Mathematical inverse problems

In mathematics the solution to an inverse problem has come to mean the ``determination'' of material properties from wavefields. Often this is achieved with a ``convergent sequence.'' Geophysicists are less precise (or more inclusive) about what they mean by ``determination.'' In some chapters of this book reflectors are ``determined'' by the exploding-reflection concept. In chapter shot-to-geophone offset is incorporated, and reflectivity c(x,z) and velocity v(z) are ``determined'' with a buried-experiment concept. In chapter the concept is developed of suppressing multiple reflections and finding the ``true'' amplitudes of reflections by having the upcoming wave vanish before the onset of the downgoing wave. Other imaging concepts seem likely to result from future processing schemes. It might be possible to show that some of our ``determinations'' coincide with those of mathematicians, but such coincidence is not our goal here. Such a goal is formulated more directly in my third book .