Accounting for sub-wavelength heterogeneities in full waveform inversion based on wavefield gradient measurements

Seismic gradient measurements from distributed acoustic sensors, rotational sensors and otherinstruments are becoming increasingly available for field surveys. Such measurements providea wealth of information and are currently being considered for many applications. In this work,using a simple 2-D numerical approach, we tackle the implications of such wavefield gradientmeasurements on full waveform inversion (FWI) techniques using a simple two-dimensionalnumerical test. In particular, we study the impact of the wavefield gradient measurement sen-sitivity to heterogeneities that are much smaller than the minimum wavelength. Indeed, asshown previously through the homogenization method, small scale heterogeneities induce anunexpected coupling of the strain components to the wavefield gradient measurement. We fur-ther show that this coupling introduces a potential limitation to the FWI results if it is nottaken into account. We demonstrate that a gradient measurement-based FWI can only reachthe accuracy of a classical displacement field-based FWI if the coupling coefficients are alsoinverted. Furthermore, there appears to be no specific gain in using gradient measurementsinstead of conventional displacement (or velocity, acceleration) measurements to image struc-tures. Nevertheless, the inverted correctors contain fine-scale heterogeneities information thatcould be exploited to reach an unprecedented resolution, particularly if an array of receivers isused.