Frequency-domain least-squares generalized internal multiple imaging with the energy norm

Recorded seismic data contain various types of scattered energy, including those corresponding to multiples. Traditional imaging techniques are focused on the single-scattering events, and thus, may fail to image crucial structures, such as salt flanks and faults that sometimes are only illuminated by the multiple scattered energy. The recently introduced generalized internal multiple imaging (GIMI) offers an opportunity to image multiples by projecting the recorded data back into the subsurface, followed by an interferometric cross-correlation of the subsurface wavefield with the recorded data. During this process, the interferometric step converts the first-order scattering to a tomographic component and the double-scattering forms the primary reflectivity. Dealing with a large volume of data consisting of full wavefields over the image space, renders the interferometric step computationally expensive in time-domain. To make the implementation of GIMI tractable, we formulate its frequency-domain version. Moreover, we use the energy norm imaging condition to separate the reflectivity part from the tomographic component. We demonstrate these features with numerical experiments.