismic faults and employs it to present both the static deformation of the Earth's crust in epicentral regions and the seismic waves and the main shock which appear on any typical seismogram. This later point is the solution of the so-called Lamb seismological problem. The book describes the determination of the seismic-moment tensor, earthquake magnitude, the volume of the focal region, the duration of the seismic activity in the focus, the fault orientation and the fault slip from measurements of the seismic waves at the Earth's surface. This is the solution of the inverse seismological problem. A special point is a qualitative estimation of these parameters which can be practised by everyone in real time. The book presents the vibrations of the Earth viewed as a solid sphere and the vibrations of an elastic half-space. The static deformations of the elastic half-space under the action of point forces are also included. Finally, earthquake correlations, Bath's law and earthquake entropy are discussed. The book is an original monograph of Seismology, intended for the use of the students, researchers and the public who wish to become familiar with the physics and mathematics of the earthquakes. It provides the understanding of the earthquakes and specific knowledge we may have of them.

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.

The first effective seismographs were built between 1879 and 1890. In 1885, E. S. Holden, an astronomer and then president of the University of California, instigated the purchase of the best available instruments of the time "to keep a register of all earthquake shocks in order to be able to control the positions of astronomical instruments." These seismographs were installed two years later at Lick Observatory on Mt. Hamilton and at the Berkeley campus of the University. Over the years those stations have been upgraded and joined by other seismographic stations administered at Berkeley, to become the oldest continuously operating stations in the Western Hemisphere. The first hundred years of the Seismographic Stations of the University of California at Berkeley, years in which seismology has often assumed an unforeseen role in issues of societal and political importance, ended in 1987. To celebrate the centennial a distinguished group of fellows, staff, and friends of the Stations met on the Berkeley campus in May 1987. The papers they presented are gathered in this book, a distillation of the current state of the art in observatory seismology. Ranging through subjects of past, present, and future seismological interest, they provide a benchmark reference for years to come. The first effective seismographs were built between 1879 and 1890. In 1885, E. S. Holden, an astronomer and then president of the University of California, instigated the purchase of the best available instruments of the time "to keep a register of all earthquake shocks in order to be able to control the positions of astronomical instruments." These seismographs were installed two years later at Lick Observatory on Mt. Hamilton and at the Berkeley campus of the University. Over the years those stations have been upgraded and joined by other seismographic stations administered at Berkeley, to become the oldest continuously operating stations in the Western Hemisphere. The first hundred years of the Seismographic Stations of the University of California at Berkeley, years in which seismology has often assumed an unforeseen role in issues of societal and political importance, ended in 1987. To celebrate the centennial a distinguished group of fellows, staff, and friends of the Stations met on the Berkeley campus in May 1987. The papers they presented are gathered in this book, a distillation of the current state of the art in observatory seismology. Ranging through subjects of past, present, and future seismological interest, they provide a benchmark reference for years to come.