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.
Least-squares migration, Helmholtz equation, Wave equation, Frequency domain, Multigrid method, GPU acceleration, Matrix storage format, Frequency decimation
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)
Null option (theme 11)
dx.doi.org/10.1007/s10596-015-9546-z
Computational Geosciences
Scientific Computing

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