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Mathematics of Multidimensional Seismic Imaging, Migration and Inversion

In the last 40 years geophysicists have found that it is possible to construct images and even determine important physical characteristics of rocks that can yield information about oil and gas bearing structures in the earth. To make these images and extract this information requires the application of an advanced understanding of the mathematical physics of wave propagation. The oil and gas industry labels a major collection of the necessary seismic data processing methods by the name seismic "migration". This text ist the first to treat many kinds of migration in a unified mahtematical way. The audience is mathematically oriented geophysicists or applied mathematicians working in the field of "inverse scattering imaging". The text can serve as a bridge between the applied math and geophysics community by presenting geophysicists with a practical introduction to advanced engineering mathematics, while presenting mathematicians with a window into the world of the mathematically sophistiated geophysicist.
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Table of Contents

Preface.- Multi-Dimensional Seismic Inversion.- The One- Dimensional Inverse Problem.- Inversion in Higher Dimensions.- Large-Wavenumber Fourier Imaging.- Inversion in Heterogeneous Media.- Two-and-One Half Dimensional Inversion.- The General Theory of Data Mapping.- Distribution Theory.- The Fourier Transform of Causal Functions.- Dimensional vs. Dimensionless Variables.- An Example of Ill-Posedness.-An Elementary Introduction to Ray Theory.- Author Index.- Subject Index.


From the reviews: PURE APPLIED GEOPHYSICS "The presentation is exceptionally good, with a systematic progression from simpler to more sophisticated problems. This is very helpful to those readers not familiar with the subject...Every seismological term and every necessary mathematical concept is explained so that the book is actually self-contained...The mathematics are...kept are at a sufficiently low level of mathematical sophistication to make the book easy for its intended readership...Another advantage of the book is a careful choice of the variables...Exercises stimulate the reader's initiative and inquisitiveness. This is rather unusual in geophysical literature...Even for seasoned seismologists the book will provide an incentive to upgrade their know-how."

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