The SS-wave traveltimes can be derived from PP- and PS-wave data with the previously derived method. We have extended this method as follows. (1) The previous requirement that sources and receivers be located on a common acquisition surface is removed, which makes the method directly applicable to PS-waves recorded on the ocean bottom and PP-waves recorded at the ocean surface. (2) By using the concept and properties of surface-to-surface propagator matrices, the second-order traveltime derivatives of the SS-waves are obtained. In the same way as for the original method, the proposed extension is valid for arbitrary anisotropic media. The propagator matrix and geometric spreading of an SS-wave reflected at a given point on a target reflector are obtained explicitly from the propagators of the PP- and PS-waves reflected at the same point. These additional parameters provided by the extended method can be used for a partial reconstruction of the SS-wave amplitude as well as for tomographic estimation of the elastic velocity model. A full simulation of the SS-wave, which includes reflection and transmission coefficients, cannot be obtained directly from recorded PP- and PS-wave amplitudes.