Basic performance of a spatial autocorrelation method for determining phase velocities of Rayleigh waves from microtremors, with special reference to the zero-crossing method for quick surveys with mobile seismic arrays
Authors: Cho Ikuo , Senna Shigeki , Wakai Atsushi , Jin Kaoru , Fujiwara Hiroyuki 
Published: April 2021

SUMMARY
We theoretically and empirically demonstrate the usability of the zero-crossing method for quick microtremor surveys in earthquake engineering (i.e. microtremor array surveys), namely shallow (&lt; a few kilometres) surveys with small-scale (&lt; 1 kilometre in radius) mobile seismic arrays with a short observation time (&lt; a few hours). The zero-crossing method is a type of spatial autocorrelation (SPAC) method that determines phase velocities based on multiple frequencies at which the SPAC coefficient curve crosses zero. It is theoretically shown that the zero-crossing method is robust against incoherent noise and that the use of the first zero crossings (i.e. those at the lowest frequencies) is more robust against inadequate conditions of the microtremor wavefield than the use of later zero crossings (i.e. those at higher frequencies). We used microtremor array data with maximum array radii and observation durations of 400 m and 120 min on average, respectively, at 445 observation sites in the Kanto Plain, Japan, for validating the practicality of using the first zero crossings. As an illustration of the robustness against low signal-to-noise ratios (SNRs), we show that with the zero-crossing method, low-sensitivity (i.e. low-SNR) seismometers provide the same analysis results as those obtained with high-sensitivity seismometers, even when the power spectral densities for the low-sensitivity seismometers are close to the self-noise level. We then show that a reference phase velocity dispersion curve (RPVDC), created mainly based on the first zero crossings at each site, has a spatial distribution that well corresponds to the geology and topography and is consistent with that obtained in a previous study. We inverted five RPVDCs to model 1-D S-wave profiles and validated them using S-wave profiles obtained from velocity logs at nearby deep (e.g. hundreds of metres) boring wells. The accuracy of phase velocities at the later zero crossings for three-sensor/four-sensor arrays and all zero crossings for two-sensor arrays are statistically examined (maximum of 9805 data) based on a comparison with the RPVDCs. The disadvantage of the zero-crossing method is that it can only provide information on phase velocities at discrete wavelengths up to a maximum wavelength of 2.6r (i.e. corresponding to the first zero-crossing point), where r is the radius of a seismic array. Therefore, the RPVDCs were then used to examine the upper limit of the analysable wavelength ranges for the conventional SPAC method for microtremor array surveys. Based on a few hundred three-sensor/four-sensor arrays, it was found that for arrays with radii larger than several tens of metres, three-quarters of the upper limit wavelengths (ULWs) stayed within 5r. For arrays with radii smaller than this value, the ULWs strongly depended on the array radius; the ULWs dramatically increased with decreasing array radius. For example, for arrays with an r value of 0.6 m, half of 336 data ranged between 26r and 54r, and the maximum ULW reached 186r. This strong size dependence can be explained by differences in SNR.