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Quantitative imaging of subsurface earth properties in elastic media is performed from distributed acoustic sensing data. A new misfit functional based upon the reciprocity gap is designed, taking crosscorrelations of displacement and strain, and these products further associate an observation with a simulation. In comparison with other misfit functionals, this functional has the advantage of only requiring little a priori information on the exciting sources. In particular, the misfit criterion enables the use of data from regional earthquakes (teleseismic events can be included as well), followed by exploration data to perform a multiresolution reconstruction. The data from regional earthquakes contain the low-frequency content that is missing in the exploration data, allowing for the recovery of the long spatial wavelength, even with very few sources. These data are used to build prior models for the subsequent reconstruction from the higher frequency exploration data. This results in the elastic full reciprocity-gap waveform inversion method, and we illustrate its performance with a pilot experiment for elastic isotropic reconstruction.