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. Provided that we understand 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.
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