Stacking operators:
Adjoint versus asymptotic inverse

Sergey Fomel

sergey@sep.stanford.edu

ABSTRACT

The paper addresses the theory of stacking operators used in seismic data processing. I compare the notion of asymptotically inverse operators with the notion of adjoint operators. These two classes of operators share the same kinematic properties, but their amplitudes (weighting functions) are defined differently. I introduce the notion of the asymptotic pseudo-unitary operator, which possesses both the property of being adjoint and the property of being asymptotically inverse. The weighting function of the asymptotic pseudo-unitary stacking operator is completely defined by its kinematics. I exemplify the general theory by considering such stacking operators as Kirchhoff datuming, migration, offset continuation, DMO, and velocity transform.