We have developed the slant stacking approach in the generalized S-transform (GST) domain of seismic data for the estimation of the group velocity of the multimodal surface wave. We used two versions of the GST. The constant-scale GST uses a constant scaling factor in the Gaussian window to control the spectral time-frequency localization. We found that a smaller scaling factor should be chosen for the low-frequency surface wave, whereas for higher frequencies, a larger scaling factor should be chosen. Therefore, the transform exhibits a trade-off in the group velocity resolution of low frequencies with small values of the scaling factor and the group velocity resolution of high frequencies with large values of the scaling factor. The modified S-transform (MST), another version of the GST used in this study, enhanced the time-frequency resolution by projecting the frequency into a linear frequency function in the Gaussian window. This property allowed us to estimate the group velocity for a broad range of frequencies. We demonstrated the robustness of the MST for the estimation of the group velocity by synthetic and real data examples.

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