Variational principles for surface wave propagation on a laterally heterogeneous Earth—II. Frequency-domain JWKB theory

Authors

  • Jeroen Tromp,

    1. Department of Geological and Geophysical Sciences, Princeton University, Princeton, New Jersey 08544, USA
    Search for more papers by this author
    • *

      Now at: Department of Earth and Planetary Sciences, Harvard University, Cambridge, Massachusetts 02138, USA.

  • F. A. Dahlen

    1. Department of Geological and Geophysical Sciences, Princeton University, Princeton, New Jersey 08544, USA
    Search for more papers by this author

SUMMARY

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.

Ancillary