An analysis on bias using the SPAC method in records of microtremors
微震记录的空间自相关法误差特性分析

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.