Since accurate imaging of reflections is more important in the neighborhood of the reservoir, a target-oriented strategy can be applied to explicitly compute the inversion Hessian. This allows us to study the characteristics of the Hessian in different acquisition geometries and subsurface situations (low illumination, faults, etc. ) and will make possible the design of a strategy to approximate its inverse.
Results on the Sigsbee model show that inside the shadow zones, the Hessian ellipses split and reduce their energy. Something different happened close to faults, as can be seen in the Marmousi model. There, the Hessian ellipses are distorted but do not split. The latest results suggest that in complex areas the usual diagonal-matrix approximation of the Hessian might be insufficient to obtain the correct position and amplitude of the reflectors.