Limits and Benefits of the Spatial Autocorrelation Microtremor Array Method Due to the Incoherent Noise, With Special Reference to the Analysis of Long Wavelength Ranges

To examine the upper limit of the analyzable wavelength ranges (upper limit wavelength, ULW) of the spatial autocorrelation (SPAC) method in microtremor surveys, we have derived a formula evaluating stochastic errors of a phase velocity estimate obtained by the SPAC method. We then followed our previous paper to evaluate biases generated in a phase velocity estimate that come from the presence of the incoherent noise so that we could discuss which is the crucial factor determining the ULW. As a result, the incoherent noise is considered as the crucial factor. In the consequence, we proposed a formula to evaluate signal‐to‐noise ratio (SNR) and to determine phase velocity with the effects of the incoherent noise compensated. We used observed data to validate the above theory. Through the validation procedure, we obtained an approximation equation , where NULW means ULW normalized by array radius and A is a constant. The parameter A took a value from about 1/2 to 2 in the cases of this study. Finally, an additional and simple analysis was executed, which indicates that the incoherent noise not only limits the SPAC analysis but also can provide benefits: they are possibly used for evaluating the attenuation of soils. A microtremor array survey with the traditional SPAC method of Okada (2003, https://doi.org/10.1190/1.9781560801740 ) can be a mobile tool for evaluating the very local attenuation at a site of interest (i.e., gaining a high spatial resolution), in frequency ranges suited for earthquake engineering and by using simple seismic arrays with short time observations.