A generalization of the wave-equation target-oriented inversion to the prestack image domain needs regularization, since the condition number of the target-oriented Hessian matrix can be high. Two prestack regularization methods to stabilize the subsurface-offset domain inversion were compared. The first, an identity operator which penalizes the size of the overall image (damping). The second, a differential semblance operator that penalizes the energy in the image not focused at zero subsurface-offset Shen et al. (2003).
While imaging the Sigsbee model, both prestack inversion methods obtained better zero subsurface-offset images than migration, increasing the resolution and the continuity of the events into the shadow zones. The main differences between them is away from zero subsurface-offset where the the second method present less energy as imposed by the regularization.
The effects that both regularizations might produce in the angle domain image, after applying a subsurface-offset to angle transformation following Sava and Fomel (2003), will be a subject of future study.