  Quantitative imaging of sub-surface Earth's properties in elastic media is
performed from Distributed Acoustic Sensing data. A new misfit functional based
upon the reciprocity-gap is designed, taking cross-correlations of displacement
and strain, and these products further associate an observation with a
simulation. In comparison with other misfit functionals, this one has the
advantage to only require 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 multi-resolution reconstruction. The data from
regional earthquakes contain the low-frequency content which is missing in the
exploration ones, 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
gives the elastic Full Reciprocity-gap Waveform Inversion method, and we
demonstrate its performance with a pilot experiment for elastic isotropic
reconstruction.
