


 Accelerating seismic computations using customized number representations on FPGAs  

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For downward continued based migration there are four potential computational
bottlenecks that vary depending on the flavor of the downward continuation
algorithm. In many cases the dominant cost is the FFT step. The dimensionality
of the FFT varies from 1D (tilted planewave migration (Shan and Biondi, 2007)) to 4D (narrow azimuth migration (, ). The FFT cost is often dominant due its
cost ratio, being the number of points in the transform, and the
noncache friendly nature of multidimensional FFTs. The FK step,
which involves evaluating a square root function and performing
complex exponential is a second potential bottleneck. The high operational count
per sample can eat up significant cycles. The FX step, which involves a complex
exponential, or sine/cosine multiplication, has a similar, but computationally
less demanding, profile. Creating subsurface offset gathers for shot
profile or planewave migration, particularly 3D subsurface offset gathers,
can be an overwhelming cost. The large opcount per sample and the noncache
friendly usage can be problematic. Finally, for finite difference
based schemes a significant convolution cost is involved.
Last summer the focus was on speeding up 1 and 2D FFTs.
Speedup ranged from 8x16x depending on the required data precision. (Pell and Clapp, 2007) demonstrated that the subsurface offset
calculation can be sped up by a factor of 20x40x. This summer, the
focus was speeding up the FK step by implementing both a table lookup
and complex exponential on the FPGA.



 Accelerating seismic computations using customized number representations on FPGAs  

Next: Reverse time migration
Up: Project overview
Previous: Project overview
20070918