An experimental study on the upper limits of wavelength of Rayliegh wave estimated by the Frequency-Wavenumber spectrum method or the Spatial Autocorrelation method using a microtremor array technique

摘要

In a microtremor array technique phase velocities must be obtained in a wide-range of wavelength in order to estimate underground structures precisely. Frequency-wavenumber spectrum (F-K) method and Spatial auto-correlation (SPAC) method are used to estimate phase velocities of surface waves in microtremors. Recent studies using techniques of numerical simulation or field experiment show that SPAC method can observe longer wavelength possible to estimate phase velocities in microtremors than F-K method. We also examine and discuss the upper limits of wavelength calculated using microtremor array data by the two kinds of methods. For the above purpose, microtremor array observations were carried out in four sites of Morioka city, Iwate Prefecture. The array configuration is a triangle with seven vertical seismometers. The array size defined by the distance between a center and an apex of the triangle ranges from 10 m to 100 m. Three or four arrays with different sizes were used at one observation site. Phase velocities of Rayleigh wave in microtremors were observed by F-K method and SPAC method. We defined a standard phase velocity which was calculated from all the array records at one site. To estimate the upper limits of wavelength, a residual between standard phase velocity and observed phase velocity for each array was defined within 0.1. The range of the estimated upper limits of wavelengths by F-K method were from 2.3 to 6.8 times for a distance between a center and an apex of the triangle array, and those by SPAC method were ranging from 3.2 to 17.2 times. These results show that SPAC method can observe longer wavelength possible to estimate phase velocities in microtremors than F-K method.