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Calculation of the Characteristics of Traveling Waves in Layered Media

Calculation of the Characteristics of Traveling Waves in Layered Media A new method is considered for the calculation of traveling-wave characteristics in a layered medium. It is mainly based on the transfer-matrix method [2–10] and the generalized reflection-transmission coefficient (GRTC) method [11–14] for the calculation of characteristics. Introducing an impedance tensor of rank 2, Ẑ (z), in the boundary-value stress problem and utilizing in this way the boundary conditions and the Lame equation, we obtain a system of differential equations which is solved by the fourth-order Runge-Kutta method. Specifying a model of the layered medium in terms of known constants, we find the traveling-wave characteristic γ as a function of frequency ω . Given γ, we easily calculate the dispersion curves, which closely fit the GRTC method. Compared with the GRTC method, the impedance-tensor method fully solves the dispersion curve of the normal-mode traveling waves, and it is applicable to both a homogeneous planar Earth model and a model with a slow layer. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Computational Mathematics and Modeling Springer Journals

Calculation of the Characteristics of Traveling Waves in Layered Media

Computational Mathematics and Modeling , Volume 29 (3) – Jun 1, 2018

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Publisher
Springer Journals
Copyright
Copyright © 2018 by Springer Science+Business Media, LLC, part of Springer Nature
Subject
Mathematics; Mathematical Modeling and Industrial Mathematics; Computational Mathematics and Numerical Analysis; Applications of Mathematics; Optimization
ISSN
1046-283X
eISSN
1573-837X
DOI
10.1007/s10598-018-9409-2
Publisher site
See Article on Publisher Site

Abstract

A new method is considered for the calculation of traveling-wave characteristics in a layered medium. It is mainly based on the transfer-matrix method [2–10] and the generalized reflection-transmission coefficient (GRTC) method [11–14] for the calculation of characteristics. Introducing an impedance tensor of rank 2, Ẑ (z), in the boundary-value stress problem and utilizing in this way the boundary conditions and the Lame equation, we obtain a system of differential equations which is solved by the fourth-order Runge-Kutta method. Specifying a model of the layered medium in terms of known constants, we find the traveling-wave characteristic γ as a function of frequency ω . Given γ, we easily calculate the dispersion curves, which closely fit the GRTC method. Compared with the GRTC method, the impedance-tensor method fully solves the dispersion curve of the normal-mode traveling waves, and it is applicable to both a homogeneous planar Earth model and a model with a slow layer.

Journal

Computational Mathematics and ModelingSpringer Journals

Published: Jun 1, 2018

References