Inverse wavefield extrapolation revisited: limitations of single‐ and multi‐valued operators

Abstract

Most approaches to inverse wavefield extrapolation have in common that the operator is defined as the time-reversed (or complex conjugated) forward operator. Despite the time-symmetry of the wave equation, this time-reversal introduces errors even for the simple situation of a homogeneous medium and an infinite aperture. In strongly inhomogeneous media the kinematical aspects of multi-valued events are handled correctly, but angledependent errors occur in their dynamical behaviour. Introduction Inverse wavefield extrapolation plays a central role in seismic migration. Independent of the actual numerical implementation, most approaches have in common that the inverse extrapolation operator is defined as the time-reversed or, in the frequency domain, complex conjugated forward operator. This stems from the simple fact that the acoustic wave equation is symmetrical in time. In this paper we analyze the limitations of inverse extrapolation with time-reversed forward operators.