Asymptotic pseudounitary stacking operators

Conclusions

Stacking operators such as Kirchoff migration, datuming, dip moveout, velocity transform, etc. are widely used in seismic imaging and data processing, and the need often arises to invert them.

This paper fills the gap between the concept of asymptotically inverse operators and the concept of adjoint operators by introducing the notion of asymptotic pseudo-unitary stacking operators. A pair of asymptotic pseudo-unitary operators possesses the property of being both adjoint and asymptotically inverse to each other. The amplitude (weighting) functions of these operators are completely defined by the derivatives of their kinematics (stacking surfaces).

The practical advantage of this unification is in the ability to construct asymptotically optimal preconditioning for iterative least-squares solution of inverse problems. Simple preliminary tests are encouraging, but further practical experience is needed to confirm the theoretical expectations.