Published:January 01, 2008
Propagating waves represent an aspect of more general forms of motion that can be described by the exact equation of continuum mechanics. Although a study of general forms of motion is practically possible only by means of numerical methods, their wave aspects can be expressed in terms of an elementary theory. The basic concepts of such a theory were established as a generalization of experimental facts long before mechanics itself appeared as a branch of mathematical physics. Only much later were they derived as consequences of the exact equations of mechanics. This system of concepts has an important property — it allows us to build a simple wave-propagation theory common to waves of any kind. That is why the basic concepts of wave-propagation theory can be introduced by considering the simplest equation of motion and then generalizing to more complex situations. Here we consider these concepts in the case of the scalar wave equation where f* and F* are functions of space coordinates (x1, x2, x3) and time t and c is a function of space coordinates only.
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Edge and Tip Diffractions: Theory and Applications in Seismic Prospecting
In Edge and Tip Diffractions: Theory and Applications in Seismic Prospecting (SEG Geophysical Monograph Series No. 14), the theoretical framework of the edge and tip wave theory of diffractions has been elaborated from fundamental wave mechanics. Seismic diffractions are inevitable parts of the recorded wavefield scattered from complex structural settings and thus carry back to the surface information that can be exploited to enhance the resolution of details in the underground. The edge and tip wave theory of diffractions provides a physically sound and mathematically consistent method of computing diffraction phenomena in realistic geologic models. In this book, theoretical derivations are followed by their numerical implementation and application to real exploration problems. The book was written initially as lecture notes for an internal course in diffraction modeling at Norsk Hydro Research Center, Bergen, Norway, and later was used for a graduate course at Novosibirsk State University in Russia. The material is drawn from several previous publications and from unpublished technical reports. Edge and Tip Diffractions will be of interest to geoscientists, engineers, and students at graduate and Ph.D. levels.