Wavenumber, group velocity, phase velocity, and frequency-dependent attenuation characterize the propaga-tion of surface waves in dispersive, attenuating media. We use a mathematical model based on the generalized S trans-form to simultaneously estimate these characteristic para-meters for later use in joint inversion for near-surface shear wave velocity. We use a scaling factor in the generalized S transform to enable the application of the method in a highly dispersive medium. We introduce a cost function 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, the estimated wavenumber is perturbed. As a solution, we estimate wave-number perturbation by minimizing the cost function, using Simulated Annealing. We use synthetic and real data to show the efficiency of the method for the estimation of the propa-gation parameters of highly dispersive and noisy media.
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