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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.
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 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 assumes 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.