MODELING SURFACE-WAVES IN ANISOTROPIC STRUCTURES-I - THEORY

Surface-wave theory in generally-anisotropic laterally-homogeneous med ia is partially reformulated in order to obtain intuitively-expected e xtensions of classic body-wave ideas such as Maslov plane-wave summati on, the geometrical-ray/WKBJ limit and source-receiver reciprocity. Th is is done using the 'reversal' symmetry of Chapman [Chapman, C.H., 19 94. Reflection/transmission coefficient reciprocities in anisotropic m edia. Geophys. J. Int. 116, 498-501] to generalize the point-source tr eatment of Kennett [Kennett, B.L N., 1983. Seismic Wave Propagation in Stratified Media. Cambridge Univ. Press, Cambridge, UK] to a stack of anisotropic layers with complex elastic parameters, lateral slowness and frequency. The 2D-integral representation over horizontal slowness es is reduced by residues to a 1D integral over each mode's slowness o r dispersion curve at fixed frequency and this may be considered a 1D Maslov summation over local plane waves tangential to the phase front. The residue calculation involves a modified form of the usual variati onal principle, in which the Lagrangian now contains reversed modes. T he 1D slowness integral may be reduced by stationary-phase arguments t o the geometrical-ray or WKBJ limit, provided the dispersion-surface c urvature does not vanish. This limit satisfies reciprocity, as the rev ersal symmetry shows. Dimples on the dispersion surface will correspon d to folds on the phase front and multiple arrivals. An appendix conta ins a discussion of orthogonality of the surface-wave modes in relatio n to the various wave-equation symmetries. (C) 1997 Elsevier Science B .V.