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\title{The Seismic Data Compression Limitations of the Singular Value Decomposition} 

\begin{center}
{\bigit
Ray Abma}
\end{center}
\righthead{Seismic Data Compression}
\lefthead{Abma}

\ABS{
  Reflection seismic data require large volumes of digital storage at a great 
technique is not practical.
}

\shead{Introduction}

    The cost of storing reflection seismic data is enormous and could be reduced
for cases where very-accurate reconstruction is needed.

\shead{The Need for Compression} 

    An effective seismic data compression method
  would be useful in storing 
the need for these costly
new technologies.

\shead{Data Compression with the Singular Value Decomposition}

A traditional method of compressing 
images
using the singular value decomposition

% \passivesideplot{Fig1}{width=7.in,height=4.in}{.}{A photograph
% and its decomposition. Notice the sharp drop in the magnitudes of the
%singular values shown in Sigma. Also notice the low frequency data
%in the lower part of the U and V matrices.}

 \passiveplot{FigR}{}{.}{Reconstructed photographs
using 5, 10, 15, and 30 singular values.  The reconstruction using 30
singular values is practically identical to the original.}

 \passiveplot{FigM}{}{.}{Reconstructed photographs
using 5, 10, 15, and 30 singular values.  The reconstruction using 30
singular values is practically identical to the original.}

\shead{Reconstruction Problems with Seismic Data}

Compared to photographs, reflection seismic datasets are 


\shead{Conclusions}

Reflection seismic data cannot be reconstructed accurately from
compressed forms using the singular value decomposition 
because dipping events
and high frequency detail map into the small singular values,
violating the assumption that these small singular values can be ignored in
reconstructing the compressed image.
While other applications of singular value decomposition compression
exist in the seismic industry, this technique fails to compress
the largest amount of data stored, the seismic reflection data.

\REF 
\reference{Alford, R., 1986, Shear data in the presence of
azimuthal anisotropy: Dilley, Texas: 56th Ann. Internat. Mtg., Soc.
Explor. Geophys., Expanded Abstracts, 476--479.} 

\reference{Herrmann, P., Verschuur, D.J., Wapenaar, C.P.A., and Berkhout, A.J., 1989, Decomposition of multicomponent data into primary P- and S-wave responses: 51st Mtg. of the EAEG, Abstracts of papers, 69--70.} 

\reference{Nichols, D.E., 1989, Converting surface motions to
subsurface wavefields: SEP--{\bf 61}, 179--200.} 

\reference{Nichols, D.E., 1991, Simple anisotropic modeling: SEP--{\bf 70}, 337--356.}