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define CDOT ' { "" sup { bold { ^.^ } } }  '
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define DE ' { \(de } '
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.nr VS 18
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Parallel finite-difference migration
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Stewart A. Levin
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SUMMARY
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Finite-difference migration in the natural $x-t$ coordinates,
e.g. the $15\(de$ implicit wave-equation method,
has been in common use for over a decade of geophysical data
processing.
As such, it predated the invention of large vector computers,
such as the Cray-1S introduced in 1977,  and so was organized and optimized
to achieve the sensible objectives of reducing the number of computations
and I/O operations as much as possible.  Outboard array processors,
employed to accelerate computations,  changed the relative weights of
computation and I/O but still fit comfortably into existing
program designs.
.LP
Research interest has since moved to other methods of migration,
such as Fourier domain algorithms,  prestack and 3-D processing.
These developments were fueled by the appearance of new parallel
and vector computer architectures.  Quite naturally these new migration
techniques mirror the new architectures on which they were developed.
Little attention is paid to adapting the older,
workhorse migration algorithms to these new architectures.
For practical reasons, conversion efforts concentrate
on emulating the old array processor codes.
.LP
In this presentation I will use the example of $15\(de$
implicit finite-difference migration as convincing evidence
that conventional migration programs may not be well suited to
modern vector and parallel computers.  By completely reorganizing
computations along parallel lines I show how to produce the identical
migrated section much more efficiently.  Actual tests on a Convex C-1
vector computer ran an impressive five times faster than the
conventional, though highly optimized, organization.