Trégourès Nicolas P, van Tiggelen Bart A
Laboratoire de Physique et Modélisation des Milieux Condensés, CNRS/Université Joseph Fourier, Boîte Postale 166, 38042 Grenoble Cedex 09, France.
Phys Rev E Stat Nonlin Soft Matter Phys. 2002 Sep;66(3 Pt 2B):036601. doi: 10.1103/PhysRevE.66.036601. Epub 2002 Sep 3.
A theory for multiple scattering of elastic waves is presented in a heterogeneous plate bounded by two flat free surfaces, whose horizontal size is infinite and whose transverse size is smaller than the mean free path of the waves. We derive a time-dependent, quasi-two-dimensional radiative transfer equation (i.e., two horizontal dimensions with a finite number of vertical mode) that describes the coupling of the eigenmodes of the layer (surface Rayleigh waves, shear horizontal waves, and Lamb waves). The fundamentally different element is that the traction-free boundary conditions are treated on the level of the wave equation, whereas at the same time elastic transfer can be considered over macroscopic horizontal distances. Expressions are found that relate the small-scale fluctuations to the lifetime of the modes and to their mode-coupling rates. We discuss the diffusion approximation that simplifies the mathematics of this model significantly, and which should apply at large lapse times. Finally, this model facilitates a study of coherent backscattering near the plate surface for different sources and for different detection configurations.
本文提出了一种弹性波多重散射理论，该理论适用于由两个平坦自由表面界定的非均匀板，其水平尺寸为无限大，横向尺寸小于波的平均自由程。我们推导了一个与时间相关的准二维辐射传输方程（即具有有限数量垂直模式的两个水平维度），该方程描述了层的本征模式（表面瑞利波、水平剪切波和兰姆波）之间的耦合。根本不同的一点是，在波动方程层面处理无牵引边界条件，而同时可以考虑在宏观水平距离上的弹性传输。我们找到了将小尺度涨落与模式寿命及其模式耦合率联系起来的表达式。我们讨论了扩散近似，它显著简化了该模型的数学，并且应该在大延迟时间适用。最后，该模型有助于研究不同源和不同探测配置下板表面附近的相干背散射。
