Cooperation of the leading order terms in an inverse-scattering subseries for imaging: 1-D analysis and evaluation

Summary Our ability to image targets beneath complex overburdens is compromised by our ability, under these circumstances, to find the precise velocity model with which to downward continue the measured wavefield. As part of a research effort responding to this challenge, a subseries of the inverse scattering series has been identified that is responsible for locating seismic events in depth using measured reflection data and only the wave velocity of a reference medium – not the actual medium. Analytical and numerical studies of this subseries for a 1-D constant density acoustic medium have revealed a welcome property. The leading order contributions to this imaging subseries cooperate to locate reflectors at the correct depth. In the context of the convergence of the imaging subseries, this cooperative behavior suggests that the leading order terms in the subseries will not have the deleterious property that successive terms overshoot/undershoot the correct depth. This cooperation also serves to unambiguously indicate whether the reference velocity is slower or faster than the actual medium velocity. The information comes from the amplitudes and kinematics of the data at and above the reflector being imaged.