期刊
JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA
卷 125, 期 1, 页码 164-174出版社
ACOUSTICAL SOC AMER AMER INST PHYSICS
DOI: 10.1121/1.3021312
关键词
eigenvalues and eigenfunctions; elastic waves; Green's function methods; inhomogeneous media; white noise; Wigner distribution
资金
- Pole Grenoblois d'Etudes et de Recherche pour la Prevention des Risques Naturels
- French Agence Nationale de la Recherche (ANR) [SIS-DIF (JCJC08_313906)]
The spectral decomposition of the elastic wave operator in a layered isotropic half-space is derived by means of standard functional analysis methods. Particular attention is paid to the coupled P-SV waves. The problem is formulated directly in terms of displacements which leads to a 2x2 Sturm-Liouville system. The resolvent kernel (Green's function) is expressed in terms of simple plane-wave solutions. Application of Stone's formula leads naturally to eigenfunction expansions in terms of generalized eigenvectors with oscillatory behavior at infinity. The generalized eigenfunction expansion is employed to define a diffuse field as a white noise process in modal space. By means of a Wigner transform, we calculate vertical to horizontal kinetic energy ratios in layered media, as a function of depth and frequency. Several illustrative examples are considered including energy ratios near a free surface, in the presence of a soft layer. Numerical comparisons between the generalized eigenfunction summation and a classical locked-mode approximation demonstrate the validity of the approach. The impact of the local velocity structure on the energy partitioning of a diffuse field is illustrated.
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