Guided wave propagation across sharp lateral heterogeneities: the complete wavefield at plane vertical discontinuities

Abstract

S U M M A R Y 3-D wave propagation in a waveguide composed of laterally homogeneous partitions separated by vertical interfaces is treated in an exact manner. In each laterally homogeneous subregion, the wavefield is represented by Love-and Rayleigh-type modes, combined in such a way that displacements and tractions are continuous at the vertical discontinuities. In order t o achieve exact continuity at the interfaces, near-field modes which exponentially decay in the propagation direction and are associated to fully complex wavenumbers, must be included in the modal representation. The expansion coefficients of the mode series are computed directly by exploiting orthogonality relations between modes of different type, order and propagation direction. Since the boundary conditions at the discontinuities are satisfied exactly, the resulting expansion of the wavefield is valid even on the interfaces themselves. Numerical results are presented for a single vertical discontinuity and a lamella.

Remarks on the travelling wave decomposition

“…Hence, evanescent waves with imaginary phase velocity, of which there are generally in®nitely many if there are any at all, cannot be admitted in a spherical geometry. This notion is at odds with the fact that other geometries that are bounded in one dimension admit evanescent wave solutions travelling in an orthogonal direction, for example, elastic wave propagation parallel to the axis of a cylinder (Love 1944, article 200;Gray & MacRobert 1952, Section XVI.3) or parallel to a plane-layered medium bounded by two planes (Malischewsky 1987;Nolet et al 1989;Stange & Friederich 1992). The mathematical form of the minor arc (®rst-arriving) term approaches the plane-layered case as the radius of curvature of the sphere approaches in®nity, and the question arises as to why evanescent waves should be present in the latter but not in the former.…”

Approximation of surface wave mode conversion at a passive continental margin by a mode-matching technique

“…Alsop 1966;McGarr & Alsop 1967;Malischewsky 1976Malischewsky , 1987Meier et al 1997a). Stange & Friederich (1992a) described a mode-matching technique in a closed waveguide for a sequence of vertical discontinuities and included modes with complex wavenumbers in order to obtain a complete mode set. Stange & Friederich (1992a) described a mode-matching technique in a closed waveguide for a sequence of vertical discontinuities and included modes with complex wavenumbers in order to obtain a complete mode set.…”

Guided wave propagation across sharp lateral heterogeneities: the complete wavefield at a cylindrical inclusion

“…In most textbooks the theory of surface waves is developed for a layered halfspace. However, when dealing with the propagation of surface waves across a plane vertical discontinuity (Stange & Friederich 1992, henceforth referred to as SF1) we had to accept the fact that on a layered halfspace it is impossible to obtain an exact solution of this problem by mode-matching techniques. The simple reason is that the surface wave modes for a layered halfspace with bounded shear wave velocity at large depth do not form a complete set.…”