Accurate estimation of the group velocity of surface waves using sparse S-transform and sparse slant-stacking

Surface wave group velocity is an important property by which we can obtain an S-wave velocity model of subsurface through an inverse procedure. The S- wave velocity modeling using the group velocity has some advantages over the phase velocity because it does not require an estimation of the initial phase or to have a dense array of geophones. In addition, the group velocity estimation is not distorted when the geophone interval is significant. However, uncertainties associated with the transformation by which the group velocity is calculated might introduce some errors to the estimated group velocity. In this study, we introduce a new approach for the estimation the group velocity of the surface waves using the sparse S-transform and sparse slant-stacking that is based on the proximal forward-backward splitting algorithm. Compare to the conventional methods for the estimation of the group velocity using the generalized S-transform, it yields a more accurate estimation of the group velocity. We demonstrate the robustness of our method by synthetic and field data examples