The effect of random isotropic inhomogeneities on the phase velocity of seismic waves
The effect of random isotropic inhomogeneities on the phase velocity of seismic waves
复制标题
随机各向同性不均匀性对地震波相速度的影响
DOI：
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发表时间：
1996
期刊：
影响因子：
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通讯作者：
N. Gold
中科院分区：
文献类型：
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作者：
S. Shapiro;R. Schwarz;N. Gold
本文从理论上和数值上研究了二维和三维随机各向同性平稳不均匀性对初始平面波（或球面波）透射纵波场相速度的影响。由于不均匀性的散射，当波通过介质传播时，波场变得扭曲。当考虑在平行于初始波的波前的表面的点处获取的不同波场配准时，走时波动。通常观察到，由平均走时得到的慢度不同于介质的平均慢度。在地球物理学中，这种效应被称为“速度漂移”。
利用Rytov近似，我们建立了二维和三维随机非均匀介质中透射波场的频率和传播距离相关的相速度公式。我们还比较了我们的分析结果与有限差分模拟。数值模拟和理论之间观察到良好的一致性。我们的分析结果的低频限制与已知的有效介质限制的相速度在统计各向同性的非均匀流体具有恒定的密度。在高频极限下，我们的结果与以前用射线微扰理论得到的结果一致。然而，与射线理论相反，我们的描述并不限于具有波动的微分相关函数的介质。此外，我们的研究结果量化的中频范围内的速度偏移的频率依赖性。这种频率依赖性对于在现实情况下估计这种效应是非常重要的。
In this paper we study, theoretically and numerically, the influence of 2-D and 3-D random isotropic stationary inhomogeneities on the phase velocities of the transmitted compressional wavefield of an initially plane (or spherical) wave. Due to scattering by the inhomogeneities the wavefield becomes distorted as the wave propagates through the medium. The traveltimes fluctuate when considering different wavefield registrations acquired at the points of surfaces that are parallel to the wavefront of the initial wave. It is usually observed that the slowness obtained from the averaged traveltime differs from the averaged slowness of (he medium. In the geophysical lilerature this effect has been termed the ‘velocity shift’.
Using the Rytov approximation we establish formulas for the frequency- and travel-distance-dependent phase velocity of the transmitted wavefield in 2-D and 3-D randomly inhomogeneous media. We also compare our analytical results with finite-difference simulations. Good agreement between numerical simulations and theory is observed. The low-frequency limit of our analytical results coincides with the known effective-medium limit of the phase velocity in statistically isotropic inhomogeneous fluids with constant densities. In the high-frequency limit our results coincide with the results previously obtained by the ray-perturbation theory. However, in contrast to the ray theory, our description is not restricted to media with differentiate correlation functions of fluctuations. Moreover, our results quantify the frequency dependence of the velocity shift in the intermediate-frequency range. This frequency dependence is of major importance for estimating this effect in realistic situations.