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\title{An Application of Parallel Interval Techniques to Geophysics}
\author{Dara Morgenstein$^1$ and John Murphy$^2$}

\pagestyle{myheadings}

\markright{APIC'95, El Paso,
Extended Abstracts,
A Supplement to the international journal of {\rm Reliable
Computing}\ \ \ \ \ \ \ \ \ \ \  \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \
\ \ \ \ \ \ \ \ \ \ \ \ \ }

\maketitle

\section{Geophysical Problem}
In order to find out where the deposits (of oil, minerals, etc) are
located, we must know the 3--D structure of the area. To determine
this structure, we can dig several wells, place sound- and impulse-generating
devices and sensors in them, generate the impulses, and measure the
responses. These measurement results need to be further processed:
e.g., the time that it took the sound to travel from the generator to
the sensor depends on the properties of the media in between the
generator and the sensor. 

The problem of reconstructing the 3--D structure from these measurements
is therefore similar to the medial tomography problem, and it is
therefore called {\it geophysical tomography} \cite{Doser}. 

\section{It Is Necessary To Estimate Errors}
The measurements are imprecise, so, the results of this reconstruction
are also imprecise. So, it is necessary to determine the accuracy of
these results. 

\section{Sequential Methods}
To determine the accuracy of geophysical tomography methods, 
in \cite{Doser}, the general methods of error
estimation from \cite{Kreinovich et al 1991} have been implemented on a
sequential computer. 

\section{Parallel Techniques}
We have implemented algorithms from \cite{Doser}
in parallel, using a C--based
parallel language SR \cite{Andrews}. 

This program is implemented on a
network of SUN SPARC stations. The implementation is {\it flexible} 
in the sense that the user can tell it which machines are available at
present, and it will automatically distribute the computations between these
available machines. 
  
\auffil{The authors are with $^1$Department of Computer Science,
University of Arizona,
Gould-Simpson 721B, 
Tucson, AZ 85721, and $^2$Department of Computer Science, University
of Texas at El Paso, El Paso, TX 79968. 
The authors are grateful to A. Bernat, M. Baker, and D. Doser 
for valuable discussions.}

\begin{thebibliography}{99}
\bibitem{Andrews}
G. R. Andrews and R. A. Olsson, 
{\bf The SR Programming Language: Concurrency in Practice}, 
The Benjamin Cummings Publ. Co., 1993.

\bibitem{Doser}
D. I. Doser, K. D. Crain, M. R. Baker, V. Kreinovich, M. C. 
Gerstenberger, and J. L. Williams,
``Estimating Uncertainties for Geophysical Tomography'', {\it These
Proceedings}. 

\bibitem{Kreinovich et al 1991}
V. Kreinovich, A. Bernat, E. Villa, and Y. Mariscal, 
``Parallel computers estimate errors caused by imprecise 
data'', {\it Interval Computations}, 1991, No. 2, pp. 31--46.

\end{thebibliography}

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