Spatially averaged coherencies (krSPAC) and Rayleigh effective-mode modeling of microtremor data from asymmetric arrays

The spatial autocorrelation and spatially averaged coherency (SPAC) methods of processing Rayleigh-wave microtremor noise observations for estimation of S-wave velocity profiles traditionally require a circular or triangular array symmetry to allow spatial (azimuthal) averaging of interstation coherencies over a constant station separation. Common processing methods allow for station separations to vary by typically ±10% in the azimuthal averaging before degradation of the SPAC spectrum is excessive. Transformation of a set of frequency-coherency spectra to wavenumber-coherency spectra (kr spectra) allows spatial averaging of spectra from multiple pairs of sensors irrespective of differences in spatial separation of the pairs. The method is called krSPAC and is implemented by iterative direct fitting of observed and model kr spectra to determine an optimal layered-earth S-wave velocity model. The observed kr spectra are updated with each iteration of the velocity model because the wavenumber is a function of model phase velocity that varies with each iteration of the modeling process. The method proves applicable when modeling either with the assumption of fundamental mode Rayleigh-wave propagation or with a summation of fundamental and higher modes. The method proves robust when compared with alternative methodologies using symmetric and asymmetric arrays on a sample of synthetic data and on field data in which station spacings vary from 70 to 800 m side lengths.