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An introductory text to a range of numerical methods used today to simulate time-dependent processes in Earth science, physics, engineering and many other fields. It looks under the hood of current simulation technology and provides guidelines on what to look out for when carrying out sophisticated simulation tasks.
Among all the numerical methods in seismology, the finite-difference (FD) technique provides the best balance of accuracy and computational efficiency. This book offers a comprehensive introduction to FD and its applications to earthquake motion. Using a systematic tutorial approach, the book requires only undergraduate degree-level mathematics and provides a user-friendly explanation of the relevant theory. It explains FD schemes for solving wave equations and elastodynamic equations of motion in heterogeneous media, and provides an introduction to the rheology of viscoelastic and elastoplastic media. It also presents an advanced FD time-domain method for efficient numerical simulations of earthquake ground motion in realistic complex models of local surface sedimentary structures. Accompanied by a suite of online resources to help put the theory into practice, this is a vital resource for professionals and academic researchers using numerical seismological techniques, and graduate students in earthquake seismology, computational and numerical modelling, and applied mathematics.
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.
Recent progress in numerical methods and computer science allows us today to simulate the propagation of seismic waves through realistically heterogeneous Earth models with unprecedented accuracy. Full waveform tomography is a tomographic technique that takes advantage of numerical solutions of the elastic wave equation. The accuracy of the numerical solutions and the exploitation of complete waveform information result in tomographic images that are both more realistic and better resolved. This book develops and describes state of the art methodologies covering all aspects of full waveform tomography including methods for the numerical solution of the elastic wave equation, the adjoint method, the design of objective functionals and optimisation schemes. It provides a variety of case studies on all scales from local to global based on a large number of examples involving real data. It is a comprehensive reference on full waveform tomography for advanced students, researchers and professionals.
Methods in Computational Physics, Volume 11: Seismology: Surface Waves and Earth Oscillations is a five-chapter text that deals with the computational analysis of surface waves and the eigenvibrations of the Earth. Chapter 1 describes the advances in the numerical modeling of geological structures where the appropriate partial differential equations with boundary conditions for heterogeneous materials are solved using an intricate finite difference scheme. Chapter 2 presents the computer techniques of processing seismograms to obtain information on the dispersion of seismic surface waves, while Chapter 3 explains the fast algorithms for computation of eigenvalues in surface wave and terrestrial eigenvibration problems. Chapter 4 presents a competing method, much used in structural engineering and soil mechanics. Chapter 5 is devoted to the propagation of surface waves in layered media, which indicate that density and elasticity vary only in the vertical direction. This chapter also provides the fundamentals and numerical aspects of the theory of seismic surface waves. This book is an invaluable source for seismologists, earthquake engineers, and graduate students.
A concise and accessible introduction to seismic theory, focusing on the mathematical fundamentals of global seismology. Aimed at advanced undergraduate and graduate students, this new edition has been updated to include recent advances in the field as well as new examples, review questions and computer-based exercises in MATLAB®/Python.
As recognized universally by both seismology and earthquake engineering communities, the amplitude and frequency content of ground motions are influenced by local site effects, including the effects of near-surface geologic materials, surface topographic and basin effects, and so on. Strong linkage between seismic site effect and earthquake damage has been commonly demonstrated from many past earthquakes. Therefore, quantitative and reliable evaluation of the seismic site effect is one of the crucial aspects in seismic hazard assessment and risk mitigation. With the significant advancement of modern seismic monitoring networks and arrays, huge amounts of high-quality seismic records are now being accumulated. This encourages us to measure the site responses and its associated uncertainty for selected seismic stations by some record-dependent approaches, such as horizontal-to-vertical spectral ratio (HVSR) measurements, generalized spectral inversion (GIT) methods, etc. Machine learning techniques also show significant promise in characterization of the near-surface geologic properties and prediction of site response. These data-driven approaches help us to better understand the physics of spatial and temporal variabilities of ground motions. Due to more and more site-specific data being captured, invoking non-ergodic assumptions in seismic response analysis has recently been a topic of great interest in the community. For specific site response analysis, numerical simulations are carried out to model the dynamic process of seismic waves propagating and scattering in the subsurface strata. With development of modeling capacity, great efforts have been taken to evaluate quantitatively the complex 2D and 3D effects on seismic site response.
This book provides a guide to understanding of seismograms for graduate students, researchers, professionals in academia and the petroleum industry.
Significant progress in our understanding of the Earth's structure and functioning is dependent on new and original observations. However, these observations cannot be interpreted in a quantitative way without tools to model them, and developing adequate modelling methods is also a prerequisite for progress. Seismological raw data in the 21st century are mostly three-component broadband recordings, and require advanced numerical tools to be modelled, especially if lateral variations in the model are accounted for in addition to the radial stratification of the Earth. Considerable progress has been made concerning modelling of elastic waves in laterally heterogeneous structures in the last decades, taking advantage of the development of computer power. The number of articles related to new developments of diverse methods is enormous and it can be very difficult for newcomers to get an overview of the different methods available, and to be able to find which method is most appropriate for his or her applications. This book aims at giving introductions and basic reviews of the modelling methods for elastic waves in laterally heterogeneous structures which are most commonly used in contemporary seismology, or may have great potential for the future.