Experiments on the stability of the spatial autocorrelation method (SPAC) and linear array methods and on the imaginary part of the SPAC coefficients as an indicator of data quality

Abstract

In recent years, microtremor array observations have been used for estimation of shear-wave velocity structures. One of the methods is the conventional spatial autocorrelation (SPAC) method, which requires simultaneous recording at least with three or four sensors. Modified SPAC methods such as 2sSPAC, and linear array methods, allow estimating shear-wave structures by using only two sensors, but suffer from instability of the spatial autocorrelation coefficient for frequency ranges higher than 1.0 Hz. Based on microtremor measurements from four different size triangular arrays and four same-size triangular and linear arrays, we have demonstrated the stability of SPAC coefficient for the frequency range from 2 to 4 or 5 Hz. The phase velocities, obtained by fitting the SPAC coefficients to the Bessel function, are also consistent up to the frequency 5 Hz. All data were processed by the SPAC method, with the exception of the spatial averaging for the linear array cases. The arrays were deployed sequentially at different times, near a site having existing Parallel Seismic (PS) borehole logging data. We also used the imaginary part of the SPAC coefficients as a data-quality indicator. Based on perturbations of the autocorrelation spectrum (and in some cases on visual examination of the record waveforms) we divided data into so-called ‘reliable’ and ‘unreliable’ categories. We then calculated the imaginary part of the SPAC spectrum for ‘reliable’, ‘unreliable’, and complete (i.e. ‘reliable’ and ‘unreliable’ datasets combined) datasets for each array, and compared the results. In the case of insufficient azimuthal distribution of the stations (the linear array) the imaginary curve shows some instability and can therefore be regarded as an indicator of insufficient spatial averaging. However, in the case of low coherency of the wavefield the imaginary curve does not show any significant instability.