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/lp/springer_journal/calculation-of-the-characteristics-of-traveling-waves-in-layered-media-10i1TSemg0
- 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 Modeling – Springer Journals
Published: Jun 1, 2018