Estimation of phase velocity using array observation of microtremors with arbitrary shape

• Published in: Earth, planets, and space Vol. 75; no. 1; pp. 88 - 26
• Main Authors: Kimura, Harusato, Morikawa, Hitoshi, Tomobe, Haruka, Iiyama, Kahori
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.12.2023; Springer; Springer Nature B.V; SpringerOpen
• Subjects: 4. Seismology; Algorithms; Arbitrary array shape; Array observation; Arrays; Complex coherency function (CCF); Earth and Environmental Science; Earth Sciences; Earthquakes; Effects of Surface Geology on Seismic Motion (ESG): General State-of-Research; Estimation errors; Geology; Geophysics/Geodesy; Heuristic methods; Japan; Mathematical optimization; Microtremor survey; Numerical simulation; Numerical simulations; Particle swarm optimization; Phase velocity; Random variables; Representations; Seismic waves; Triangles; Velocity; Japan; Microtremor survey; Direct spatial auto-correlation (DSPAC) method; Phase velocity; Complex coherency function (CCF); Arbitrary array shape; Particle swarm optimization (PSO); Spatial auto-correlation (SPAC); Array observation; Numerical simulation
• ISSN: 1880-5981; 1343-8832; 1880-5981
• DOI: 10.1186/s40623-023-01831-6

To estimate the phase velocity using the array observations of microtremors, some algorithms for the estimation include constraints on the array shape, such as equilateral triangles or the placement of receivers on a circle, in order to reduce the estimation error of the phase velocity. In the present study, a direct estimation technique is introduced for the phase velocity using records obtained through an array with an arbitrary shape based on a complex coherency function (CCF), where CCF is defined as the normalized cross spectrum of the microtremor records observed simultaneously by two receivers. The particle swarm optimization (PSO) method, one of metaheuristic optimization methods, is applied and optimal values are provided for the phase velocity and other unknown parameters. Approximate representations of the stochastic properties for the unknown variables are analytically derived based on the discrete representation of the CCF, for a case where the arrival directions of microtremors are treated as random variables following a uniform distribution. Furthermore, the validity of the proposed method is confirmed using numerical simulations and actual observation records. Graphical Abstract