Prof. John Sylvester

University of Washington, Seattle, WA

"1-D Inverse Scattering by the Splitting of Layers"


We will give an elementary introduction to scattering and inverse scattering, requiring only familiarity with basic complex analysis and a little knowledge of the Fourier Transform. We will describe an approach to inverse scattering called Layer Stripping.       A layer is just a piece (an interval) of a medium (e.g. the top 50 centimeters of a sheet of ice). It is useful to think of a thick medium as a stack of thin layers, just it is useful to think of the Riemann integral as a sum of integrals over small intervals.       We wish to recover the medium properties (i.e. the speed of light) from observations of a reflected electromagnetic signal. There are three basic ingredients to our approach:       The Born Approximation A thin layer of a medium is easy to recognize from how it reflects an incoming wave.       The principle of Causality The reflections from the layers of the medium nearest the transmitter/receiver arrive before the reflections from deeper within the medium.       The Stacking and Splitting of Layers By making use of the principle of causality, and the conservation of energy, we develop rules for computing the signal reflected by a stack of layers from the reflections of the individual layers. To attack the inverse scattering problem, we develop a method to separate out the responses of the individual layers from the response of the composite stack of layers. The new ingredient in this approach is a strictly convex optimization problem, whose solution implements the layer splitting in the third step.

Friday, April 28, 2000
3:00 PM in 335 Jabara Hall

Please join us for refreshments before the lecture at 2:30p.m. in room 353 Jabara Hall.

[ Spring 2000]