An unsupervised wavelet transform method for simultaneous inversion of multimode surface waves

Dispersive surface waves are sensitive to the geometry of layered structures and the compressional and shear wave velocities within each layer. Therefore they can be used to estimate the structure and lithology of shallow soils. It is common practice to use the low frequency fundamental mode for inversion; thus, it is necessary to separate the single modes contained in the data interactively, which is time consuming and a source of error. The fast algorithm presented in this paper interprets all excited modes of a surface wave simultaneously and avoids the need to identify individual mode-numbers. The inversion is based on the group travel time of a Rayleigh wave, estimated from a single seismic trace by application of the Continuous Wavelet Transform (CWT). The resulting CWT distribution is fitted by a composition of wavelets determined from theoretical group-velocity dispersion relations of possible models, in connection with appropriate boundary conditions. A feasibility test on a synthetic dispersion dataset with dominant higher modes shows that the systematic inversion error associated with a fundamental-mode assumption does not arise, and both layer thicknesses and elastic properties can converge rapidly to the true values. However, two possible problems with the proposed method are the imperfect reconstruction (in this case especially at low frequencies), owing to the limited number of wavelets and theoretical modal dispersion curves used for approximation, and possible convergence to local minima, due to the increased nonlinearity of the misfit function.