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ISSN  2096-3955

CN  10-1502/P

Citation: YouShan Liu, Tao Xu, YangHua Wang, JiWen Teng, José Badal, HaiQiang Lan, 2019: An efficient source wavefield reconstruction scheme using single boundary layer values for the spectral element method, Earth and Planetary Physics. doi: 10.26464/epp2019035

doi: 10.26464/epp2019035


An efficient source wavefield reconstruction scheme using single boundary layer values for the spectral element method


State Key Laboratory of Lithospheric Evolution, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing 100029, China


Chinese Academy of Sciences Center for Excellence in Tibetan Plateau Earth Sciences, Beijing 100101, China


Department of Earth Science and Engineering, Imperial College London, SW7 2AZ, UK


Physics of the Earth, Sciences-B, University of Zaragoza, Pedro Cerbuna 12, 50009 Zaragoza, Spain

Corresponding author: Tao Xu,

Received Date: 2019-01-28
Web Publishing Date: 2019-07-01

In the adjoint-state method, the forward-propagated source wavefield and the backward-propagated receiver wavefield must be available simultaneously either for seismic imaging in migration or for gradient calculation in inversion. A feasible way to avoid the excessive storage demand is to reconstruct the source wavefield backward in time by storing the entire history of the wavefield in perfectly matched layers. In this paper, we make full use of the elementwise global property of the Laplace operator of the spectral element method (SEM) and propose an efficient source wavefield reconstruction method at the cost of storing the wavefield history only at single boundary layer nodes. Numerical experiments indicate that the accuracy of the proposed method is identical to that of the conventional method and is independent of the order of the Lagrange polynomials, the element type, and the temporal discretization method. In contrast, the memory-saving ratios of the conventional method versus our method is at least N when using either quadrilateral or hexahedron elements, respectively, where N is the order of the Lagrange polynomials used in the SEM. A higher memory-saving ratio is achieved with triangular elements versus quadrilaterals. The new method is applied to reverse time migration by considering the Marmousi model as a benchmark. Numerical results demonstrate that the method is able to provide the same result as the conventional method but with about 1/25 times lower storage demand. With the proposed wavefield reconstruction method, the storage demand is dramatically reduced; therefore, in-core memory storage is feasible even for large-scale three-dimensional adjoint inversion problems.

Key words: spectral element method; source wavefield reconstruction; single boundary layer; memory-saving ratio; adjoint method; reverse time migration

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An efficient source wavefield reconstruction scheme using single boundary layer values for the spectral element method

YouShan Liu, Tao Xu, YangHua Wang, JiWen Teng, José Badal, HaiQiang Lan