  Seismic waves are the most sensitive probe of the Earth's interior we have.
With the dense data sets available in exploration, images of subsurface
structures can be obtained through processes such as migration. Unfortunately,
relating these surface recordings to actual Earth properties is non-trivial.
Tomographic techniques use only a small amount of the information contained in
the full seismogram and result in relatively low resolution images. Other
methods use a larger amount of the seismogram but are based on either
linearization of the problem, an expensive statistical search over a limited
range of models, or both. We present the development of a new approach to full
waveform inversion, i.e., inversion which uses the complete seismogram. This
new method, which falls under the general category of inverse scattering, is
based on a highly non-linear Fredholm integral equation relating the Earth
structure to itself and to the recorded seismograms. An iterative solution to
this equation is proposed. The resulting algorithm is numerically intensive but
is deterministic, i.e., random searches of model space are not required and no
misfit function is needed. Impressive numerical results in 1D are shown for
several test cases.
