Overview
Provides a tutorial on the rational approximation methods for parabolic equations
Demonstrates applicability to a wide range of geophysical phenomena
Written by experts responsible for many key innovations in the field
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Table of contents (4 chapters)
Keywords
- parabolic wave equation
- rational approximation method
- split-step Padé solution
- three-dimensional parabolic equation
- elastic wave equation
- elastic parabolic equation
- anisotropic elastic wave
- acoustic wave equation
- poro-elastic wave equation
- poro-elastic parabolic equation
- partial differential equations
About this book
The book covers progress made following the parabolic equation’s ascendancy in geophysics. It begins with the necessary preliminaries on the elliptic wave equation and its analysis from which the parabolic wave equation is derived and introduced. Subsequently, the authors demonstrate the use of rational approximation techniques, the Padé solution in particular, to find numerical solutions to the energy-conserving parabolic equation, three-dimensional parabolic equations, and horizontal wave equations.
The rest of the book demonstrates applications to seismology, ocean acoustics, and beyond, with coverage of elastic waves, sloping interfaces and boundaries, acousto-gravity waves, and waves in poro-elastic media. Overall, it will be of use to students and researchers in wave propagation, ocean acoustics, geophysical sciences and more.
Authors and Affiliations
About the authors
William L. Siegmann was born in Pittsburgh, Pennsylvania. He received the B.S. and M.S. degrees in mathematics and the Ph.D. in applied mathematics from the Massachusetts Institute of Technology. From 1968 to 1970, he was a Postdoctoral Fellow in the Department of Mechanics at Johns Hopkins University. Since 1970, he has been in the Department of Mathematical Sciences at Rensselaer Polytechnic Institute. His research interests are ocean acoustics and wave propagation methods. Dr. Siegmann is a member of the IEEE Ocean Engineering Society, the Acoustical Society of America, and The Oceanography Society.
Bibliographic Information
Book Title: Parabolic Wave Equations with Applications
Authors: Michael D. Collins, William L. Siegmann
DOI: https://doi.org/10.1007/978-1-4939-9934-7
Publisher: Springer New York, NY
eBook Packages: Physics and Astronomy, Physics and Astronomy (R0)
Copyright Information: Springer Science+Business Media, LLC, part of Springer Nature 2019
Hardcover ISBN: 978-1-4939-9932-3Published: 05 November 2019
eBook ISBN: 978-1-4939-9934-7Published: 04 November 2019
Edition Number: 1
Number of Pages: IX, 135
Number of Illustrations: 37 b/w illustrations, 37 illustrations in colour
Topics: Acoustics, Numerical Analysis, Oceanography, Partial Differential Equations, Geophysics/Geodesy