Lithologic Reservoirs ›› 2018, Vol. 30 ›› Issue (2): 93-109.doi: 10.12108/yxyqc.20180211

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Mixed-grid finite-difference methods for wave equation numerical modeling in time-space domain

YANG Zhe, LIU Wei, HU Ziduo, WANG Shujiang, HAN Linghe, WANG Yanxiang   

  1. PetroChina Research Institute of Petroleum Exploration & Development-Northwest, Lanzhou 730020, China
  • Received:2018-01-12 Revised:2018-02-13 Online:2018-03-21 Published:2018-03-21

Abstract: Traditional high-order finite-difference (FD)scheme (T2 M-FD)and time-space-domain high-order finite-difference scheme (TS2 M-FD)are the most widely used higher-accuracy numerical modeling methods for seismic wave equation. T2 M-FD, with its FD coefficients calculated only based on space-domain dispersion relationship, has relatively low accuracy. TS2 M-FD, with its FD coefficients calculated based on time-space-domain dispersion relationship and plane wave theory, has relatively higher accuracy. However, T2 M-FD and TS2 M-FD have the same FD scheme only using the grid points in the general coordinate system to approximate the Laplace operator in the wave equation, having not taking full use of the grid points in the rotated coordinate system to further improve the modeling accuracy. We proposed to use the grid points in the general and rotated coordinate system together to conduct difference approximation for the Laplace operator, and constructed a new kind of mixed 2 M+N style FD schemes, M2 M+N-FD for short, and derived the approach for calculating the FD coefficients based on the time-space domain dispersion relationship and plane wave theory. And then we carried out dispersion analysis and stability analysis. Dispersion analysis shows that, comparing to T2 M-FD and TS2 M-FD, M2 M+N-FD can more effectively suppress the numerical dispersion and have higher modeling accuracy. Stability analysis shows that, M2 M + N-FD has better stability than T2 M-FD, and has almost the same stability with TS2 M-FD. In the end, we conduct numerical modeling test on homogeneous and layer model with M2 M+N-FD, and implement RTM on Marmousi model with M2 M+N-FD. The high accuracy modeling and migration results demonstrate the superiority and universal applicability of M2 M+N-FD.

CLC Number: 

  • P631.4
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