Now at: Department of Earth and Planetary Sciences, Harvard University, Cambridge, Massachusetts 02138, USA.
Variational principles for surface wave propagation on a laterally heterogeneous Earth—II. Frequency-domain JWKB theory
Article first published online: 2 APR 2007
Geophysical Journal International
Volume 109, Issue 3, pages 599–619, June 1992
How to Cite
Tromp, J. and Dahlen, F. A. (1992), Variational principles for surface wave propagation on a laterally heterogeneous Earth—II. Frequency-domain JWKB theory. Geophysical Journal International, 109: 599–619. doi: 10.1111/j.1365-246X.1992.tb00120.x
- Issue published online: 2 APR 2007
- Article first published online: 2 APR 2007
- Accepted 1991 December 20. Received 1991 October 20; in original form 1991 April 5
- JWKB theory;
- lateral heterogeneity;
- surface waves;
- variational principles
We present a JWKB theory for the propagation of monochromatic Love and Rayleigh waves on a smooth, laterally heterogeneous Earth model. The analysis is based upon a slowly varying Lagrangian which yields local Love and Rayleigh eigenfunctions, local dispersion relations, and transport equations which determine the variation in surface wave amplitude along a ray. The amplitude of a monochromatic Love or Rayleigh wave varies only as a result of geometrical spreading; the amplitude diverges and the phase is shifted by /2 each time the wave passes through a caustic singularity, where the width of the ray tube vanishes. We obtain the JWKB surface wave Green's tensor and derive an explicit expression for the JWKB response to a moment tensor source. The theory allows for slowly varying topography of the Earth's surface and any internal discontinuities, and incorporates the effect of self-gravitation and slight anelasticity on surface wave propagation.