A staggered-grid convolutional differentiator for elastic wave modelling
The computation of derivatives in governing partial differential equations is one of the most investigated subjects in the numerical simulation of physical wave propagation. An analytical staggered-grid convolutional differentiator (CD) for first-order velocity-stress elastic wave equations is deriv...
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| Published in | Journal of computational physics Vol. 301; pp. 59 - 76 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier Inc
15.11.2015
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| Subjects | |
| Online Access | Get full text |
| ISSN | 0021-9991 1090-2716 |
| DOI | 10.1016/j.jcp.2015.08.017 |
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| Abstract | The computation of derivatives in governing partial differential equations is one of the most investigated subjects in the numerical simulation of physical wave propagation. An analytical staggered-grid convolutional differentiator (CD) for first-order velocity-stress elastic wave equations is derived in this paper by inverse Fourier transformation of the band-limited spectrum of a first derivative operator. A taper window function is used to truncate the infinite staggered-grid CD stencil. The truncated CD operator is almost as accurate as the analytical solution, and as efficient as the finite-difference (FD) method. The selection of window functions will influence the accuracy of the CD operator in wave simulation. We search for the optimal Gaussian windows for different order CDs by minimizing the spectral error of the derivative and comparing the windows with the normal Hanning window function for tapering the CD operators. It is found that the optimal Gaussian window appears to be similar to the Hanning window function for tapering the same CD operator. We investigate the accuracy of the windowed CD operator and the staggered-grid FD method with different orders. Compared to the conventional staggered-grid FD method, a short staggered-grid CD operator achieves an accuracy equivalent to that of a long FD operator, with lower computational costs. For example, an 8th order staggered-grid CD operator can achieve the same accuracy of a 16th order staggered-grid FD algorithm but with half of the computational resources and time required. Numerical examples from a homogeneous model and a crustal waveguide model are used to illustrate the superiority of the CD operators over the conventional staggered-grid FD operators for the simulation of wave propagations. |
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| AbstractList | The computation of derivatives in governing partial differential equations is one of the most investigated subjects in the numerical simulation of physical wave propagation. An analytical staggered-grid convolutional differentiator (CD) for first-order velocity-stress elastic wave equations is derived in this paper by inverse Fourier transformation of the band-limited spectrum of a first derivative operator. A taper window function is used to truncate the infinite staggered-grid CD stencil. The truncated CD operator is almost as accurate as the analytical solution, and as efficient as the finite-difference (FD) method. The selection of window functions will influence the accuracy of the CD operator in wave simulation. We search for the optimal Gaussian windows for different order CDs by minimizing the spectral error of the derivative and comparing the windows with the normal Hanning window function for tapering the CD operators. It is found that the optimal Gaussian window appears to be similar to the Hanning window function for tapering the same CD operator. We investigate the accuracy of the windowed CD operator and the staggered-grid FD method with different orders. Compared to the conventional staggered-grid FD method, a short staggered-grid CD operator achieves an accuracy equivalent to that of a long FD operator, with lower computational costs. For example, an 8th order staggered-grid CD operator can achieve the same accuracy of a 16th order staggered-grid FD algorithm but with half of the computational resources and time required. Numerical examples from a homogeneous model and a crustal waveguide model are used to illustrate the superiority of the CD operators over the conventional staggered-grid FD operators for the simulation of wave propagations. |
| Author | Sun, Weijia Fu, Li-Yun Zhou, Binzhong |
| Author_xml | – sequence: 1 givenname: Weijia orcidid: 0000-0001-9530-8558 surname: Sun fullname: Sun, Weijia email: swj@mail.iggcas.ac.cn organization: Key Laboratory of Earth and Planetary Physics, Institute of Geology and Geophysics, Chinese Academy of Science, Beijing 10029, China – sequence: 2 givenname: Binzhong surname: Zhou fullname: Zhou, Binzhong email: Binzhong.Zhou@csiro.au organization: CSIRO Energy, PO Box 883, Kenmore, QLD 4069, Australia – sequence: 3 givenname: Li-Yun surname: Fu fullname: Fu, Li-Yun email: lfu@mail.iggcas.ac.cn organization: Key Laboratory of Petroleum Resources, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing 100029, China |
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| CitedBy_id | crossref_primary_10_1007_s00024_019_02277_2 crossref_primary_10_1016_j_jcp_2016_09_019 crossref_primary_10_1080_08123985_2020_1838243 crossref_primary_10_1002_num_22217 crossref_primary_10_1190_geo2020_0240_1 crossref_primary_10_1190_geo2017_0546_1 crossref_primary_10_1071_EG16094 crossref_primary_10_1190_geo2019_0081_1 crossref_primary_10_1016_j_jcp_2016_03_031 crossref_primary_10_1080_08123985_2020_1737519 |
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| SubjectTerms | Accuracy Computation Computer simulation Convolutional differentiator Derivatives Elastic wave Forward modelling Mathematical analysis Mathematical models Operators Staggered-grid Window functions |
| Title | A staggered-grid convolutional differentiator for elastic wave modelling |
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