Abstract
Group velocity measurement by cross correlating long-term microtremor data has exploded. However, since it has been shown that the Green's function can be retrieved from cross correlation function, we examine the behavior of amplitude of cross correlation function in this study. A theoretical framework by Tsai(2011) shows that the signal part of cross correlation function depends on parameters of subsurface structure and amplitude of noise part is proportional to the root of the data amount for the analysis. Comparing this theoretical result with the observed cross correlation functions obtained from half a year microtremor data in the southern Kanto region, the maximum amplitudes of the observed cross correlation functions also show constant values for the data amount for the analysis, while the noise parts show a dependency for the root of the data amount. We also found that amplitude values fit a power law in which the noise level at long period is relatively low to the noise at short period. However, the maximum amplitude values also show a similar tendency to the noise amplitude especially in the short periods probably due to the lack of the data amount for the analysis. These results allow us to estimate a required data amount for the cross correlation analysis and we can estimate the minimum data in observations for seismic interferometry quantitatively. We also show the effect of data processing focusing on amplitudes of signal and noise of cross correlation functions. Although time domain normalization such as 1-bit normalization is very effective, it requires an appropriate filter for raw microtremor data in advance. We also show that the shorter window for the data division of long-term microtremor data into segments gives better convergence of cross correlation functions. Finally we show attenuation of maximum amplitudes of cross correlation functions because a theoretical study suggests a possibility of the identification of the parameters of subsurface structure.
