Chapter 9 The Rotational Transform Of Wavefield
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Introduction to Computer Holography
This book covers basic- to expert-level applications in computer holography, a strong candidate for the ultimate 3D display technology. The computer holography developed in the course of the past decade represents the basis of wave optics. Accordingly, the book presents the basic theory of wave optics and practical techniques for handling wave fields by means of the fast Fourier transform. Numerical techniques based on polygons, as well as mask-based techniques, are also presented for calculating the optical fields of virtual 3D models with occlusion processing. The book subsequently describes simulation techniques for very large-scale optical fields, and addresses the basics and concrete applications of simulation, offering a valuable resource for readers who need to employ it in the context of developing optical devices. To aid in comprehension, the main content is complemented by numerous examples of optical fields and photographs of reconstructed 3D images.
Wave Fields in Real Media
Authored by the internationally renowned José M. Carcione, Wave Fields in Real Media: Wave Propagation in Anisotropic, Anelastic, Porous and Electromagnetic Media examines the differences between an ideal and a real description of wave propagation, starting with the introduction of relevant stress-strain relations. The combination of this relation and the equations of momentum conservation lead to the equation of motion. The differential formulation is written in terms of memory variables, and Biot's theory is used to describe wave propagation in porous media. For each rheology, a plane-wave analysis is performed in order to understand the physics of wave propagation. This book contains a review of the main direct numerical methods for solving the equation of motion in the time and space domains. The emphasis is on geophysical applications for seismic exploration, but researchers in the fields of earthquake seismology, rock acoustics, and material science - including many branches of acoustics of fluids and solids - may also find this text useful. New to this edition: This new edition presents the fundamentals of wave propagation in Anisotropic, Anelastic, Porous Media while also incorporating the latest research from the past 7 years, including that of the author. The author presents all the equations and concepts necessary to understand the physics of wave propagation. These equations form the basis for modeling and inversion of seismic and electromagnetic data. Additionally, demonstrations are given, so the book can be used to teach post-graduate courses. Addition of new and revised content is approximately 30%. Examines the fundamentals of wave propagation in anisotropic, anelastic and porous media Presents all equations and concepts necessary to understand the physics of wave propagation, with examples Emphasizes geophysics, particularly, seismic exploration for hydrocarbon reservoirs, which is essential for exploration and production of oil
3C Seismic and VSP: Converted waves and vector wavefield applications
3C seismic applications provide enhanced rock property characterization of the reservoir that can complement P-wave methods. Continued interest in converted P- to S-waves (PS-waves) and vertical seismic profiles (VSPs) has resulted in the steady development of advanced vector wavefield techniques. PS-wave images along with VSP data can be used to help P-wave interpretation of structure in gas obscured zones, of elastic and fluid properties for lithology discrimination from S-wave impedance and density inversion in unconventional reservoirs, and of fracture characterization and stress monitoring from S-wave birefringence (splitting) analysis. The book, which accompanies the 2016 SEG Distinguished Instructor Short Course, presents an overview of 3C seismic theory and practical application: from fundamentals of PS-waves and VSPs, through to acquisition and processing including interpretation techniques. The emphasis is on unique aspects of vector wavefields, anisotropy, and the important relationships that unify S-waves and P-waves. Various applications and case studies demonstrate image benefits from PS-waves, elastic properties and fluid discrimination from joint inversion of amplitude variations with offset/angle (AVO/A), and VSP methods for anisotropic velocity model building and improved reservoir imaging. The book will be of interest to geophysicists, geologists, and engineers, especially those involved with or considering the use of AVO/A inversion, fracture/stress characterization analyses, or interpretation in gas-obscured reservoirs.