An Extension of Linear Inverse Scattering Methods for Absorptive Media to the Case of an Absorptive Reference

We cast and present inverse scattering quantities appropriate for the description of a two-parameter (P-wave velocity and Q) absorptive medium given an absorptive reference, and present a tentative procedure for carrying them out on measured seismic primary data. We note particularly that (1) this procedure involves a Q compensation component, and therefore must be expected to require regularization in the presence of noise, and (2) the formalism does not tend to our earlier non-absorptive reference procedure as reference Q goes to infinity; the absorptive, or the non-absorptive reference case must be chosen at the outset. These linear inverse results form part of a developing framework for direct non-linear Q compensation, or data-driven enhancement of resolution lost due to absorptive processes.