Parabolic Wave Equations with Applications
This book introduces parabolic wave equations, their key methods of numerical solution, and applications in seismology and ocean acoustics. The parabolic equation method provides an appealing combination of accuracy and efficiency for many nonseparable wa
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arabolic Wave Equations with Applications
Parabolic Wave Equations with Applications
Michael D. Collins • William L. Siegmann
Parabolic Wave Equations with Applications
Michael D. Collins Naval Research Laboratory Washington, DC, USA
William L. Siegmann Department of Mathematical Sciences Rensselaer Polytechnic Institute Troy, NY, USA
ISBN 978-1-4939-9932-3 ISBN 978-1-4939-9934-7 https://doi.org/10.1007/978-1-4939-9934-7
(eBook)
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Contents
1
Basic Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 The Elliptic Wave Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2.1 The Frequency Domain . . . . . . . . . . . . . . . . . . . . . . . . 1.2.2 The Uncoupled Azimuth Approximation . . . . . . . . . . . . 1.2.3 The Far-Field Equation . . . . . . . . . . . . . . . . . . . . . . . . 1.2.4 Source Conditions and Transmission Loss . . . . . . . . . . . 1.2.5 Lossy Media and Absorbing Layers . . . . . . . . . . . . . . . 1.2.6 The Normal Mode Solution . . . . . . . . . . . . . . . . . . . . . 1.2.7 The Spectral Solution . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3 The Parabolic Wave Equation . . . . . . . . . . . . . . . . . . . . . . . . . 1.3.1 Derivation by Factoring the Operator . . . . . . . . . . . . . . 1.3.2 Derivation with Normal Modes . . . . . . . . . . . . . . . . . . . 1.4 Depth Numerics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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