微震记录的空间自相关法误差特性分析

本文定量研究了当面波能量分布不遵循各向均匀的假设时，运用空间自相关法（SPAC法）出现的误差.通过分析合成微震记录，研究了方位局限的入射、站台的数量对空间自相关系数的影响，明确了一些圆形排列的SPAC系数偏差空间构造.它可分为两个部分：低频域的零偏差部分和高频域的偏差部分.在高频偏差域，存在排列特色的周期特性.其角度周期是排列圆周上相邻站点之间夹角的一半.研究中要强调的是对于每种圆形排列存在一些特殊的入射方向的现象（如，对三角形排列，那些方向角度为 15°, 45°, 75°,…）.当瑞利波沿着这些角度之一传播时，在SPAC谱中，有效的无偏差频率范围扩展到先前研究结果的两倍.这个现象为提高野外SPAC法勘探精度提供了一个新的可能.

An analysis on bias using the SPAC method in records of microtremors

This paper presents a numerical study of the errors incurred by using the spatial autocorrelation (SPAC) method when wavefields do not obey the basic assumption of the method; i.e., propagation of surface waves with equal power in all directions. The effects of azimuth-restricted wave incidence and of limited number of stations on the SPAC coefficients are studied by analyzing synthetic signal records.  Through the work, the spatial structures of deviation in SPAC spectrum for some circular arrays are made clearly. It can be divided into two subsections: zero deviation section in low frequency range and non-zero deviation section. The deviation sections at high frequency show specific periodic features with azimuth. The angular period is exactly the half of the angle between adjacent two stations on the array circle. A fact to be noticed is the existence of some special incidence directions of minimum deviation for each array (e.g., for triangular array, the angles corresponding to those directions are 15°, 45°, 75°, …). In the case when surface waves come from one of those single directions, the effective non-deviation range in the SPAC spectrum becomes twice that pointed in previous studies. This fact will give us a new possibility of enhancing the accuracy of SPAC measurement in field work.