This paper is the result of a year-long e-mail correspondence. Its final outline was created when the first author visited the Colorado School of Mines. We acknowledge the support of the Stanford Exploration Project and the Center for Wave Phenomena Consortium Project and their directors, Jon Claerbout and Norman Bleistein. We are thankful to Ilya Tsvankin, Ken Larner, and the members of CWP's ``A-team'' for insightful discussions.