Abstract
In geophysical applications, the interest in least-squares 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.
Highlights
In the oil and gas industry, one of the challenges is to obtain an accurate image of the subsurface to find hydrocarbons
In Knibbe et al [17], we have shown that solving the wave equation in the frequency domain, i.e., the Helmholtz equation, can compete with a time domain solver given a sufficient number of parallel computational nodes with a limited usage of disk space
A decimation was done over sources and frequencies to take advantage of the redundant information present in the data during the CGNR iterations, which is used to solve the optimization problem within the leastsquares migration (LSM) framework
Summary
In the oil and gas industry, one of the challenges is to obtain an accurate image of the subsurface to find hydrocarbons. Part of the waves is transmitted through the subsurface, another part of the waves is reflected at the interfaces between layers with different properties. The wave amplitude is recorded at the receiver locations, for example, by geophones. The recorded signal in time forms a seismogram. The data in frequency domain can be obtained by the Fourier transform of the signal in time. There are several techniques, called depth migration, to map it to the depth domain, given a sufficiently accurate velocity model. The result is a reflectivity image of the subsurface. The techniques include ray based and wave equation based algorithms and can be formulated in time or in frequency domain
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