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Time High-order Generalized Finite Difference Method and Stability Condition for Scalar Wave Equation
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Ye YUAN1, Jian-liang HUANG1, Wei-xiang TAO1, Wan-chun LIU1, Guo-chen WU2
Science Technology and Engineering | 2025, 25(21) : 8796 - 8804
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Science Technology and Engineering | 2025, 25(21): 8796-8804
• Papers·Astronomy and Geosciences •
Time High-order Generalized Finite Difference Method and Stability Condition for Scalar Wave Equation
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Ye YUAN1, Jian-liang HUANG1, Wei-xiang TAO1, Wan-chun LIU1, Guo-chen WU2
Affiliations
  • 1 Global Technology Supporting Center, CNOOC International Ltd., Beijing 100028, China
  • 2 School of Geosciences, China University of Petroleum, Qingdao 266580, China
Published: 2025-07-28 doi: 10.12404/j.issn.1671-1815.2405936
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The generalized finite difference method for seismic wavefields numerical simulation is capable of adapting to undulating stratigraphic interfaces, eliminating the staircase scattering effect caused by such interfaces, and enhancing the accuracy of forward modeling. However, when the second-order generalized finite difference method is used to solve the wave equation, low temporal accuracy can lead to temporal dispersion at larger time intervals, affecting the precision of forward simulation. A fourth-order generalized finite-difference forward modeling algorithm for the scalar wave equation was studied, along with its stability conditions and dispersion characteristics. By transferring the fourth-order time derivative to the spatial derivative term, fourth-order accuracy in time was achieved, effectively suppressing temporal dispersion. Compared to the second-order generalized finite-difference method, the fourth-order approach allows for larger time intervals, thereby reducing computational costs to some extent. Experimental results demonstrate that the proposed algorithm effectively mitigates both staircase scattering and temporal dispersion, yielding higher computational accuracy. When applied to reverse time migration, it produces high-quality imaging profiles.

generalized finite difference method  /  stepped scattering  /  high-order difference scheme  /  time dispersion  /  stability conditions
Ye YUAN, Jian-liang HUANG, Wei-xiang TAO, Wan-chun LIU, Guo-chen WU. Time High-order Generalized Finite Difference Method and Stability Condition for Scalar Wave Equation[J]. Science Technology and Engineering, 2025 , 25 (21) : 8796 -8804 . DOI: 10.12404/j.issn.1671-1815.2405936
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Year 2025 volume 25 Issue 21
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Article Info
doi: 10.12404/j.issn.1671-1815.2405936
  • Receive Date：2024-08-07
  • Online Date：2026-01-13
  • Published：2025-07-28
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  • Received：2024-08-07
  • Revised：2025-04-09
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    1 Global Technology Supporting Center, CNOOC International Ltd., Beijing 100028, China
    2 School of Geosciences, China University of Petroleum, Qingdao 266580, China
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