Linux clusters in Earth Sciences Seismic and Geothermal examples.

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Linux clusters in Earth Sciences - Seismic and
Geothermal examples.

• Tomasz Danek, Anna Pieta
• AGH - University of Science and Technology
• Faculty of Geology, Geophysics and Environmental
  Protection
• Department of Geoinformatics and Applied Computer
  Science

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Linux clusters in Earth Sciences

• hardware is available form multiple sources
• no reliance on a single software/hardware vendor
• support from Linux community
• usually based on standards
• LOT OF SOFTWARE
• High performance/cost ratio

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Clusters used in experiments
Our clusters of workstations
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Clusters used in experiments
CINECA clusters
System Linux SuSE SLES 8 Queuing LSF (PBS
during some experiments) Parallel Libraries MPI
System AIX 5.2 Queuing LoadLeveler Parallel
Libraries MPI, openMP, LAPI
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Decomposition and parallelization coefficients

• Decomposition
• Old idea Federico Luigi Menabrea(1842)
• Types
• Functional decomposition
• Data decomposition

• Coefficients
• Time T
• Acceleration
• Efficiency

P number of processors
Amdahls law
? percentage of serial code
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Seismic modelingbackgrounds and results

• Full wave-field modeling based on FDM
• Easy to solve and decompose
• Lot of arithmetic operations

Example Modeling in 2D anisotropic media



Left border condition

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Seismic modelingbackgrounds and results
Elastic solution
Acoustic solution
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Seismic modelingbackgrounds and results
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Seismic modelingbackgrounds and results
Model size 500 x 500 Shoot point 1 Method
serial
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Seismic modelingbackgrounds and results
Elastic modeling Number of shoot points 20
Relation between time of computations and number
of computers in elastic case. White bars
represent domain decomposition, black
bars represent one PC - one shoot point
decomposition.
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Seismic modelingbackgrounds and results
Data pack size 256 MB Ethernet Fast and
Gigabit Procedure MPI_Bcast
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Seismic modelingbackgrounds and results
Model size 500 x 500 Kernels 2.4.22 and
2.6.11 Acoustic modeling One process or two
processes on single processor with HT technology
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Migration A dipping reflector model
EARTH SECTION
RECORD SECTION
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Kirchhoff migration SINGLE TRACE
Each point of the Earth interion may be seismic
energy refractor.
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F-x migrationACOUSTIC WAVE EQUATION
where P(x,z,t) - pressure, v(x,z) velocity
of the acoustic wave, t time,
where kx x-component of the wave vector ? -
angular frequency kz- dispersion relation
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Kirchhoff migrationSPEEDUP EFFICIENCY
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F-x migration SPEEDUP EFFICIENCY
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Geothermal heat modeling

• Heat moves by
• conduction
• convectin
• radiation

The two dimensional heat equqtion .
where T(x,z,t) temperature ? - thermal
conductivity ? - density c specific heat
capacity Qw radioactive heat
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Explicit method
where , ?t time sampling interval, ?x i
?z distance between grid points respectively
in the x and z direction, nx i nz model
dimensions respectively in the x and z
direction
The scheme is stable whenever
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Implicit method
where
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Geological area
Legend
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Computing time and memorymodel size 300x50,
number of processors 5
Computing time s for one year simulation.
Memory 1,1 GB
Master 237kB Slave 60kB
Explicit method 0,14 s
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Conclusion

• Decrease of computing time with increase of
  number of processors
• Monotonical increase of speedup for both
  migration method
• Increase of the computing time for Kirchhoff
  migration for 30 processors

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Conclusion

• explicit methods for large scale geothermal
  modeling
• implicit methods equal decomposition better
  than block decomposition