Inverse theory pdf

Data analysis can be a mathematically complex activity, but the treatment in this volume is carefully designed to emphasize those mathematical techniques that readers will find the most familiar and to systematically introduce less-familiar ones.

Using problems and case studies, along with MATLAB computer code and summaries of methods, the book provides data scientists and engineers in geophysics with the tools necessary to understand and apply mathematical techniques and inverse theory.

Includes material on probability, including Bayesian influence, probability density function and metropolis algorithm Offers detailed discussion of the application of inverse theory to tectonic, gravitational and geomagnetic studies Contains numerous examples, color figures and end-of-chapter homework problems to help readers explore and further understand presented ideas Includes MATLAB examples and problem sets Updated and refined throughout to bring the text in line with current understanding and improved examples and case studies Expanded sections to cover material, such as second-derivation smoothing and chi-squared tests not covered in the previous edition.

This unique textbook provides the foundation for understanding and applying techniques commonly used in geophysics to process and interpret modern digital data. The geophysicist's toolkit contains a range of techniques which may be divided into two main groups: processing, which concerns time series analysis and is used to separate the signal of interest from background noise; and inversion, which involves generating some map or physical model from the data.

These two groups of techniques are normally taught separately, but are here presented together as parts I and II of the book. Part III describes some real applications and includes case studies in seismology, geomagnetism, and gravity. This textbook gives students and practitioners the theoretical background and practical experience, through case studies, computer examples and exercises, to understand and apply new processing methods to modern geophysical datasets.

Parameter Estimation and Inverse Problems, Second Edition provides geoscience students and professionals with answers to common questions like how one can derive a physical model from a finite set of observations containing errors, and how one may determine the quality of such a model. This book takes on these fundamental and challenging problems, introducing students and professionals to the broad range of approaches that lie in the realm of inverse theory.

The authors present both the underlying theory and practical algorithms for solving inverse problems. The authors' treatment is appropriate for geoscience graduate students and advanced undergraduates with a basic working knowledge of calculus, linear algebra, and statistics.

Parameter Estimation and Inverse Problems, Second Edition introduces readers to both Classical and Bayesian approaches to linear and nonlinear problems with particular attention paid to computational, mathematical, and statistical issues related to their application to geophysical problems.

The textbook includes Appendices covering essential linear algebra, statistics, and notation in the context of the subject. Includes appendices for review of needed concepts in linear, statistics, and vector calculus. Accessible to students and professionals without a highly specialized mathematical background. The problems of making inferences about the natural world from noisy observations and imperfect theories occur in almost all scientific disciplines.

This book addresses these problems using examples taken from geophysical fluid dynamics. It focuses on discrete formulations, both static and time-varying, known variously as inverse, state estimation or data assimilation problems.

Starting with fundamental algebraic and statistical ideas, the book guides the reader through a range of inference tools including the singular value decomposition, Gauss-Markov and minimum variance estimates, Kalman filters and related smoothers, and adjoint Lagrange multiplier methods.

The final chapters discuss a variety of practical applications to geophysical flow problems. Discrete Inverse and State Estimation Problems is an ideal introduction to the topic for graduate students and researchers in oceanography, meteorology, climate dynamics, and geophysical fluid dynamics. It is also accessible to a wider scientific audience; the only prerequisite is an understanding of linear algebra.

This book presents state-of-the-art geophysical inverse theory developed in modern mathematical terminology.

The book brings together fundamental results developed by the Russian mathematical school in regularization theory and combines them with the related research in geophysical inversion carried out in the West. It presents a detailed exposition of the methods of regularized solution of inverse problems based on the ideas of Tikhonov regularization, and shows the different forms of their applications in both linear and nonlinear methods of geophysical inversion.

This text is the first to treat many kinds of inversion and imaging techniques in a unified mathematical manner. The book is divided in five parts covering the foundations of the inversion theory and its applications to the solution of different geophysical inverse problems, including potential field, electromagnetic, and seismic methods.

The first part is an introduction to inversion theory. The second part contains a description of the basic methods of solution of the linear and nonlinear inverse problems using regularization. The following parts treat the application of regularization methods in gravity and magnetic, electromagnetic, and seismic inverse problems. The key connecting idea of these applied parts of the book is the analogy between the solutions of the forward and inverse problems in different geophysical methods.

