2016

# Reduction of computing time for least-squares migration based on the Helmholtz equation by graphics processing units

## Publication

### Publication

*Computational Geosciences , Volume 20 - Issue 2 p. 297- 315*

In geophysical applications, the interest in leastsquares
migration (LSM) as an imaging algorithm is
increasing due to the demand for more accurate solutions
and the development of high-performance computing. The
computational engine of LSM in this work is the numerical
solution of the 3D Helmholtz equation in the frequency
domain. The Helmholtz solver is Bi-CGSTAB preconditioned
with the shifted Laplace matrix-dependent multigrid
method. In this paper, an efficient LSM algorithm is presented
using several enhancements. First of all, a frequency
decimation approach is introduced that makes use of redundant
information present in the data. It leads to a speedup of
LSM, whereas the impact on accuracy is kept minimal. Secondly,
a new matrix storage format Very Compressed Row
Storage (VCRS) is presented. It not only reduces the size of
the stored matrix by a certain factor but also increases the
efficiency of the matrix-vector computations. The effects of
lossless and lossy compression with a proper choice of the
compression parameters are positive. Thirdly, we accelerate
the LSM engine by graphics cards (GPUs). A GPU is used
as an accelerator, where the data is partially transferred to
a GPU to execute a set of operations or as a replacement,
where the complete data is stored in the GPU memory. We
demonstrate that using the GPU as a replacement leads to
higher speedups and allows us to solve larger problem sizes.
Summarizing the effects of each improvement, the resulting
speedup can be at least an order of magnitude compared to
the original LSM method.

Additional Metadata | |
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Keywords | Least-squares migration, Helmholtz equation, Wave equation, Frequency domain, Multigrid method, GPU acceleration, Matrix storage format, Frequency decimation |

MSC | Explicit machine computation and programs (not the theory of computation or programming) (msc 65-04), Multigrid methods; domain decomposition (msc 65N55), Seismology (msc 86A15), Parallel computation (msc 65Y05), Explicit machine computation and programs (not the theory of computation or programming) (msc 65-04) |

THEME | Null option (theme 11) |

Persistent URL | dx.doi.org/10.1007/s10596-015-9546-z |

Journal | Computational Geosciences |

Citation |
Knibbe, H, Vuik, C, & Oosterlee, C.W. (2016). Reduction of computing time for least-squares migration based on the Helmholtz equation by graphics processing units.
Computational Geosciences, 20(2), 297–315. doi:10.1007/s10596-015-9546-z |