TY - JOUR

T1 - Response of a Source on Top of a Vertically Stratified Half-Space

AU - Chew, Weng Cho

N1 - Copyright:
Copyright 2015 Elsevier B.V., All rights reserved.

PY - 1985/6

Y1 - 1985/6

N2 - The solution of the response of a source on top of a horizontally stratified half-space is well-known. However, when the half-space is vertically stratified, the problem can only be solved with numerical methods like the finite element method. Here a semi-analytic approach to solve such a problem is presented. The three-dimensional variation of the problem is reduced to two-dimensional variation by Fourier transform in one coordinate variable. The remaining two-dimensional problem is solved by finding the eigensolution in each of the half-spaces. The eigensolutions of each region are found from the partial differential equation directly using the same basis set of expansion functions. This makes the calculation of the reflection and transmission operators very efficient. The reflection and transmission operators account for the mode-conversion, reflection, and transmission of the waves. With the reflection and transmission operators, the field everywhere can be calculated. The solution reduces to that of the Sommerfeld's half-space problem when the two half-spaces are homogeneous.

AB - The solution of the response of a source on top of a horizontally stratified half-space is well-known. However, when the half-space is vertically stratified, the problem can only be solved with numerical methods like the finite element method. Here a semi-analytic approach to solve such a problem is presented. The three-dimensional variation of the problem is reduced to two-dimensional variation by Fourier transform in one coordinate variable. The remaining two-dimensional problem is solved by finding the eigensolution in each of the half-spaces. The eigensolutions of each region are found from the partial differential equation directly using the same basis set of expansion functions. This makes the calculation of the reflection and transmission operators very efficient. The reflection and transmission operators account for the mode-conversion, reflection, and transmission of the waves. With the reflection and transmission operators, the field everywhere can be calculated. The solution reduces to that of the Sommerfeld's half-space problem when the two half-spaces are homogeneous.

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U2 - 10.1109/TAP.1985.1143634

DO - 10.1109/TAP.1985.1143634

M3 - Article

AN - SCOPUS:0022082478

VL - 33

SP - 649

EP - 654

JO - IEEE Transactions on Antennas and Propagation

JF - IEEE Transactions on Antennas and Propagation

SN - 0018-926X

IS - 6

ER -