Geophysical Data Analysis

Discrete Inverse Theory

Author: William Menke

Publisher: Academic Press

ISBN: 0123971608

Category: Mathematics

Page: 293

View: 1198

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Please use extracts from reviews of first edition Key Features * Updated and thoroughly revised edition * additional material on geophysical/acoustic tomography * Detailed discussion of application of inverse theory to tectonic, gravitational and geomagnetic studies

Seismology and Plate Tectonics

Author: David Gubbins

Publisher: Cambridge University Press

ISBN: 9780521379953

Category: Science

Page: 339

View: 2150

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This introduction to seismological theory and the principles of plate tectonics also develops a practical approach to the interpretation of seismograms for physicists and mathematicians as well as geologists.

Geophysical Data Analysis

Discrete Inverse Theory

Author: William Menke

Publisher: Elsevier

ISBN: 9780080507323

Category: Science

Page: 289

View: 5462

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Please use extracts from reviews of first edition Key Features * Updated and thoroughly revised edition * additional material on geophysical/acoustic tomography * Detailed discussion of application of inverse theory to tectonic, gravitational and geomagnetic studies

Geophysical Data Analysis: Understanding Inverse Problem Theory and Practice

Author: Max A. Meju

Publisher: SEG Books

ISBN: 156080257X

Category: Geophysics

Page: 296

View: 9443

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This publication is designed to provide a practical understanding of methods of parameter estimation and uncertainty analysis. The practical problems covered range from simple processing of time- and space-series data to inversion of potential field, seismic, electrical, and electromagnetic data. The various formulations are reconciled with field data in the numerous examples provided in the book; well-documented computer programmes are also given to show how easy it is to implement inversion algorithms.

Inverse Problem Theory and Methods for Model Parameter Estimation

Author: Albert Tarantola

Publisher: SIAM

ISBN: 9780898717921

Category: Engineering

Page: 342

View: 3962

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While the prediction of observations is a forward problem, the use of actual observations to infer the properties of a model is an inverse problem. Inverse problems are difficult because they may not have a unique solution. The description of uncertainties plays a central role in the theory, which is based on probability theory. This book proposes a general approach that is valid for linear as well as for nonlinear problems. The philosophy is essentially probabilistic and allows the reader to understand the basic difficulties appearing in the resolution of inverse problems. The book attempts to explain how a method of acquisition of information can be applied to actual real-world problems, and many of the arguments are heuristic.

Deconvolution and Inverse Theory

Application to Geophysical Problems

Author: V. Dimri

Publisher: Elsevier

ISBN: 1483291375

Category: Science

Page: 249

View: 7021

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This is the first study to present simultaneously both deconvolution and inversion, two powerful tools of data analysis. Featured within this volume are various geophysical convolution models and a treatment of deconvolution for a time-varying signal. The single channel time-varying deconvolution is shown equivalent to the multichannel time-invariant deconvolution, thus a formalism and associated algorithms can handle both. Inverse theory as well as various inversion schemes are presented on the basis of a relationship between a small perturbation to the model and its effects on the observation. The information theory inversion scheme is discussed, and several types of norm of minimization presented. Additionally, concepts and results of inverse theory are applied to design a new deconvolution operator for estimating magnetization and density distribution, and the constraint of the Backus-Gilbert formalism of inverse theory is used to design a new prediction error filter for maximum entropy spectral estimates. Maximum likelihood, another high resolution method is also presented. This volume can be utilised as a graduate-level text for courses in Geophysics. Some chapters will be of use for graduate courses in Applied Mathematics, Applied Statistics, and Oceanography.

An Introduction to Data Analysis and Uncertainty Quantification for Inverse Problems

Author: Luis Tenorio

Publisher: SIAM

ISBN: 1611974925

Category: Mathematics

Page: 269

View: 2113

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Inverse problems are found in many applications, such as medical imaging, engineering, astronomy, and geophysics, among others. To solve an inverse problem is to recover an object from noisy, usually indirect observations. Solutions to inverse problems are subject to many potential sources of error introduced by approximate mathematical models, regularization methods, numerical approximations for efficient computations, noisy data, and limitations in the number of observations; thus it is important to include an assessment of the uncertainties as part of the solution. Such assessment is interdisciplinary by nature, as it requires, in addition to knowledge of the particular application, methods from applied mathematics, probability, and statistics. This book bridges applied mathematics and statistics by providing a basic introduction to probability and statistics for uncertainty quantification in the context of inverse problems, as well as an introduction to statistical regularization of inverse problems. The author covers basic statistical inference, introduces the framework of ill-posed inverse problems, and explains statistical questions that arise in their applications. An Introduction to Data Analysis and Uncertainty Quantification for Inverse Problems÷includes many examples that explain techniques which are useful to address general problems arising in uncertainty quantification, Bayesian and non-Bayesian statistical methods and discussions of their complementary roles, and analysis of a real data set to illustrate the methodology covered throughout the book.