Abstract

We propose a simple technique for taking account of the impact of incoherent noise in the spatial autocorrelation (SPAC) microtremor array method for estimating phase velocities of Rayleigh waves. More specifically, the method consists of solving a system of simultaneous observation equations that use more than one SPAC coefficient—an intermediate quantity that is generated in the SPAC method to obtain Rayleigh‐wave phase velocity estimates—while considering the impact of incoherent noise. The proposed method allows the velocity estimates to be obtained as a solution of simultaneous equations, which is expressed in the form of an algebraic formula that involves SPAC coefficients. The method, however, relies on a long‐wavelength approximation for simplifying a model function, so it is usable only in a range of long wavelengths relative to the seismic‐array size. Because our method uses more than one seismic‐array radius that corresponds to a SPAC coefficient, it would be practical to designate it as a noise compensation technique for the extended SPAC method, which also uses multiple intersensor distances as seismic‐array radii. The method also assumes that all sensors have identical incoherent noise levels, so it is thought to work effectively for seismic arrays of relatively modest scales (less than several tens of meters) with homogeneous measurement instrument properties. We use field data taken in the vicinity of a PS log borehole to illustrate the applicability of our method, and we use numerically synthesized data to study the impact of higher modes and of a failure of underlying model assumptions on the analysis results.

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