1. Time and Depth Imaging Algorithms in a Hardware Accelerator Paradigm
G.Satta, A.Cristini, G.Siddi Moreau,
G.Caddeo, D.Theis, C.Gallo,
Z.Heilmann, E.Bonomi
CRS4

2. Imaging and Numerical Geophysics at CRS4
Center for Advanced Studies, Research and Development in Sardinia
Imaging and Numerical Geophysics at CRS4
Seismic imaging combined to High Performance Computing is a competitive sector where CRS4 is involved since 1992
Development and implementation of mathematical methods for ground characterization and subsurface reconstruction
Wave propagation modeling;
Seismic depth migration;
Common-reflection-surface stacking;
Seismic attributes computation;
Inverse problem for environmental sciences

3. Outline Imaging Algorithms in a Hardware Accelerator Paradigm
Introduction 1
Motivation
Data-driven solutions 2
Migration scheme 3
Synthetic data examples 4
Conclusion 5

4. Motivation
HPC trends in seismic
Highly accurate imaging techniques (example RTM) require an increase in powerful computational resources.
Advances in computing led to an explosion in the amount of data being generated.
Whereas the performance of a single core is non longer increasing like in the past.

5. … Hardware solutions Multicore systems Hybrid multicore systems
Motivation
Hardware solutions …
Multicore systems
Hybrid multicore systems
Dedicated Hardware (FPGAs)

6. Motivation
In spite of their spectacular speed, FPGAs and multicores obey a restrictive programming paradigm that makes the numerical solution of many algebraic problems less attractive.
For example, the current, easiest way to implement RTM is to use a finite-difference approximation and an explicit time marching scheme.
Drawbacks:
Limit on time-step size
only conditionally stable
Decreasing time step High-order schemes
numerical dispersion problems

7. Motivation
The real challenge for the developer is the reduction of a mathematical model to a sequence of computational tasks that perfectly fit the paradigm supported by these extreme architectures.

8. Data-driven solutions
Algorithmic solution
Data-driven CRS technique is the perfect example of such a problem that fits the challenge. Properties of this technique are:
A concurrent optimization problem that maximizes the coherence of traveltime prototypes and recorded data,
A lack of need for the numerical solution of algebraic equations,
A lack of need to input medium velocity.

9. Data-driven solutions
The 3D ZO CRS problem
The CRS traveltime formula approximated around the normal incidence ray:
2 angular parameters ( emergence angle & azimuth )
3 Normal Wave front parameters
3 NIP Wave front parameters
There are eight attributes to find for each pixel of the zero-offset section.

10. Semblance Coherence computation:
Data-driven solutions
Semblance
Coherence computation:
each ti is provided by the CRS traveltime formula
The eight parameters are determined by maximizing the semblance S.
Since 0  S  1, it is a usual practice to solve an equivalent problem by minimizing F = 1−S.

11. From serial to parallel programming
Data-driven solutions
From serial to parallel programming
The serial CRS implementation takes advantage of:
The overlapping of spatial apertures,
The slight difference of the attributes between near pixels along the same trace.

12. From serial to parallel programming
Data-driven solutions
From serial to parallel programming
To extract two levels of parallelism:
Reload the traces for every aperture,
Do not take into consideration the similarity of attributes corresponding to neighboring pixels.

13. First level: spatial parallelism
Data-driven solutions
First level: spatial parallelism
Distributed Mem Cache
D a t a p u l l
P a r a d i g m

14. CPU Performance Running on Intel Xeon 5450 3GHz Data-driven solutions
209 seconds per output sample
116 seconds in line search

15. Multi-core Performance
Data-driven solutions
Multi-core Performance 16

16. Second level of parallelism
Data-driven solutions
Second level of parallelism
FPGA/GPGPU
ALU

17. Axis time parallelism with FPGA
Data-driven solutions
Axis time parallelism with FPGA
Each kernel works in one trace at a time to calculate the Semblance
There is a double buffer to not lock the calculation
Memory of PCI card
Kernels
Manager

18. Axis time parallelism with GPGPU
Data-driven solutions
Axis time parallelism with GPGPU
Every arithmetic logic unit (ALU) calculates a Semblance
Every ALU reads the new traces
Memory of PCI card
ALU

19. Data Usage for multiple t0
Data-driven solutions
Data Usage for multiple t0
Data Use with 1 t0
Data Use with 4 t0
Data Use with 16 t0
Data Use with 64 t0 20

20. Data-driven time imaging
Migration scheme
Data-driven time imaging
Is it possible to design an accurate scheme for time imaging (stacking and migration) that:
Does not require the knowledge of a velocity model,
Is solely driven by data,
Uses the existing optimized CRS infrastructure,
Perfectly fits the hardware accelerator?
Work in progress:
New traveltime formula with less attributes.
…very fast time imaging!

21. Time migration: flow Chart
Migration scheme
Time migration: flow Chart
Input prestack data
Fix a point in image space
Choose an initial set of parameters
Map the point into the stack space
Collect seismic prestack traces
Calculate the coherency
Step of data-driven optimization
Is the optimum reached?
yes no

22. Same computing program but two outputs.
Migration scheme
Same computing program but two outputs.
Migrated volume
Post-stack volume

23. Synthetic data examples
Migration scheme
Synthetic data examples
Dip Angle
Time Velocity

24. Depth Migration algorithms
Depth migration scheme
Depth Migration algorithms
Question: What kind of algorithm has an intrinsic data parallel structure and maintains good numerical properties?
60x on FPGA
A possible candidate: PSPI
It was developed for data parallel architecture.
First version for Connection Machine
After many years of development, PSPI is a standard tool, but, of course, is a one-way method.
20x on GPGPU
Is it possible to keep good numerical properties while preserving the data parallel structure of PSPI in order to solve the Helmholtz equation?

25. Depth migration scheme
Migration algorithms
Our goal is to write a solution for the Helmholtz equation by factoring the two-way operator into two one-way operators.
Both operators describe a propagation along the vertical axis where z becomes the marching variable.
The factorization is exact only when media are uniform. For non-uniform media, an additive correction operator is necessary to iteratively compensate the truncation error.

26. Depth migration scheme
Wedge model

27. Depth migration scheme
Wedge model

28. Vertical gradient model
Depth migration scheme
Vertical gradient model

29. Vertical gradient model
Depth migration scheme
Vertical gradient model

30. Depth migration scheme
Edge model

31. Depth migration scheme
Edge model

32. Depth migration scheme
2.5D: Migration example
Velocity model

33. 2.5D: Migration example First iteration One-way Two-way
Depth migration scheme
2.5D: Migration example
One-way
Two-way
First iteration

34. Thank you for your attention!
Algorithm Imaging in a Hardware Accelerator Paradigm
Conclusions
The perfect match between an algorithm and the corresponding hardware is possible at the price of rethinking the data structure and the algebraic problem.
Two-way depth, data-driven stacking and time migration that fall in the above description can be potentially accelerated on the dedicated SIMD hardware.
Thank you for your attention!