Elastic wave scattering by a random medium and the small‐scale inhomogeneities in the lithosphere
Elastic wave scattering by a random medium and the small‐scale inhomogeneities in the lithosphere
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DOI：
10.1029/jb090ib12p10261
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发表时间：
1985-10
影响因子：
--
通讯作者：
R. Wu;K. Aki
中科院分区：
文献类型：
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作者：
R. Wu;K. Aki
本文用玻恩近似导出了以弹性常数和密度扰动为特征的弹性随机介质的P-P、P-S、S-P和S-S散射场的均方振幅。我们还得到了入射P波时的总散射功率或散射系数。我们发现，无论是在空间散射模式上，还是在散射系数的频率依赖性上，标量波散射与弹性波散射都存在显著差异。当波长与短周期地震体波研究中经常遇到的非均匀性大小相当时，这些差异最为显著。在一定条件下，介质参数的扰动可以分解为阻抗项和速度项。在正向方向上，散射波主要受速度扰动的控制。对于后向散射，散射波主要是由阻抗扰动产生的。我们导出了方向散射系数和总散射系数的低频和高频渐近形式。在低频范围内，出现了与四工频相关的瑞利散射。在高频范围内，共模散射的散射功率与第二功率频率相关，这归因于速度扰动。对于指数相关函数，转换波的散射功率在高频范围内达到最大值。我们发现标量波理论只能近似地用于高频范围内的前向散射问题，例如大型地震阵的相位和振幅波动。局部地震尾波激发的情况是一个后向散射或大角度散射问题，必须用全弹性波理论来处理。利用我们的理论对过去观测结果进行的初步分析表明，岩石圈可能具有多尺度的不均匀性。除了LASA和NORSAR的前向散射观测显示的10-20 km尺度的速度不均匀性外，构造活动区的岩石圈可能富含小尺度（小于1 km）的不均匀性。
In this paper we use Born approximations to derive the mean square amplitudes of the scattered field for P-P, P-S, S-P, and S-S scattering by an elastic random medium characterized by perturbations of elastic constants and density. We also obtain the total scattered power or the scattering coefficient for the case of an incident P wave. We find that, in both the spatial scattering pattern and the frequency dependence of the scattering coefficient, there are some significant differences between scalar wave scattering and elastic wave scattering. These differences are most striking when the wavelength is comparable to the size of inhomogeneities, which is often encountered in the study of short-period seismic body waves. Under certain conditions, the perturbations of the medium parameters can be decomposed into an impedance term and a velocity term. In the forward direction, scattered waves are primarily controlled by the velocity perturbations. For backscattering, scattered waves are generated mainly by impedance perturbations. We derive low- and high-frequency asymptotic forms of the directional and total scattering coefficients. In the low-frequency range, Rayleigh scattering with fourth-power frequency dependence occurs. For the high-frequency range the scattered power for common-mode scattering has a second-power frequency dependence, which is attributed to velocity perturbations. The scattered power of converted waves reaches a maximum, for the case of an exponential correlation function, in the high-frequency range. We find that the scalar wave theory can be only approximately used for the forward scattering problem in the high-frequency range, such as the phase and amplitude fluctuations in large seismic arrays. The case of coda wave excitation by local earthquakes, which is a backscattering or a large-angle-scattering problem, must be handled by the full elastic wave theory. A preliminary analysis of past observations using our theory suggests that the lithosphere may have multiple-scale inhomogeneities. Besides the 10–20 km scale velocity inhomogeneities revealed by the forward scattering observations at LASA and NORSAR, the lithosphere in tectonically active regions may be rich in small-scale (less than 1 km) inhomogeneities.