TRANSPORTATION THEORY OF MULTIPLE SCATTERING AND ITS APPLICATION TO SEISMIC CODA WAVES OF IMPULSE SOURCE

The energy distribution of elastic waves in an infinite elastic medium with uniformly and randomly distributed scatterers has been researched. The scattering process is assumed to be isotropic and without conversions between wave types. We get the equation on the distribution of energe density in time and space covering single as well as multiple scattering. Taking physical symmetry of the field into account, it can be simplified. In the case of small earthquakes, the energy source of elastic waves can be assumed as a short pulse emitted isotropically at t=0. The first-order approximate solution in the 3-dimensional space can be obtained, and it is equivalent to Sato's solution for single scattering. In the 2-dimensional space the complete analytical solution has been derived by the mathematical inductance which leads to a conclusion that the codas of surface waves can give the Q-factor related to intrinsic absorption. The equation obtained in this paper is more general.     

多次散射的传输理论及其在脉冲源的地震尾波问题上的应用

本文研究了均匀分布着散射体的无界弹性介质中的弹性波能量分布。研究的散射过程是各向同性的,无波型转换的。导出了能量密度的时间、空间分布方程。假定弹性波能量是在t=0时以短促脉冲的形式由波源各向同性地辐射出来,利用球对称性,可进一步简化方程。由此积分方程出发在三维空间中可以较容易的求出一级近似解,它与Sato用另外的方法所得到的单次散射近似相同;在二维空间中用数学归纳法求出任意M级近似解,据此求出一完整分析解,它说明面波尾波的衰减形态可给出与介质内耗性能有关的品质因数。