Formulation of the multiple non-isotropic scattering process in 3-D space on the basis of energy transport theory
Formulation of the multiple non-isotropic scattering process in 3-D space on the basis of energy transport theory
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DOI：
10.1111/j.1365-246x.1995.tb05730.x
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发表时间：
1995-05
影响因子：
2.8
通讯作者：
H. Sato
中科院分区：
文献类型：
--
作者：
H. Sato
局部地震的高频地震记录被认为是由地球介质中随机非均匀性散射的非相干体波组成的。对于地震包线的研究，我们可以根据能量输运理论，将随机不均匀性表示为分布的点状散射体来描述散射过程。通过引入能量密度方向分布的概念，提出了三维空间中多重非各向同性散射过程的计算公式。假设轴对称非各向同性散射用方向散射系数来描述，介质以一波速为特征，源辐射为球形。在求解各向同性散射介质中能量密度时，除了采用空间上的傅里叶变换和时间上的拉普拉斯变换外，还采用了实体角上的球谐级数展开。那么，以积分形式给出的能量输运方程可以写成联立线性方程，其中系数由Wigner 3-j符号给出，方向散射系数为球谐展开系数。球谐级数的最低项对应于各向同性散射。将定向散射系数写成有限长球谐级数时，可以求解有限未知数的线性方程组，得到能量密度的时空分布。对强前向散射情况的数值计算表明，在大时延下，震源周围能量密度分布均匀。
Summary High-frequency seismograms of local earthquakes are considered to consist of incoherent body waves scattered by random inhomogeneities in the earth medium. For the study of seismogram envelopes, we can describe the scattering process on the basis of energy transport theory by representing the random inhomogeneities as distributed point-like scatterers. By introducing the concept of directional distribution of energy density, we propose a formulation of the multiple non-isotropic scattering process in 3-D space. We suppose that the axially symmetric non-isotropic scattering is described by a directional scattering coefficient, the medium is characterized by one wave velocity, and the source radiation is spherical. In addition to the Fourier transformation in space and the Laplace transformation in time used to solve for energy density in isotropic scattering media, we use a spherical harmonic series expansion in solid angle. Then, the energy transport equation given as an integral can be written as simultaneous linear equations, where coefficients are given by the Wigner 3-j symbols and the spherical harmonic expansion coefficients of the directional scattering coefficient. The lowest term of the spherical harmonic series corresponds to isotropic scattering. When the directional scattering coefficient is written as a finite-length spherical harmonic series, the simultaneous linear equations can be solved for a finite number of unknowns and we can obtain the spatio-temporal distribution of energy density. The numerical calculation for a case with strong forward scattering shows a uniform distribution of energy density around the hypocentre at large lapse times.