Frequency domain generalized internal multiple imaging with energy norm

Seismic data often includes scattered energy of all types including those corresponding to multi scattering. Traditional imaging techniques are focused on the primary reflections, and thus, may fail to image crucial structures, like faults, which sometimes are only illuminated by the higher-order scattering. A process, referred to as generalized internal multiple imaging (GIMI), offers an opportunity to image higher order scattering by incorporating an interferometric cross-correlation step of the back propagated wavefield with the recorded data into the standard imaging process. The interferometric step is performed on a large portion of the data, which leads to a considerable increase in the cost of imaging, especially in the time domain. Therefore, we formulate a frequency domain GIMI to replace the cross correlation with a simple multiplication, which makes the implementation more practical. In addition, we apply the energy norm imaging condition to isolate the scattering component or its tomographic term. We show these features on numerical experiments.