We present simple and novel formulas that help to directly infer phase velocities of Love waves (cL) using two-component, horizontal-motion, circular-array records of microtremors. Our formulas are analogous to those of the spatial autocorrelation (SPAC) method, a technique of microtremor exploration that is popularly used to infer phase velocities of Rayleigh waves (cR). Although the existing theory of the SPAC method does provide the possibility to estimate cL, this can only be done by solving a nonlinear system of equations, wherein the unknowns to be solved for also include cR and the Rayleigh-to-Love power partition ratios. By contrast, cL is the only unknown to appear in our formulas.
The field applicability of the cL estimation methods based on the proposed formulas—which we name the SPAC+L, SPAC-L, and CCA-L (where CCA stands for centerless circular array) methods—is demonstrated by analysis results for two test sites. Among the three techniques proposed, the SPAC+L method distinguished itself as the best-performing. The valid wavelength ranges of the three methods had lower limits in the area of 2–5 times the array radius r and upper limits in the area of 10–25r.
Similar circular-array microtremor techniques that involve cL alone were proposed in recent years, but the methods we present here are either logistically less expensive or mathematically simpler than any of them.