An Alternative Approach to the spac Analysis of Microtremors: Exploiting Stationarity of Noise

The spac (Spatial autocorrelation) method to analyze ambient vibration records was introduced by Aki (1957). Currently, this method is being used for the analysis of microtremor data from an array of stations: crosscorrelation functions are computed between pairs of stations, and then averaged for different station pairs, at the same interstation distance but with different orientation. In this article we propose the idea of exploiting recordings of microtremors over long times as a substitute for spatial averaging, as was suggested in Aki (1957). This idea has several advantages. The two most important are, first, that it is not required to obtain simultaneous recordings using an array of stations, whose locations must obey a very rigid scheme; and second, the ability to obtain results for a large number of closely-spaced distance intervals. Our proposal is tested using data from the Parkway, Wainuiomata, temporary array. These data are supplemented with additional measurements performed during February 2003, to resolve an uncertainty regarding the low-frequency part of our results. Given the irregular distribution of our array, we are able to obtain results for many different station pairs. The phase-velocity dispersion curves we derive from our measurements, interpreted with the spac method, are compared with previous results in this sedimentary basin. Our results suggest that the spac method is more general than appears in recently published papers.