Research examining a spatial autocorrelation imaging method based on stationary characteristics of microtremors

The spatial autocorrelation method is an important method for extracting the velocity dispersion curve from microtremor data. However, site data typically cannot strictly meet spatial and temporal stationary feature, and this greatly affects the accuracy of the calculation results of this method. Therefore, based on the cosine similarity theory, this study deduces the applicability of the spatial autocorrelation method to unidirectional Rayleigh surface waves and again verifies the applicability of this method to spatially and temporally stationary Rayleigh waves. The numerical simulation results demonstrate that the velocity dispersion curve can be extracted from a one-way Rayleigh wave using the spatial autocorrelation method to obtain an accurate geological profile, whereas the superposition of finite groups of Rayleigh waves in different directions cannot yield an accurate geological profile. In this study, we quantitatively analyzed the impact of the spatial autocorrelation method on the extraction of the velocity dispersion curve when the signal could not meet the characteristics of temporal and spatial stationarity through numerical simulation. The results reveal that the velocity-dispersion curve can be accurately extracted only when the signal satisfies both spatial and temporal stationarity. When a signal is closer to the spatial and temporal stationary characteristics, this indicates that a more accurate velocity dispersion curve can be extracted. These results provide a reference for improving the calculation accuracy of spatial autocorrelation methods.