In characterizing reservoirs, we are often interested in retrieving detailed elastic parameters for only a very limited part of the subsurface. One way of doing so involves studying the seismic reflection response within the region of interest. To that end, we introduce a local solver that uses an acoustic solver to propagate the wavefield to a subdomain on which we use a local elastic solver. This avoids the use of an expensive full-domain elastic solver while still incorporating elastic physics in the region where it is most important. We then study whether this modeled phase is sufficiently accurate for recovering important subsurface reservoir properties in an inversion procedure.