Statistical Validity Control on SPAC Microtremor Observations Recorded with a Restricted Number of Sensors

The interpretation of an observed spatially averaged coherency (SPAC) spectrum assumes spatial and temporal stationarity of the microtremor wave field. This hypothesis gains in importance when recording coherency spectra (COHs) with a limited number of sensors. SPAC observations were recorded at three separate sites in Launceston (Australia) using a pair of sensors, triangular arrays, and hexagonal arrays to study the effect of the number of sensors, length of time series, and frequency interval for evaluating the shear-wave velocity (SWV) profile. The imaginary component of the observed complex COH is separated into roughened and smoothed parts. The root mean square of the roughened imaginary COH (rms (Im)) is an expression of the statistical noise in the observed coherency, while the behavior of the smoothed imaginary COH gives some indication of the distribution of the microtremor wave field. The mean square of residuals (MSR) between observed and theoretical COHs is an indication of the confidence level on the SWV profile interpreted. MSR values evaluated at pairs of sensors of different orientations give some indication of the azimuth distribution of the microtremor wave field and provide some guidelines on the field procedure when using a limited number of sensors to record SPAC observations. Observed COHs at site KPK demonstrate the importance of recording longer time series to increase the stability of the observed COHs. The increasing level of statistical noise with increasing frequency at site DBL suggests the SPAC method can be used with a single pair of sensors by restricting its upper frequency limit to the first minimum of the COH. Low values of MSR on observed COHs from most pairs of sensors further strengthen that hypothesis. SPAC observations at site RGB give further insights into the capabilities of the SPAC method to evaluate the SWV profile in limited azimuth microtremor wave-field distribution.