DOI: https://doi.org/10.26089/NumMet.v18r326

Acceleration of seismic data processing with wave-packet decomposition using NVidia CUDA

Authors

  • V.V. Nikitin
  • A.A. Duchkov
  • F. Andersson

Keywords:

Gaussian wave packet
Fourier transform
CUDA

Abstract

Seismic data are characterized by multidimensionality, large data sizes, and irregular structures. In this paper we consider an optimal decomposition of seismic data using the basis of Gaussian wave packets. We implemented and optimized a number of fast algorithms for forward and inverse transforms for three-dimensional seismic data decomposition. The algorithms implemented on GPU demonstrate 2-6x speedup compared to 20-core CPUs. The programs were tested on synthetic seismic data sets: data reconstruction by Gaussian wave-packet coefficients, data compression, denoising, and interpolation in the case of missing traces.

New computational technologies

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Published

2017-08-06

Issue

Vol. 18 (2017): Issue 3.

Section

Section 1. Numerical methods and applications

Author Biographies

V.V. Nikitin

Lund University,
MAX IV Laboratory
• Postdoctoral Researcher

A.A. Duchkov

Trofimuk Institute of Petroleum Geology and Geophysics of SB RAS
• Head of Laboratory

F. Andersson

Lund University,
Center for Mathematical Sciences
• Senior Lecturer

References

  1. I. I. Gurvich and G. N. Boganik, Seismic Prospecting (Nedra, Moscow, 1980) [in Russian].
  2. F. Andersson, M. V. de Hoop, H. F. Smith, and G. Uhlmann, “A Multi-Scale Approach to Hyperbolic Evolution Equations with Limited Smoothness,” Commun. Part. Diff. Eq. 33 (6), 988-1017 (2008).
  3. A. A. Duchkov, F. Andersson, and M. V. de Hoop, “Discrete Almost-Symmetric Wave Packets and Multiscale Geometrical Representation of (Seismic) Waves,” IEEE Trans. Geosci. Remote Sens. 48 (9), 3408-3423 (2010).
  4. E. J. Candès  and D. L. Donoho, “Continuous Curvelet Transform: I. Resolution of the Wavefront Set,” Appl. Comput. Harmon. Anal. 19 (2), 162-197 (2005).
  5. E. Candès, L. Demanet, D. Donoho, and L. Ying, “Fast Discrete Curvelet Transforms,” Multiscale Model. Simul. 5 (3), 861-899 (2006).
  6. R. Neelamani, A. I. Baumstein, D. G. Gillard, et al., “Coherent and Random Noise Attenuation Using the Curvelet Transform,” The Leading Edge 27 (2), 240-248 (2008).
  7. A. A. Duchkov, M. V. de Hoop, and F. Andersson, “Migration Velocity Analysis Using Wave Packets - Geometric Approach,” SEG Technical Program Expanded Abstracts 2009.
    doi 10.1190/1.3255704
  8. F. Andersson, M. Carlsson, and L. Tenorio, “On the Representation of Functions with Gaussian Wave Packets,” J. Fourier Anal. Appl. 18 (1), 146-181 (2012).
  9. G. Beylkin, “On Applications of Unequally Spaced Fast Fourier Transform,” in Mathematical Geophysics Summer School (Stanford Univ., Stanford, 1998).
  10. A. Dutt and V. Rokhlin, “Fast Fourier Transforms for Nonequispaced Data,” SIAM J. Sci. Comput. 14 (6), 1368-1393 (1993).
  11. A. A. Duchkov, F. Andersson, and R. Ojala, “Prestack Shot-Gather Depth Migration by a Rigid Flow of Gaussian Wave Packets,” Stud. Geophys. Geod. 56 (1), 83-106 (2012).
  12. B. M. Glinskii, V. N. Martynov, and A. F. Sapetina, “Technology of Supercomputer Simulation of Seismic Wave Fields in Complicated Media,” Vestn. South Ural State Univ. Ser. Vychisl. Mat. Inf. 4 4, 101-116 (2015).
