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首页> 外文期刊>Earth, planets and space: EPS >Envelope syntheses of cylindrical vector-waves in 2-D random elastic media based on the Markov approximation
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Envelope syntheses of cylindrical vector-waves in 2-D random elastic media based on the Markov approximation

机译：基于马尔可夫近似的二维随机弹性介质中圆柱矢量波的包络合成

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摘要

Seismograms of microearthquakes are complex; however, their envelopes broaden as the travel distance increases. P-waves are recorded in transverse components, S-waves are recorded in the longitudinal component, and waves are observed at sites even in the nodal direction of the source radiation. These phenomena, which are typically found in short-period seismograms, can be interpreted to be the result of scattering due to lithospheric inhomogeneity. We report here our study of a simple statistical model in which the propagation of waves radiated from a point source in two-dimensional (2-D) random elastic media is characterized by a Gaussian autocorrelation function. For the case that the wavelength is shorter than the correlation distance, two methods based on the Markov approximation are introduced for the direct synthesis of vector wave envelopes. One is to analytically solve the stochastic equation for the two-frequency mutual coherence function; the validity of the solution is confirmed by using finite difference simulations. The second is to numerically solve the stochastic equation for the mutual coherence function. The two methods are equivalent, but the latter is applicable to nonisotropic source radiation. For the case of a point shear dislocation source, a peak delay from the onset and a smoothly decaying tail are found to be common to synthesized envelopes in all azimuths. Scattered waves are excited even at receivers in the nodal direction, and amplitudes become independent of the radiation pattern as lapse time increases.
机译：微地震的地震图很复杂。但是，它们的信封随着行进距离的增加而变宽。 P波记录在横向分量中，S波记录在纵向分量中，甚至在源辐射的节点方向上的位置处也观察到了波。这些现象通常在短周期地震图中发现，可以解释为由于岩石圈非均质性造成的散射的结果。我们在这里报告我们对简单统计模型的研究，其中在二维（2-D）随机弹性介质中从点源辐射的波的传播以高斯自相关函数为特征。对于波长短于相关距离的情况，引入了两种基于马尔可夫近似的方法来直接合成矢量波包络线。一种是解析求解两频互相干函数的随机方程。该解决方案的有效性通过使用有限差分仿真得到了证实。第二是用数值方法求解相互相干函数的随机方程。这两种方法是等效的，但后者适用于非各向同性源辐射。对于点剪切位错源，发现从起始峰开始的峰延迟和尾部平滑衰减在所有方位角都是合成包络所共有的。甚至在节点方向的接收器处也会激发散射波，并且随着经过时间的增加，振幅变得与辐射图无关。

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