A revised spatial autocorrelation method to study shear wave velocity

Recordings of ambient noise or microtremors are increasingly used to find valuable information on soil in one dimension at a given site. Ambient vibrations, which are assumed to be mainly composed of surface waves, can be used to determine the surface wave dispersion curve in order to retrieve shear wave velocity profile. In this regard, microtremors are usually recorded simultaneously in an array of stations and they are processed in two steps; finding the dispersion (autocorrelation) curve and then inversing it to estimate the shear wave velocity profile. Microtremors are usually recorded in various apertures in order to get the spectral curves over a wide frequency band, and different methods also exist for processing the raw signals.
The two most popular microtremor processing techniques are frequency-wave number (F-K) and spatial autocorrelation (SPAC). The SPAC method, which generally employs a circular array of stations and one central station, permits an in-depth understanding of the temporal and spatial spectra of seismic waves. Nowadays, it is widely used to estimate the structure of sub-surface layers and the shear wave velocities of sediments. In the SPAC method, the dispersion curves (phase velocity versus frequency) of surface waves are deduced by analyzing the normalized correlations between microtremors recorded at different stations. The dispersion curves are then used to characterize the structure of the medium. The method is based on a statistical analysis of the observed signal, which is assumed to be stationary and ergodic in time and space.
In this paper to find reliable results in the processing of microtremors in shallow structures, the spatial autocorrelation coefficients are calculated for the vertical components of recorded signals using the MSPAC method and a new one (the revised SPAC method). Both methods are based on considering all possible autocorrelation pairs among the circumference stations. Their difference is that the new model considers all possible autocorrelation pairs among the circumference stations and makes an average on the calculated autocorrelations, on the other hand in the MSPAC model the pairs are put in different rings according to the distance between each pair. The deduced autocorrelation coefficients are then inverted. The results of applying the two models on real data are presented and compared. This comparison reveals that the results of both models are in good agreements with the site geology, although the new method expresses the Vs profile at depths smaller than 10 meters more successfully than the MSPAC method.