**Prof. John Sylvester**

University of Washington, Seattle, WA

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

**Abstract:**

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]