Direct estimation of the Rayleigh wave phase velocity in microtremors

Abstract

We present a new estimation technique using a circular array for the Rayleigh wave phase velocity in microtremors. This technique allows us to employ more flexible sensor arrangements than that of Aki's spatial autocorrelation(SPAC) technique. One of the features is that the array output is represented by simultaneous equations consisting of complex coherence functions(CCFs). A CCF consists of two components:the Bessel function J0(r/c)(ω:angular frequency, r:radius, c:phase velocity) and an error term that varies with the azimuth of the sources. An analysis of the SPAC operation has demonstrated that the azimuthal averaging of the CCFs reduces the error term, and the average value can be approximated to J0(r/c). This result suggests the phase velocity can be determined by extracting J0(r/c) from the CCFs. Therefore, we tried to directly estimate J0(r/c) without the azimuthal averaging and developed a solution method referred to as the direct estimation method(DEM).