Seismic Migration: Imaging of Acoustic Energy by Wave Field Extrapolation derives the migration theory from first principles. This book also obtains a formulated forward modeling and migration theory by introducing the propagation matrices and the scattering matrix. The book starts by presenting the basic results from vector analysis, such as the scalar product, gradient, curl, and divergence. It also describes the theorem of Stokes, theorem of Gause and the Green's theorem. The book also deals with discrete spectral analysis, two-dimensional Fourier theory and plane wave analysis. It also describes the wave theory, including the plane waves and k-f diagram, spherical waves, and cylindrical waves. This book explores the forward problem and the inward problem of the wave field extrapolation, as well as the modeling by wave field extrapolation. Furthermore, the book explains the migration in the wave number-frequency domain. It also includes the summation approach and finite-difference approach to migration, as well as a comparison between the different approaches to migration. Finally, the book offers the limits of lateral resolution as the last chapter.

Seismic Migration: Imaging of Acoustic Energy by Wave Field Extrapolation, Second Edition, Volume A: Theoretical Aspects covers the theoretical aspects of seismic migration techniques. This volume is divided into 11 chapters that consider the concept of propagation and scattering matrices. This book begins with a presentation of a selection of concepts and properties of seismic migration from vector analysis. These topics are followed by considerable chapters on the mathematical aspects of migration, including discrete spectral analysis, two-dimensional Fourier transforms, and wave theory. The subsequent chapters describe the derivation of the Kirchhoff integral for upward traveling wave field and wave field extrapolation for downward traveling source waves and upward traveling reflected waves. These chapters also propose a matrix formulation to represent single seismic record and multi-record data sets, along with different modeling algorithms. A chapter examines inverse wave field extrapolation, in which the medium must be horizontally layered, the layers being homogeneous. The book ends with a summary and comparison of different approaches to seismic migration.

An indispensable guide to 3-D seismic data for graduate students and petroleum industry professionals.

Extrapolation of seismic waves from the earth's surface to any level in the subsurface plays an essential role in many advanced seismic processing schemes, such as migration, inverse scattering and redatuming. At present these schemes are based on the acoustic wave equation. This means not only that S-waves (shear waves) are ignored, but also that P-waves (compressional waves) are not handled correctly. In the seismic industry there is an important trend towards multi-component data acquisition. For processing of multi-component seismic data, ignoring S-waves can no longer be justified. Wave field extrapolation should therefore be based on the full elastic wave equation.In this book the authors review acoustic one-way extrapolation of P-waves and introduce elastic one-way extrapolation of P- and S-waves. They demonstrate that elastic extrapolation of multi-component data, decomposed into P- and S-waves, is essentially equivalent to acoustic extrapolation of P-waves. This has the important practical consequence that elastic processing of multi-component seismic data need not be significantly more complicated than acoustic processing of single-component seismic data. This is demonstrated in the final chapters, which deal with the application of wave field extrapolation in the redatuming process of single- and multi-component seismic data. Geophysicists, and anyone who is interested in a review of acoustic and elastic wave theory, will find this book useful. It is also a suitable textbook for graduate students and those following courses in elastic wave field extrapolation as each subject is introduced in a relatively simple manner using the scalar acoustic wave equation. In the chapters on elastic wave field extrapolation the formulation, whenever possible, is analogous to that used in the chapters on acoustic wave field extrapolation. The text is illustrated throughout and a bibliography and keyword index are provided.

Providing a pictorial presentation of the basic principles of Kirchhoff-type imaging and proceeding to a comprehensive treatment of its kinematic and dynamic aspects, this book is a valuable addition for anyone interested in the theory and practices of seismic data processing for imaging and parameter estimation with all its attendant processes.

Part 1: SCATTERING OF WAVES BY MACROSCOPIC TARGET -- Interdisciplinary aspects of wave scattering -- Acoustic scattering -- Acoustic scattering: approximate methods -- Electromagnetic wave scattering: theory -- Electromagnetic wave scattering: approximate and numerical methods -- Electromagnetic wave scattering: applications -- Elastodynamic wave scattering: theory -- Elastodynamic wave scattering: Applications -- Scattering in Oceans -- Part 2: SCATTERING IN MICROSCOPIC PHYSICS AND CHEMICAL PHYSICS -- Introduction to direct potential scattering -- Introduction to Inverse Potential Scattering -- Visible and Near-visible Light Scattering -- Practical Aspects of Visible and Near-visible Light Scattering -- Nonlinear Light Scattering -- Atomic and Molecular Scattering: Introduction to Scattering in Chemical -- X-ray Scattering -- Neutron Scattering -- Electron Diffraction and Scattering -- Part 3: SCATTERING IN NUCLEAR PHYSICS -- Nuclear Physics -- Part 4: PARTICLE SCATTERING -- State of the Art of Peturbative Methods -- Scattering Through Electro-weak Interactions (the Fermi Scale) -- Scattering Through Strong Interactions (the Hadronic or QCD Scale) -- Part 5: SCATTERING AT EXTREME PHYSICAL SCALES -- Scattering at Extreme Physical Scales -- Part 6: SCATTERING IN MATHEMATICS AND NON-PHYSICAL SCIENCES -- Relations with Other Mathematical Theories -- Inverse Scattering Transform and Non-linear Partial Differenttial Equations -- Scattering of Mathematical Objects.

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. 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. It's the first book of its kind 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. 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.Written by one of the world's foremost experts, this work is widely recognized as the ultimate researcher's reference on geophysical inverse theory and its practical scientific applications. - 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 300 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