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Computer Engineering of Wave Machines for
Seismic Modeling and Seismic Migration
R. Phillip Bording
March 10, 2005
0 Max Address
Husky Energy Chair in Oil and Gas ResearchMemorial University of Newfoundland
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Cache Memory- Three LevelsArchitecture
Address Pointer
MemoryMulti-
Gigabytes
Large and Slow160 X
16XL3 CacheMemory
Cache ControlLogic
L2 CacheMemory
L1 CacheMemory
2X 8X
16 Megabytes128 Kilobytes32 Kilobytes
2 Gigahertz Clock
Featuring Really Non-Deterministic Execution
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Problem Solving – 3DExample of Array
Addressing
Address = (k-1)*Lx*Ly +(j-1)*Lx+(i-1) + base
Grid Points
i,j,ki-1,j,k i+1,j,k
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Cache Memory Access Streams
1D Streams – 100%
1D +/-1 100%
2D +/-1 100%
2D +/-N 80%
2D +/-1 +/-N 26%
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Cache Memory Access Streams
3D +/-1 100%
3D +/-N 80%
3D +/-N*N 28%
3D ALL 7%
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IEEE 754 Floating Point
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IEEE 754 Floating Point
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IEEE 754 Floating Point
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SeismicModeling and the
Inverse Problem
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12 Streamers x 5.1 Kilometers Long Data collected for 70 continuous daysOver 2300 Square Km.
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3D Seismic Modeling1. Large Scale 3D ~200+ Wave Lengths2. Acoustic and Elastic Wave Equations3. In-Homogeneous Earth has widely varying parameters. 4. Complexity limits use of 3D elastic modeling5. Problem Scale
• Nx=Ny=Nz ~ 1000• Ntime ~ 10,000• Work per Grid Point ~ 100• Number of Seismic Shots per Survey ~ 100,000• Single Survey Simulation is 10^20 Operations.
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The Babbage Difference Engine, circa 1853
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Wave Equation Difference Engine (WEDE)
for Seismic Modeling
Four Processors
Acoustic Wave Equation
My PhD thesis project at the
University of Tulsa
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Wave Equation Difference Engine
Finite DifferencesElastic or Acoustic Wave EquationsRegular GridsSponge/One-Way Wave Equation
Boundary ConditionsAny Source/Receiver GeometryExplicit 4th order in Time & 8th order in Space?
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Wave Equation Difference Engine
No Cache MemoryDeterministic ExecutionNot a MIMD or SIMD or Data Flow
Data movement and control matches the algorithmEach grid point has control wordThree levels of parallelism, ( Amount of Parallelism)
Instruction trees, ~ 10-20Multiple Instructions with selection, ~2-3Multiple Grid points, ~Hundreds of Thousands
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Acoustic, Constant Density
Density is so constant it does not appear in the equation.
2 2 2 2
2 2 2 2 2
1
, ,src t
C
C is the P Wave Velocity.The source energy is in src.Psi is the wave field.
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Wave Equation Difference Engine
Machine Performance
100 operations in pipeline
1,000,000 grid point processors
100 Megahertz Clock
10^16 Operations per second
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Application Specific Parallel Computing
•Choose carefully an application which is BIG.•Find an algorithm which is suitable.
Good data locality.Regular structure in data movementHigh memory data transfers
•Map the algorithm into hardware
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Application Specific Parallel Computing
What it is not!
•Not suitable for just any algorithm•Not general purpose, we will have an efficient but
specific memory subsystem. • Does not match the alphabet soup, SIMD,
MIMD,NUMA, etc
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What do ASP machines need??
VLSI Design Team, fabless and good?
Clever Architect for the problem.
A very good memory design!
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What do ASP machines do away with??
Language CompilersOutdated junk in the processor design, x86!Cache memories!Non-deterministic execution!
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Multiple Bank Memory Systems
Starting + 1 +2 +3Address +N +2N +3NMod 4
Memory Banks
Bank 0 1 2 3
As many as are needed!!!!
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Pipelined Instruction Trees
Each higher level offers parallel operations
Pipeline assumes all registers are loaded every cycle
Hardwired?? Actually today the instruction trees could be re-configurable using re-programmable cells!!!
r = a+b-x*y
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Pipelined Instruction Treesa b d y
-*
-
a b x y
*+
Multiple Trees offer the second level of Parallelism
+
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Three Levels of Parallelism
1. Instruction Trees, Multiple Levels
2. Multiple Results
3. Multiple Grid Point Processors
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Wave Machine
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Imaging Machine
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Wave Equationa) 8th or 10th Order in spaceb) 4th Order in time, tricky but possiblec) Sponge Boundary Conditions,
slowly varying weights along sidesd) Nominal flat topography, new schemes
are building in topographye) Any seismic source location,
any geophone location
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Elastic Wave Equationa) Grid point work is about 100 operationsb) About 20,000 time steps per shot c) 200 Wavelengths gives about 160,000 geophone locationsd) Traces have 4096 samples, 2 milliseconds, could be 1 ms.
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Elastic Wave EquationShots are placed at twice the receiver
spacing
Number of shots equals 40,000
Model Frequency is velocity dependent,assume something on the order of 60 hertz.
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Economics
Up Front Fixed Cost, $5 to $ 10 Million
Each ASP Chip is $5 to 10
A Petaflop for $5 or $10 Million
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Economics
Seismic Shot takes 0.1 seconds
5 Year life is 50,000 Models
A realistic 3D elastic seismic model would cost $200
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Comparison
10 Clusters ~ $10 Million10 models per year
One Waves in Linear Motion Analyzer (WILMA) ~$10 Million
10,000 models per year
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Comparison
Waves in Linear Motion Analyzer
1000X faster
For the same money!.
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Summary
1000 Megawatts is a good sized power station
Good memory design is worth the money!
Removing the obstacles to efficient computing gives sustainable performance
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Summary
Slower is better.Less power is better.High Efficiency is better.
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Conclusions
Deterministic Computing is important for performance………Application Specific Computing is a good fit for the wave equation…..And very cost effective………..
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Thanks
SEG – Continuing Education
Memorial University of Newfoundland
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Hamming
“The purpose of computing is insight, not numbers”