On the range of the forward map for the viscoelastic seismic inverse problem

Abstract

This paper examines the range of the forward map for the one-dimensional viscoelastic seismic inverse problem. It is shown that the viscoelastic problem inherits properties that characterize the range of the lossless system, in both the continuum and discrete cases. Furthermore, in the discrete case it is shown that the range of the forward map for a viscoelastic system is actually a proper subset of the range for a lossless system.