Reflectivity images obtained by prestack depth migration are often distorted by uneven subsurface illumination, especially in areas with complex geology, such as subsalt regions. We address the problem of uneven illumination in subsalt imaging by posing the reflectivity-imaging problem as a linear inverse problem and solving it in the image domain in a target-oriented fashion. The most computationally intensive part of the image-domain inversion is the explicit computation of the so-called Hessian operator. The Hessian is defined to be the normal operator of the associated modeling/imaging operator, which is a direct measure of the illumination deficiency of the imaging system. We can overcome the cost issue by using the phase-encoding technique in the 3D conical-wave domain for marine streamer acquisitions. We apply the inversion-based imaging methodology to a 3D field data set acquired from the Gulf of Mexico, and we precondition the inversion with nonstationary dip filters, which naturally incorporate interpreted geologic information. Numerical examples demonstrate that imaging by regularized inversion successfully recovers the reflectivities from the effects of uneven illumination, yielding images with more balanced amplitudes and higher spatial resolution.

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