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在多次各向异性散射理论的基础上,本文重新推导了方向性散射系数的球函数展开式.引入特征时间的概念,来定义震源处初始地震波脉冲宽度,并在地震波能量密度积分方程中引入任意给定频率的初始脉冲能量谱密度的解析表达.通过离散波数方法求解了修正的地震波能量密度积分方程.基于积分方程的数值解,研究了不同散射模式对S波能量密度包络曲线的影响.计算结果表明:随着震源距的增加,在S波到时之后,多次各向异性散射模式与多次各向同性散射模式合成的能量密度包络差异逐渐增大.其中通过多次前散射模式,我们可以得到不同震源距的尾波能量密度包络的同一衰减趋势,以及S波能量密度包络随着震源距的增加而出现的展宽现象.最后,利用美国内华达州Wells地震余震的台站记录验证了多次前散射模式的实用性与有效性.
Based on the theory of multiple anisotropic scattering, the spherical function expansion of directivity scattering coefficient is deduced again. The concept of characteristic time is introduced to define the initial seismic pulse width at the source and introduced into the energy density integral equation of seismic wave The analytic expression of initial pulse energy spectral density at any given frequency is obtained.The discrete integral method is used to solve the modified seismic energy density integral equation.The influence of different scattering modes on the energy density envelope curve of S wave is studied based on the numerical solution of integral equation The calculated results show that with the increase of the focal distance, the difference of the energy density envelopes of multiple anisotropic scattering modes and multiple isotropic scattering modes gradually increases after the arrival of S wave, Scattering mode, we can get the same decay tendency of the energy density envelope of the cochlea at different source distances, and the widening of the S-wave energy density envelope with the increase of the focal distance.Finally, using the Wells earthquake in the US state of Nevada Station records verify the usefulness and validity of the multiple front scattering modes.