  13. A. V. Trachenko and A. S. Prokopenko, “Solution of Large Three-Dimensional Problems of Seismicity in Layered Media on a Multi-GPU System Using CAE Fidesys,” Vestn. Lobachevskii Univ. Nizhni Novgorod, No. 4-2, 541-542 (2011).
  14. M. A. Gorodnichev, A. A. Duchkiv, and V. G. Sarychev, “Efficient GPU-Implementation of Coherent Stacking with CUDA,” in Proc. Int. Conf. on Parallel Computational Technologies, Arkhangelsk, Russia,March 28-April 1, 2016 (South Ural State Univ., Chelyabinsk, 2016), p. 118-130.
  15. E. A. Kurin and M. S. Denisov, “Application of High-Performance Computing to Seismic Multiple Attenuation,” Tekhnol. Seismorazved., No. 4, 35-40 (2011).
  16. V. V. Nikitin, F. Andersson, M. Carlsson, and A. A. Duchkov, “Fast Hyperbolic Radon Transform Represented as Convolutions in Log-polar Coordinates,” Comput. Geosci. 105, 21-33 (2017).
  17. D. R. Brillinger, Time Series. Data Analysis and Theory (Holt, Rinehart and Winston, New York, 1975; Mir, Moscow, 1980).
  18. J. A. Fessler and B. P. Sutton, “Nonuniform Fast Fourier Transforms Using Min-Max Interpolation,” IEEE Trans. Signal Process. 51 (2), 560-574 (2003).
  19. L. Greengard and J.-Y. Lee, “Accelerating the Nonuniform Fast Fourier Transform,” SIAM Rev. 46 (3), 443-454 (2004).
  20. V. I. Lebedev, “Quadratures on a Sphere,” Zh. Vychisl. Mat. Mat. Fiz. 16 (2), 293-306 (1976) [USSR Comput. Math. Math. Phys. 16 (2), 10-24 (1976)].
  21. X. Chen, Y. Qiu, and H. Yi, “Implementation and Performance of Image Filtering on GPU,” in Proc. Fourth Int. Conf. on Intelligent Control and Information Processing, Beijing, China, June 9-11, 2013 (IEEE Press, New York, 2013), pp. 514-517.
  22. O. Fialka and M. Cadik, “FFT and Convolution Performance in Image Filtering on GPU,” in Proc. Tenth Int. Conf. on Information Visualization, London, England, July 5-7, 2006 (IEEE Press, New York, 2006), pp. 609-614.
  23. C. Sigg and M. Hadwiger, “Fast Third-Order Texture Filtering,” in GPU Gems (Addison-Wesley, Reading, 2005), Vol. 2, pp. 313-329.
  24. N. Zhang, Y.-S. Chen, and J. L. Wang, “Image Parallel Processing Based on GPU,” in Proc. 2nd Int. Conf. on Advanced Computer Control, Shenyang, China, March 27-29, 2010 (IEEE Press, New York, 2010), Vol. 3, 367-370.
  25. J. W. Cooley and J. W. Tukey, “An Algorithm for the Machine Calculation of Complex Fourier Series,” Math. Comput. 19 (90), 297-301 (1965).
  26. L. Bluestein, “A Linear Filtering Approach to the Computation of Discrete Fourier Transform,” IEEE Trans. Audio and Electroacoust. 18 (4), 451-455 (1970).
  27. D. B. Kirk and W. W. Hwu, Programming Massively Parallel Processors: A Hands-on Approach (Morgan Kaufman, Boston, 2016).
  28. A. V. Boreskov and A. A. Kharlamov, The Basics of Working with CUDA Technology (Litres, Moscow, 2015) [in Russian].
  29. F. Andersson, “Fast Inversion of the Radon Transform Using Log-polar Coordinates and Partial Back-Projections,” SIAM J. Appl. Math. 65 (3), 818-837 (2005).
  30. F. Andersson, M. Carlsson, and V. V. Nikitin, “Fast Algorithms and Efficient GPU Implementations for the Radon Transform and the Back-Projection Operator Represented as Convolution Operators,” SIAM J. Imaging Sci., 9 (2), 637-664 (2016).

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