Semiclassical analysis of elastic surface waves

Abstract

In this paper, we present a semiclassical description of surface waves or modes in an elastic medium near a boundary, in spatial dimension three. The medium is assumed to be essentially stratified near the boundary at some scale comparable to the wave length. Such a medium can also be thought of as a surficial layer (which can be thick) overlying a half space. The analysis is based on the work of Colin de Verdière on acoustic surface waves. The description is geometric in the boundary and locally spectral "beneath" it. Effective Hamiltonians of surface waves correspond with eigenvalues of ordinary differential operators, which, to leading order, define their phase velocities. Using these Hamiltonians, we obtain pseudodifferential surface wave equations. We then construct a parametrix. Finally, we discuss Weyl's formulas for counting surface modes, and the decoupling into two classes of surface waves, that is, Rayleigh and Love waves, under appropriate symmetry conditions.

References in corpus (1)

• Mathematical models for passive imaging II: Effective Hamiltonians associated to surface waves

Cited by in corpus (6)

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• Rayleigh and Stoneley Waves in Linear Elasticity
• Unique recovery of piecewise analytic density and stiffness tensor from the elastic-wave Dirichlet-to-Neumann map
• Inverse spectral Love problem via Weyl-Titchmarsh function
• Inverse problem for Love waves in a layered, elastic half-space
• Semiclassical inverse spectral problem for elastic Love waves in isotropic media