Fig. 1
a Array geometry showing seven receivers in two nested triangles. There are six station separation distances r1–r6 available for spatial averaging of coherency spectra. For array S, large side-length r4 = 20 m, and the six interstation distances r1–r6 are 5.8, 10.0, 11.5, 20.0, 10.0 and 17.6 m. b Locality of arrays for microtremor observations in Kumamoto City, Japan. Centre of the array is at 32.775641°N, 130.687920°E. Red circles show a pair of nested triangles side lengths 481 and 962 m. c SPAC spectra for a small array near the center of (b) using a triangle side-length 10 m. Black line—observed SPAC; red and blue lines—model SPAC spectra for the fundamental Rayleigh mode R0 and the effective mode Re. The fitting is performed by least squares using the Re curve. Thick black horizontal line—the frequency range used in the curve fitting. d and e HVSR spectra and SPAC spectra for the radial separations (yellow dotted lines each of length 277 m) of stations LL2, LL3, LL4 from center LL1 in (b). Black line—observed spectra; red and blue lines—model spectra for the fundamental Rayleigh mode R0 and the effective mode Re; yellow, green lines—model spectra for modes R2, R3. f, g Vs profile interpreted by fitting observed and model SPAC spectra for all six array triangles including the two shown in this figure. Strong velocity contrasts in Vs at depths 26 m and 750 m are the primary cause of the HVSR peaks at 1.2 Hz and 0.35 Hz