Multimode inversion with amplitude response of surface waves in the spatial autocorrelation method

Microtremors are usually analysed without any consideration of the higher modes of surface waves. However, recent studies have demonstrated that higher modes contain useful information for improving the inverted S-wave velocity model. In this study, we propose two inversion methods that consider higher modes by using the amplitude response of each mode, which can avoid mode misidentification in the spatial autocorrelation (SPAC) method. One method is to compare the observed phase velocities by the extended spatial autocorrelation (ESPAC) method with the effective phase velocities calculated from theoretical dispersion curves and the amplitude responses of each mode. In the other method, SPAC coefficients are fit directly by comparing theoretical SPAC coefficients determined from dispersion curves and amplitude responses with the observed ones. The latter, direct-fitting approach is much simpler than the method using effective phase velocities. To investigate the effectiveness of these methods, a simulation study was conducted. Simulated microtremors that included higher modes were successfully inverted by the proposed multimode methods. The observed phase velocities and SPAC coefficients determined from field data were also consistent with theoretical ones constructed by the proposed methods except at low frequencies. The inversion using effective phase velocities required prior information about an infinite half-space to obtain a better S-wave velocity model whereas the direct-fitting inversion worked well without prior information, suggesting the direct-fitting method is more robust than the method using effective phase velocities. We conclude that our proposed inversion methods are effective for estimating the S-wave velocity structure even if higher modes of surface waves are predominant in observed microtremors.