### unfinished doctoral thesis abstract

I was in residency in the Ph.D program in Geophysics at the
University of British Columbia (UBC) from 1988-1995. A research project,
begun in 1990 on "Integral Equation Modelling of Acoustic Diffraction From
Cylindrical Shapes," resulted in one conference presentation and should
result in one or two short journal articles eventually.
In Chapter 1 I briefly review relevant literature
on techniques of modelling diffraction and scattering
and give an overview of the rest of the thesis.

In Chapter 2 the solution for acoustic diffraction by
a half plane is implemented by using a recursive ARMA
operator. This work will be padded and extended slightly in
later drafts and will be used to test the work in
later chapters. A section on the similar slant stack
operator is included in an appendix.

In Chapter 3 I use Backus-Gilbert linear inverse
theory methods, modified for complex data, to solve an
integral equation for surface field derivatives which are then
substituted into a radiation integral to get the total field
away from the cylinder. This will be extended to the
flattest model and to a parametric approach shortly

Chapter 4 extends the results of Chapter 3 with
some resolution analysis or appraisal, beginning
with averaging function analysis. Future
drafts [unlikely] will also extend the results to
arbitrary 2--D geometries and node placings, and
will connect with Chapter 4 by considering the
half plane or truncated half plane model. Complex
averaging functions and an approach that takes into
account the radiation integral, plus stuff related
to the flattest and parametric models, will also
be considered.