Dispersion and the dissipative characteristics of surface waves in the generalized S transform domain

Roohollah Askari and Robert J. Ferguson

ABSTRACT

Wave number, group velocity, phase velocity and frequency dependent attenuation characterize the propagation of surface waves in dispersive, attenuating media. Here, a mathematical model is developed based on the generalized S transform to simultaneously estimate these characteristic parameters of surface waves from a seismic record. We use a scaling factor in the generalized S transform to enable application of method in highly dispersive medium. We introduce a cost functions in the S domain to estimate an optimum value for the scaling factor. We also use the cost function to generalize the application of the method for noisy data, especially data with a low signal to noise ratio at low frequencies. In that case, experimentally we find that estimated wave number is perturbed. As a remedy, we estimate wave number perturbation by minimizing the cost function using Simulated Annealing. We present synthetic and real data to show the efficiency of the method for the estimation of the propagation parameters of highly dispersive and noisy media. We anticipate that, through inversion of the characteristic parameters of surface waves, near surface shear wave velocity will be obtainable.

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