The spectral analysis of surface waves (SASW) method, which is based on dispersive characteristics of surface waves, is an in-situ seismic method for determining the shear wave velocity (or, maximum shear modulus) profile of a site. Most of the surface wave energy exists within one wave length of depth, and in layered media, the surface wave propagation depends on the frequency (or, wavelength) of the wave because waves of different wave lengths sample different parts of the layered medium. The reliable determination of phase velocities with wavelength(or, frequency) is the most important task in the SASW method. The SASW method consists of three steps; field testing, evaluation of experimental dispersion curve, and determination of shear wave velocity profile by inversion process. In general, field testing and dispersion curve evaluation were regarded as simple and straight-forward work. However, under some field conditions when various noises exist in the field and/or the dominant modes of surface wave propagation shift with frequency, determination of experimental dispersion curve is a difficult task and the usual phase unwrapping method can lead to erroneous dispersion curve.
In this study, the evaluation method of dispersive phase and group velocities for SASW method was proposed using harmonic wavelet transform. The meanings of harmonic wavelet coefficients were interpreted in a different point of view and the step-by-step procedure to determine the dispersive phase and group velocities was suggested. In the proposed method, the group and phase delays at center frequency of bandwidth of the each wavelet were determined from magnitude and phase information of harmonic wavelet coefficients. Both phase and group velocities at each frequency can be directly obtained from information extracted from data and the problem owing to spurious cycles in wrapped angles in the phase spectrum can be overcome. The variation of signal/noise ratio with time can be considered at each frequency and the only portion of maximum signal/noise ratio is used to evaluate the phase velocities. The proposed method is less affected by the near field effect and can sample much deeper part of the site than the conventional phase unwrapping method at a given receiver spacing.
To evaluate the validity of the proposed method, the results of numerical simulations at the various kinds of multi-layered system and field data were utilized. The numerical simulations were carried out using the computer program, FIT7 developed at the Univiversity of Texas at Austin. Experimental setups in this study consists of three categoris. The first is regular soil profile in which the soil stiffness increases with depth. The second category is irregular soil profiles in which soil stiffness irregularly varies with depth. The last category is strong irregular profiles such as the pavement system in which stiffness of upper layer is much stronger than that of the other lower layers. The phase and group velocities determined by the proposed method match nicely with theoretical velocities showing good potential of applying the proposed method. The proposed method also has a possibility of the potential automation in the calculations of dispersive phase and group velocities for the SASW method.
