A Derivation of the Relation between Spatial Correlation and Green^|^rsquo;s Function Based on the Slowness Method: Isotropic Incidence of Random Scalar Waves
A Derivation of the Relation between Spatial Correlation and Green^|^rsquo;s Function Based on the Slowness Method: Isotropic Incidence of Random Scalar Waves
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基于慢度法的空间相关性与格林函数关系的推导：随机标量波的各向同性入射
DOI：
10.4294/zisin.59.159
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发表时间：
2006
期刊：
影响因子：
--
通讯作者：
H. Nakahara
中科院分区：
文献类型：
--
作者：
H. Nakahara
理论和实验已经证明，源和接收器的格林函数可以从两点之间波场的空间相关性中得到。最近，有人指出，随机波场的归一化互谱可以通过傅里叶逆变换连接到时域格林函数：必须对归一化空间相关性进行希尔伯特变换和微分，才能分别检索2D和3D的格林函数。在这些推导中，在波场的归一化空间相关性的估计中出现了关于频率和慢度的多重积分。目前，通常采用谱法，即在慢度积分后进行频率积分。然而，在本研究中，采用反转积分顺序的慢度方法，我成功地得出了与谱方法相同的结果。使用慢度方法的推导似乎更有利，因为对积分做出主要贡献的驻点可以通过图形方式理解。
It has been demonstrated theoretically and experimentally that Green’s function for a source and a receiver can be retrieved from the spatial correlation of a wave field between the two points. Recently, it was pointed out that the normalized cross spectrum of a random wave field can be connected to the time-domain Green’s function via the inverse Fourier transform: Hilbert transform and di#erentiation have to be operated on the normalized spatial correlation to retrieve Green’s function for 2D and 3D, respectively. In these derivations, a multiple integration with respect to frequency and slowness appears in the estimation of the normalized spatial correlation of the wave field. So far, the spectral method is usually used, which performs the frequency integration after the slowness integration. However, adopting the slowness method, which reverses the order of the integration, in this study, I have succeeded in deriving the same results as were derived by the spectral method. The derivation using the slowness method seems more advantageous because the stationary points, which make principal contribution to the integration, can be graphically understood.