ON THE ORTHOGONALITY OF SURFACE-WAVE EIGENFUNCTIONS IN CYLINDRICAL COORDINATES

被引：8

作者：

BOSTOCK, MG

机构：

[1] Research School of Earth Sciences, Australian National University, Canberra, Australian Capital Territory, 2601

来源：

GEOPHYSICAL JOURNAL INTERNATIONAL | 1990年 / 103卷 / 03期

关键词：

cylindrical coordinates; eigenfunction; normalization; orthogonality; surface waves;

D O I：

10.1111/j.1365-246X.1990.tb05688.x

中图分类号：

P3 [地球物理学]; P59 [地球化学];

学科分类号：

0708 ; 070902 ;

摘要：

The orthogonality of the Rayleigh wave eigenfunctions in laterally homogeneous, plane‐stratified media is guaranteed by the structure of the ordinary differential equations describing elastic wave motion in cylindrical coordinates. This coupled first‐order system is identical to that which characterizes 2‐D plane wave propagation in a Cartesian coordinate reference frame. The orthogonality relation in 2‐D can also be derived from energy considerations; however, an analogous argument in cylindrical coordinates has not hitherto been made. We derive the orthogonality relations for Rayleigh waves in 3‐D from energy considerations and demonstrate that the standard (2‐D) expression is, in fact, the generalization of a slightly more specific form. In addition, the cylindrical coordinate formulation permits the derivation of a functional orthogonality relation between Love and Rayleigh waves. The normalization of Love and Rayleigh wave eigenfunctions in cylindrical coordinates is shown to be related to the energy transport of a given outgoing Fourier–Bessel component across any surface which wholly encompasses the z‐axis. Copyright © 1990, Wiley Blackwell. All rights reserved

引用

页码：763 / 767

页数：5

共 6 条

[1]

Aki K., Richards P.G., Quantitative Seismology, Theory and Methods, pp. 298-306, (1980)

[2]

Herrara I., On a method to obtain a Green's function for a multi‐layered half space, Bull. seism. Soc. Am., 54, pp. 1087-1096, (1964)

[3]

Kennett B.L.N., Seismic Wave Propagation in Stratified Media, (1983)

[4]

Malischewsky P., Orthonormalization of plane surface and body waves, Gerl. Beitr. Geophys., 79, pp. 468-474, (1970)

[5]

McGarr A., Alsop L.E., Transmission and reflection of Rayleigh Waves at vertical boundaries, Journal of Geophysical Research, 72, pp. 2169-2180, (1967)

[6]

Takeuchi H., Saito M., Kobayashi N., Study of shear velocity distribution in the upper mantle by mantle Rayleigh and Love waves, Journal of Geophysical Research, 67, pp. 2831-2839, (1962)

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