SUGGESTION AND THEORETICAL EVALUATIONS ON THE PERFORMANCE OF A NEW METHOD TO EXTRACT PHASE VELOCITIES OF RAYLEIGH WAVES FROM MICROTREMOR SEISMOGRAMS OBTAINED WITH A CIRCLULAR ARRAY

摘要

We present a formulation of a new method to determine phase velocities of Rayleigh waves from microtremor waveforms obtained with a circular array of seismometers, as well as practical considerations on the technical details of the method. In our method the seismograms are averaged along the circumference at each time step with an appropriate set of weights. The spectral ratio of two different kinds of such time histories, obtained by averaging with different sets of weights, depends solely on the product rk (k: wavenumber, r: array radius); we can derive information on k since r is known. According to the results of theoretical calculations based on a deductive approach and conducted for the case where the wavenumber is a single-valued function of frequency, an array of three sensors is expected to be sufficiently useful in realistic situations where microseisms arrive from many directions. The theoretical calculations also revealed that the analysis method is valid for wavelengths upward of 4r; that the presence of incoherent noise makes analysis in long wavelength ranges difficu and that the upper limit of the analyzable wavelength is roughly equal to 40r and 10r for SN ratios of 100 and 10, respectively.