The correlation of microtremors: empirical limits and relations between results in frequency and time domains

The use of the correlation of microtremor records is on its way to develop into a common tool to estimate local shear wave velocity structure. For this reason, the establishment of the conditions for the correct use of this method and its limitations when applied to real data is becoming increasingly important. In addition to the use of frequency domain spatial correlation technique [the Spatial Autocorrelation (SPAC) method], the use of time domain correlation to obtain the Green's function of the medium is rapidly gaining presence. We explore the use of microtremor correlation techniques in the time domain to determine local velocity structure and compare with previous results obtained with the same data using SPAC. Our data come from three experiments carried out in Parkway and Wainuiomata valleys in New Zealand, using broad-band portable stations. Interstation distances range from 5 m to 2.1 km, and our results are useful in the frequency band from 0.1 to 7 Hz. Frequency domain correlation requires an isotropic microtremor field, a condition that need not be satisfied in the time domain. Two station correlations provide useful results due to the temporal stationarity and isotropy, in average, of the microtremor wavefield. This manifests itself in the symmetry of the temporal correlation functions with respect to zero time. Our results show that the local velocity structure and the interstation distance are the key factors conditioning the frequency range where surface wave dispersion can be correctly measured either in frequency or time domains. We confirm that, when the interstation distance becomes much larger than the dominant wavelengths, only the correlation in time domain is useful. All our results indicate that the signal obtained in the correlation of vertical component microtremors is due to the fundamental mode of Rayleigh waves, which appears as the most stable propagation mode, without any indication of body waves.