Synthesis and applicable condition of vector wave envelopes in layered random elastic media with anisotropic autocorrelation function based on the Markov approximation
Synthesis and applicable condition of vector wave envelopes in layered random elastic media with anisotropic autocorrelation function based on the Markov approximation
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基于马尔可夫近似的各向异性自相关函数层状随机弹性介质矢量波包络的合成及应用条件
DOI：
10.1111/j.1365-246x.2011.05264.x
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发表时间：
2012
期刊：
影响因子：
--
通讯作者：
T.Nishimura
中科院分区：
文献类型：
--
作者：
Emoto;K;H.Sato;T.Nishimura
马尔可夫近似是直接合成随机速度波动介质中波长小于相关距离时包络波的一种有效的随机方法。为了将马尔可夫近似应用于实际情况，我们考虑了具有各向异性自相关函数（ACF）特征的水平分层随机介质，其中不同层具有不同的随机性，不同的背景速度具有阶梯状变化。求解随机弹性介质中平面小波从底部垂直入射的两频互相干函数（TFMCF）的抛物型主方程，计算了第一速度边界前的角谱。将边界的透射系数或PS转换系数乘以角谱，计算边界另一侧的角谱和TFMCF。然后在第二层解出前向传播小波的主方程。对每一层边界采用同样的处理方法，最终得到了顶层自由表面上的均方向量包络。在实际模拟中，我们使用了以高斯ACF为特征的二维随机介质。通过与弹性波的有限差分（FD）模拟进行比较，在数值上证实了包络综合在具有各向异性ACF的层状随机介质中的有效性。考虑到地面结构，水平相关距离大于垂直相关距离，速度分数波动随深度增加而减弱，马尔可夫近似可以很好地模拟主小波，也可以很好地模拟垂直入射小波的转换小波。通过与FD模拟的比较，得出了具有各向异性ACF的随机介质的马尔可夫近似的适用范围。结果表明，当波长与垂直相关距离和水平相关距离相当或更短时，马尔可夫近似是准确的，并且MS分数波动远小于水平相关距离的平方与垂直相关距离与传播距离的乘积之比。
The Markov approximation is a powerful stochastic method for the direct synthesis of wave envelopes in random velocity fluctuated media when the wavelength is shorter than their correlation distance. To apply the Markov approximation to realistic cases, we consider horizontal layered random media characterized by an anisotropic autocorrelation function (ACF), where different layers have different randomnesses and different background velocities having step-like changes. Solving the parabolic master equation for the two frequency mutual coherence function (TFMCF) in random elastic media for the vertical incidence of a plane wavelet from the bottom, we calculate the angular spectrum just before the first velocity boundary. Multiplying transmission or PS conversion coefficients of the boundary by the angular spectrum, we calculate the angular spectrum and TFMCF on the other side of the boundary. Then we solve the master equation for the forward propagating wavelet in the second layer. Taking the same procedure for each layer boundary, we finally obtain the mean square (MS) vector envelopes on the free surface on the top layer. For the practical simulation, we use 2-D random media characterized by a Gaussian ACF. We numerically confirm the validity of the envelope synthesis for a specific case of layered random media with anisotropic ACF by comparing with finite difference (FD) simulations of elastic waves. Considering the Earth structure, the horizontal correlation distance is larger than the vertical one and the velocity fractional fluctuation becomes weak as depth increases, the Markov approximation is good for modelling the primary wavelet and also the converted wavelet for the vertical incident wavelet. We derive an applicable range of the Markov approximation for random media with anisotropic ACF by comparing with FD simulations. The results show that the Markov approximation is accurate when the wavelength is comparable or shorter than the both of vertical and horizontal correlation distances and the MS fractional fluctuation is much smaller than the ratio of squared horizontal correlation distance to the product of the vertical correlation distance and propagation distance.
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