In this study, a modified anisotropic elastic Weiskopf model for a sandy medium was introduced, satisfying the highest rotational symmetry compatible with a Weiskopf sandiness parameter greater than the unity. The developed approach was applied for computing and comparing head SP waves propagating along the free surface of the halfspace. The comparison revealed a substantial discrepancy in the SP wave pulses detected at the points of observation. The developed models for the generation and detection of SP waves are based on the FEA (finite element analysis) of the inner Lamb problem.