Discussion on Using Only One Linear Array to Estimate the Phase Velocity of Rayleigh Wave Based on Microtremor Survey

Abstract

Aims: To propose a new method of estimating the phase velocity of Rayleigh wave using one linear array based on the spatial auto-correlation (SPAC) method and complex coherence function (CCF) and confirm its availability and robustness using both the numerical simulation and a field test. Study Design: Cross-sectional study. Place and Duration of Study: Department of Built Environment, Tokyo Institute of Technology and Zoorasia Yokohama Zoological Gardens (ZRS), between August 2013 and July 2014. Methodology: Numerical simulation was conducted to test the behavior of the proposed method using linear arrays with different directions in different kind of azimuth-dependent microtremor wave field; Field test was carried out at the parking lot of ZRS, in which the proposed method was applied with 2 linear arrays with different direction and the estimation of phase velocity was compared with that from the SPAC method and theoretical one. Through the numerical simulation and field test, the SPAC method without taking azimuthal average (we call it JO method in the text) was also conducted for comparison. Results: In the numerical simulation, the estimations of phase velocity from linear arrays with different directions are accurate and coincide with each other except for some extreme case; In the field test, the estimations of the 2 linear arrays both match well with the theoretical one and that from SPAC method. On the other hand, the SPAC method without azimuthal average behaved badly and showed instability because of its intrinsic defect. Conclusion: By applying the proposed method, it is available to estimate the phase velocity of Rayleigh wave using just one linear array in a microtremor wave field, which is not a strongly azimuth-dependent one.