  Source footprints represent an inherent problem to full-waveform inversion
(FWI). They are caused by the high data sensitivity to the model parameters in
the vicinity of the seismic sources and can be exacerbated by source-related
errors in the modeling operator. We propose a simple, effective, and efficient
method to remove source footprints in FWI when sources are located near or
inside the volume of interest while robustly updating the model in their
vicinity. The method uses illumination redundancy and extends the model along
sources. Each source updates one component of the extended model, and a
regularization term ensures that these components are mutually consistent,
except for their respective footprints. We illustrate the effectiveness of our
method on the elastic inversion of synthetic guided waves. We show its
robustness in the presence of source-related errors and its superiority over
other well-known approaches, such as illumination compensation by inverse
pseudo-Hessian and gradient preconditioning. We apply the method to a field
distributed acoustic sensing dataset with elastic guided waves generated by
perforation shots in an unconventional shale reservoir. The method is able to
retrieve localized reservoir anomalies with higher elastic velocities,
indicating possible lower pore pressure or tighter shale regions.

Geophysics