Extension of the Spatial Autocorrelation (SPAC) Method to Mixed-Component Correlations of Surface Waves
Extension of the Spatial Autocorrelation (SPAC) Method to Mixed-Component Correlations of Surface Waves
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DOI：
10.1111/j.1365-246x.2012.05597.x
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发表时间：
2012-10
影响因子：
2.8
通讯作者：
M. Haney;T. Mikesell;K. van Wijk;H. Nakahara
中科院分区：
文献类型：
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作者：
M. Haney;T. Mikesell;K. van Wijk;H. Nakahara
利用环境地震噪声成像地下结构可以追溯到20世纪50年代空间自相关（SPAC）方法的发展。我们对表面波多分量记录的SPAC方法进行了理论分析，以确定所有三分量运动对之间的完整3 × 3相关性矩阵，称为相关矩阵。在各向同性入射的情况下，当瑞利波或洛夫波从各个方向以相同的功率到达时，矩阵中唯一的非零非对角线项是瑞利波存在时的垂直-径向（ZR）和径向-垂直（RZ）相关。在SPAC方法的发展中没有考虑到这种组合。该方法最初处理垂直（ZZ）、RR和TT相关性，因此称为空间自相关。我们推导出的ZR和RZ相关的理论表达式为在SPAC框架内测量瑞利波色散提供了额外的方法。在各向同性入射结果的基础上，导出了一般各向异性入射情况下的完整相关矩阵。我们表明，与ZZ和RR相关相比，ZR和RZ相关在存在面外定向波场时具有有利的性质。我们将混合分量相关性的结果应用于阿拉斯加Akutan火山的数据集，并发现与ZZ相关性相比，ZR对瑞利波相速度的估计是一致的。这项工作与最近发现的SPAC方法与环境噪声的时域相关性之间的联系一起，为从地震噪声中检索表面波格林函数提供了进一步的见解。
SUMMARY Using ambient seismic noise for imaging subsurface structure dates back to the development of the spatial autocorrelation (SPAC) method in the 1950s. We present a theoretical analysis of the SPAC method for multicomponent recordings of surface waves to determine the complete 3 × 3 matrix of correlations between all pairs of three-component motions, called the correlation matrix. In the case of isotropic incidence, when either Rayleigh or Love waves arrive from all directions with equal power, the only non-zero off-diagonal terms in the matrix are the vertical–radial (ZR) and radial–vertical (RZ) correlations in the presence of Rayleigh waves. Such combinations were not considered in the development of the SPAC method. The method originally addressed the vertical–vertical (ZZ), RR and TT correlations, hence the name spatial autocorrelation. The theoretical expressions we derive for the ZR and RZ correlations offer additional ways to measure Rayleigh wave dispersion within the SPAC framework. Expanding on the results for isotropic incidence, we derive the complete correlation matrix in the case of generally anisotropic incidence. We show that the ZR and RZ correlations have advantageous properties in the presence of an out-of-plane directional wavefield compared to ZZ and RR correlations. We apply the results for mixed-component correlations to a data set from Akutan Volcano, Alaska and find consistent estimates of Rayleigh wave phase velocity from ZR compared to ZZ correlations. This work together with the recently discovered connections between the SPAC method and time-domain correlations of ambient noise provide further insights into the retrieval of surface wave Green’s functions from seismic noise.