Direct Estimation of the Rayleigh Wave Phase Velocity in Microtremors

The mictotremor survey method (MSM) is one of the techniques used to estimate the shear-wave velocity structure of sedimentary layers. In the MSM, inverse analysis of the dispersion of the phase velocity is used for the velocity modeling. The passive nature of the MSM brings time/cost advantages over other active survey techniques, and it has been used for the strong motion prediction in the sedimentary plains in Japan (Matsuoka et al., 2003).The Spatial autocorrelation (SPAC) method (Aki, 1957), where records from a circular array of evenly spaced sensors and a central sensor is analyzed, is one of the commonly used measurement/analysis techniques in the MSM. In this method, the directional average of complex coherence functions (CCFs) between the records at the center and the circumference is equal to the Bessel function of the first kind of zero order J0(ωr/c) (ω: angular frequency, r: radius of circular array, c: phase velocity), and, hence, the phase velocities can be estimated. However, in practice, the requirement for equally spaced sensor arrangement in the SPAC often restricts the observation sites especially in urban areas.The authors have newly derived a method to directly estimate J0(ωr/c) and the phase velocity with fewer restrictions on the sensor arrangements. In this method (the Direct Estimation Method: DEM), the Bessel function J0(ωr/c) is obtained as a solution of the simultaneous equations of the CCFs. We have also found on theoretical grounds that the sensor arrangement in the DEM is much more flexible than the SPAC. In practice sensors on the circumference can be set at almost any place as long as the overall arrangement has a symmetry. A field experiment has confirmed that the phase velocity determined from the DEM agreed with the phase velocity by the SPAC method.