  Least-squares migration can, in theory, reduce the acquisition footprint and
improve the illumination of the subsurface structures. It can also recover the
amplitudes of the events to some extent. However, the migration operator is not
complete. In other words, the operator does not span the full range of the
model and the portion of the model that is in the null space of the operator
will not be recovered even by posing imaging as an inverse problem. In
geophysical terminology, in complex subsurface structures, rays or the wave
energy will penetrate poorly in some regions, e.g., subsalt region, and that
region will be a shadow zone to our acquisition system. The shadow zone is in
the null space of the migration operator and the subsurface information in that
region will not be recovered. Accordingly, in this research, we aim at using
another set of data whose ray paths are different from the surface seismic.
Seismic-while-drilling (SWD) dataset are complementary to surface data, and it
brings an opportunity to address seismic illumination issue by adding new
measurements into the imaging problem. After considering the correlative and
non-impulsive nature of the SWD source signature, the prestack least-squares
depth migration of the SWD dataset can be achieved. We study the feasibility of
the least-squares reverse time migration of the SWD dataset and its potential
in imaging the parts of the model which are in the shadow zone of the surface
seismic acquisition.
