Phase velocity estimation using horizontal partial differential components of microtremor array measurements

Abstract

To use three components fully obtained from microtremor array observation in spatial-auto correlation (SPAC) method analysis, we focused on the three new components (rotational, divergent, and gradient components) derived from the horizontal partial differentiation of the three original components (i.e., two horizontal components and vertical component). Through numerical testing using synthetic array waveform data, we confirmed that the rotational components provided the Love-wave phase velocity, and others provided the Rayleigh-wave phase velocity. In this study, we calculate the phase velocity using rotational, divergent, and gradient components from the actual microtremor array observation record and compare the results with the theoretical phase velocity based on the assumed underground structure model. Array observations were performed in and around the open space close to the Tsuruga Station, Fukui Prefecture, Japan, during the daytime on December 5, 2020, and December 12, 2020. We used six sets of JU410 (Hakusan Co., Japan) and placed them at the vertices of two nested triangles. The largest array radius was changed from 0.7 m to 80 m, and measurement time varied from 15 min to 90 min. Using the three components of six stations simultaneously obtained from the microtremor array observation, the three new components were calculated and analyzed by the SPAC method. As a result, the phase velocities using the rotational component and the gradient component showed good correspondence with the theoretical phase velocities of the Love wave and the Rayleigh wave, respectively. The phase velocity using the divergent component showed an intermediate result between the Love wave and the Rayleigh wave.