Optimization and geophysical inverse problems Page: 27 of 37
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The availability of the necessary computational facilities continues to be an important consider-
ation in the choice of geophysical inverse problems that are attempted. Fast work stations have
greatly expanded the convenience of solving small to moderate sized problems. However, for
large problems there is still a need for the resources that can only be found at specialized facili-
ties. This is because the large problems need not only fast computers but also large amounts of
memory and storage.
The solution of geophysical inverse problems can place demands upon a computational sys-
tem that are different from those of normal usage and often in conflict with normal administrative
methods. For instance, some problems require the analysis of massive amounts of observational
data both prior to and during the actual solution of the optimization problem. These data are
typically too massive to be stored in active memory and must be continuously migrated between
memory, cache, and disk. Furthermore, with allowance for monitoring of the process and in-
spection of intermediate steps, such analysis of the data could go on for weeks or even months,
even though the amount of CPU time used during that period could be quite moderate.
6.2 Massively parallel systems
There is a class of large and difficult geophysical inverse problems that at present can only be
attempted on massively parallel computer systems (Newman and Alumbaugh, 1997). This is
true of many problems that attempt a complete analysis of three-dimensional properties of the
earth, with the appraisal stage of the analysis often being more computer intensive than the
solution stage. Solving such problems on massively parallel systems usually requires special
organization of the problem and the use of special methods that take advantage of the parallel
Improvements in visualization equipment and software could contribute significantly to the so-
lution of many geophysical inverse problems. Visualization is needed not only for the display of
final results, such as the the three-dimensional distribution of some property within the earth,
but also for the display of intermediate results, such as a depiction of the progress being made
by the search algorithm.
7 Summary and Conclusions
The workshop was successful in identifying a number of areas where improvements are needed
in our ability to solve geophysical inverse problems and in suggesting some directions of research
that might possibly achieve these improvements. A summary of these targets for future study is
listed below. It should be pointed out that this list is not complete, as only a few specific topics
of geophysical inverse practice were discussed at the workshop, with the choice controlled mainly
by the interests of the participants. The list is heavily weighted toward those areas where there
were obvious connections between the fields of numerical optimization and geophysical inverse
Two general needs that always have and always will be controlling factors in the progress of
geophysical inverse methods are:
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Barhen, J.; Berryman, J.G.; Borcea, L.; Dennis, J.; de Groot-Hedlin, C.; Gilbert, F. et al. Optimization and geophysical inverse problems, report, October 1, 2000; Berkeley, California. (digital.library.unt.edu/ark:/67531/metadc901685/m1/27/: accessed January 19, 2019), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.