The effect of body waves on phase-velocity determined by the spatial autocorrelation (SPAC) method, evaluated using full-wave modelling

Abstract

Body waves may affect phase velocity obtained from microtremor array surveys in some rare cases. Fitting theoretical phase velocities based on a surface-wave theory to observed phase velocities affected by body waves would therefore result in distorted images of subsurface S-wave velocity structure. In this study, we present a method for the theoretical calculation of phase velocities in which the full-wave field (i.e. a wavefield including not only surface waves but also body waves) is taken into account. In numerical experiments conducted in this study, in which we considered the full-wave field, we generated synthetic microtremors by randomly distributing point vibration sources on the surface of a horizontally stratified velocity model. We then determined the phase velocities by applying the spatial autocorrelation (SPAC) method to the synthetic vertical-component wave data. The phase-velocity dispersion curve thus obtained exhibited a shape with a clear peak, with a peak value (peak phase velocity) exceeding the S-wave velocity of a bedrock in the model, which was not explainable with a surface-wave (Rayleigh-wave) theory. We conducted systematic numerical experiments and clarified the following two features of the peak phase velocity: (1) the peak phase velocity becomes large as the contrast of the S-wave velocities between the surface layer and the bedrock, or the P-to-S-wave velocity ratio (related to the Poisson’s ratio) in the surface layer gets large, and (2) the frequency at which peak phase velocity occurs (peak frequency) lies in the vicinity of the S-wave resonance frequency of the ground. Both the peak phase velocity and the peak frequency were theoretically reproduced by the calculation method that we propose in this study, based on a SPAC method modified to consider the full-wave field. These results imply the possible improvement in the accuracy of microtremor array survey analysis for velocity-structure inference, by applying a full-wave theory to the peak phase velocity.