The book also includes chapters related to the modern technology of geophysical imaging, based on seismic and electromagnetic migration. This volume is unique in its focus on providing a link between the methods used in gravity, electromagnetic, and seismic imaging and inversion, and represents an exhaustive treatise on inversion theory. Geophysical Inverse Theory and Applications, Second Edition, brings together fundamental results developed by the Russian mathematical school in regularization theory and combines them with the related research in geophysical inversion carried out in the West.

Unique in its focus on providing a link between the methods used in gravity, electromagnetic, and seismic imaging and inversion, it represents an exhaustive treatise on inversion theory. Presents state-of-the-art geophysical inverse theory developed in modern mathematical terminology—the first to treat many kinds of inversion and imaging techniques in a unified mathematical way.

Provides a critical link between the methods used in gravity, electromagnetic, and seismic imaging and inversion, and represents an exhaustive treatise on geophysical inversion theory. Features more than illustrations, figures, charts and graphs to underscore key concepts.

Reflects the latest developments in inversion theory and applications and captures the most significant changes in the field over the past decade. This publication is designed to provide a practical understanding of methods of parameter estimation and uncertainty analysis. McLeod, J. Bondarenko, N. Cheng, Y. Koyunbakan, H. Value Probl. Wang, W. Yilmaz, E. New Trends Math. Bairamov, E. Filomat 31 17 , — Sadovnichii, V. Hald, O.

Inverse Probl. Law, C. Pinasco, J. Discrete Impuls. A Math. Panakhov, E. Mosazadeh, S. Chen, H. Gulsen, T. A1 65 2 , 23—36 This text is the first to treat many kinds of inversion and imaging techniques in a unified mathematical manner.

The first part is an introduction to inversion theory. The second part contains a description of the basic methods of solution of the linear and nonlinear inverse problems using regularization. The following parts treat the application of regularization methods in gravity and magnetic, electromagnetic, and seismic inverse problems. The key connecting idea of these applied parts of the book is the analogy between the solutions of the forward and inverse problems in different geophysical methods.

The book also includes chapters related to the modern technology of geophysical imaging, based on seismic and electromagnetic migration. This volume is unique in its focus on providing a link between the methods used in gravity, electromagnetic, and seismic imaging and inversion, and represents an exhaustive treatise on inversion theory.

Concise, self-contained survey of data processing methods in geophysics and other sciences, for upper level science and engineering students. This collection of papers on geophysical inversion contains research and survey articles on where the field has been and where it's going, and what is practical and what is not. Topics covered include seismic tomography, migration and inverse scattering. Geophysical measurements are not done for the sake of art only. The ultimategoal is to solve some well-defined geological, tectonical or structural problems.

For this purpose, the data have to be interpreted, translated, into a physical model of the subsurface. This book describes some ofthe most important common features of different geophysical data sets. The first textbook covering spectral analysis and geophysical data inversion for undergraduate and graduate students.

Modern introduction to seismic data processing demonstrating exploration and global geophysics applications through real data and tutorial examples that can be demonstrated with the instructor's software of choice. The underlying physics and mathematics of analysis methods is presented, showing students the limitations and potential for creating models of the sub-surface.

Seabed logging SBL gathers the electromagnetic methods of marine subsoil exploration and more specifically those dedicated to the exploration of oil and gas at sea. Proposing a serious index of the presence of hydrocarbons , electromagnetic SBL coupled with seismic reflection survey is probably the first reliable method for direct detection of hydrocarbons.

Complementing the structural concepts of oil exploration used since the s, the SBL now radically modifies the approach and the philosophies of exploration especially those then including drilling and well logging activities. Electromagnetic Seabed Logging: a new tool for oil and gas prospecting, which original publication in French was in , presents these methods, its principles, advantages, limitations, instruments, modeling and applications.

It is also designed to be a tool for a reflection on the use of electromagnetic energy for the exploration in a conductive medium as sea water thus setting the theoretical and practical limits of these investigations for future developments. This book is intended of course for the geophysicists and the petroleum geologists, but also for the earth scientists, the reservoir engineers and the log analysts.

This book focuses on the the application of hydrogeophysical methods to the understanding of hydrological processes and environmental problems dealing with the flow of water and the transport of solutes and contaminants.

Taking a process-driven approach, the book offers a series of process-driven chapters, each authored by leading experts.