Direct non-linear modeling and inversion of primaries in extended heterogeneous media
Some quick definitions: an "event" is a coherent arrival of energy in a wave data set. Before they get measured, these parcels of wave energy propagate around in the medium, undergoing some set of reflections and interactions. A "primary" is an event in a reflection-type experiment that has propagated down into the medium, reflected once, and propagated back up to the surface. This is in contrast to a "multiple", which reverberates around, experiencing more than one upward reflection.
NON-LINEAR MODELING OF PRIMARIES
In scattering theory, the forward Born approximation is often used to model primary reflections. This approximation is straightforward to make, but there are lots of situations where, if you keep your chosen reference medium (needed for scattering descriptions) simple, the Born approximation can be pretty poor. We have noticed, while studying the inverse scattering problem at M-OSRP, that you can create far more accurate (though nonlinear) scattering models of primaries. Below numerical results from two such approximations are illustrated for a simple layered model.
DIRECT NON-LINEAR INVERSION
This might be useful for inverse purposes, because it turns out you can do a direct, order by order inversion of these approximation series in the same way that you can derive the full inverse scattering series. The result is a set of inverse algorithms that directly and non-linearly determine the medium from primary data. See below. It is a kind of neat result, but, maybe more importantly, we can use it as a framework for doing some of the non-linear seismic absorption processing stuff we're interested in also.
