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Zhu, Mengquan (Beijing University of Chemical Technology) | Wang, Zhiyang (Beijing University of Chemical Technology) | Yu, Duli (Beijing University of Chemical Technology) | Li, Youming (Key Laboratory of Petroleum Resources Research, Institute of Geology and Geophysics, and University of Chinese Academy of Sciences)
In this paper, we derive an improved QPSO algorithm and develop a new FD scheme based on this improved QPSO algorithm. The improved QPSO algorithm has obvious advantages of convergence speed, which can be converged in the 200th generation. Under the same condition, the convergence speed of QPSO algorithm is much lower than that of improved QPSO algorithm. Numerical dispersion analysis shows that, the optimized FD scheme based on the improved QPSO algorithm has a larger spectral coverage, and the accuracy error is controlled within a valid range, which means the improved QPSO algorithm has better ability to search for accurate global solutions. Finally, numerical modelling of elastic wave equations is performed using the optimized FD scheme based on the improved QPSO algorithm. Numerical modelling results indicate that the optimized FD scheme based on the improved QPSO algorithm can effectively suppress numerical dispersion. Presentation Date: Tuesday, October 13, 2020 Session Start Time: 9:20 AM Presentation Time: 11:25 AM Location: Poster Station 12 Presentation Type: Poster
Yan, Hongyong (Institute of Geology and Geophysics, Chinese Academy of Sciences) | Yang, Lei (Institute of Geology and Geophysics, Chinese Academy of Sciences) | Dai, Hengchang (British Geological Survey) | Li, Xiang-Yang (British Geological Survey)
Staggered-grid finite-difference (SFD) schemes have been used widely in numerical modeling. The spatial SFD coefficients are usually derived by a Taylor-series expansion (TE) method or optimization methods. However, high accuracy is not guaranteed both at small and large wavenumbers by using these conventional methods. In this paper, we present a new optimal SFD scheme using TE with a minimax approximation for high accuracy modeling. The optimal spatial SFD coefficients are calculated by using TE with a minimax approximation based on a Remez algorithm. We use the optimal SFD coefficients to solve first-order spatial derivatives of the elastic wave equations and then perform numerical modeling. Dispersion analyses and numerical modeling show the advantage of the optimal method. The optimal SFD scheme has better accuracy than the TE-based SFD scheme for the same spatial difference operator length, and can also adopt a shorter operator length to achieve the same accuracy reducing the computational cost.
Presentation Date: Wednesday, October 19, 2016
Start Time: 2:20:00 PM
Location: Lobby D/C
Presentation Type: POSTER
The anisotropy exists widely underground, and the existence of tilted transversely isotropic (TTI) media is more general in the actual anisotropic formation. Considering the advantages of rotated staggered-grid finite-difference (RSFD), we always use it to solve the anisotropic wave equations. However, RSFD can lead to serious numerical dispersion. In order to overcome the dispersion for RSFD and improve its numerical modeling accuracy, we propose to combine the high-order RSFD with a global optimization method of the coefficients, which is based on dispersion relation and least-squares method. We first calculate the RSFD coefficients of arbitrary even-order accuracy for the first-order spatial derivatives by the dispersion relation and the least-squares method, which can satisfy the specific numerical solution accuracy of the derivatives on a wide frequency zone. Then the RSFD coefficients based on the least-squares are used to solve the first-order spatial derivatives and the elastic TTI wave equations. At last, the elastic wave numerical modeling is performed, which demonstrates that the least-squares rotated staggered-grid finite-difference (LSRSFD) method can efficiently suppress the numerical dispersion. Meanwhile, the modeling accuracy is compared with that of the Taylor-series expansion rotated staggered-grid finite-difference (TERSFD) method, which shows the greater accuracy of the LSRSFD method than that of the TERSFD method.
In this paper, a new implicit staggered-grid finite-difference (ISFD) method is proposed with optimal difference coefficients, which is based on the sampling approximation (SA) to improve the numerical solution precision for elastic wave modeling. With the direct SA method and the plane wave theory, we derive the optimal ISFD coefficients of arbitrary even-order accuracy for the first-order spatial derivatives. We also apply these new SA-based ISFD coefficients to the solution of the first-order spatial derivatives. Through the numerical dispersion analysis of the ISFD schemes based on SA and the conventional Taylor-series expansion (TE) method, we find that this new SA-based ISFD method achieves great accuracy over a wider range of wavenumbers. The results of numerical modeling also demonstrate that the optimal method suppresses dispersion effectively, and achieves higher accuracy compared with the TE-based ISFD method.
Numerical modeling is significant in helping understand the seismic wave propagation in complex geological models, and it also provides theory and operation supports in the process of the seismic data acquisition, processing and interpretation. Because of the ease and flexibility, the finite-difference (FD) method is very popular in numerical modeling, especially staggered-grid FD method for its competitive accuracy and stability (Dong et al., 2000; Yang et al., 2014). At the same time, for the FD method, its numerical accuracy and efficiency are greatly dependent on the schemes used for calculating spatial derivatives (Kosloff et al., 2010), and the two main schemes are explicit and implicit schemes, respectively. Although some explicit schemes often feature the simple structures and relatively small computational cost, the implicit schemes lead to greater numerical modeling accuracy and better stability.
Zhang et al. (2007) presented implicit splitting FD schemes to solve the second-order spatial derivatives in all directions. Zhou and Zhang (2011) put forward a group of optimal implicit FD schemes for the solution of the secondorder spatial derivatives with FD coefficients calculated by Fourier analysis and the least-squares. Chu and Stoffa (2012) proposed an implicit scheme in space and time domain for the scalar wave equation, showing that the implicit scheme significantly improved the precision compared with the explicit FD schemes. However, the implicit FD methods described above are only applied in acoustic wave modeling, and are difficult to extend to the solution of the first-order spatial derivatives for elastic wave equations on staggered-grid. Liu and Sen (2009) derived the implicit staggered-grid FD schemes with evenorder accuracy for the first-order spatial derivatives and implemented elastic numerical modeling. However, the ISFD coefficients are computed by the TE method, which just has great accuracy over a small frequency or wavenumber range.
Yuan, Yuxin (Institute of Geology and Geophysics, Chinese Academy of Sciences (IGGCAS)) | Liu, Hong (Institute of Geology and Geophysics, Chinese Academy of Sciences (IGGCAS)) | Ting, Hu (Institute of Geology and Geophysics, Chinese Academy of Sciences (IGGCAS)) | Wang, Zhiyang (University of Chinese Academy of Sciences)
In this paper, we proposed a novel staggered-grid low-rank finite-difference (SGLFD) scheme to solve decoupled second-order elastic wave equation. The scheme successively employs backward and forward first-order mixed-domain symbols on a staggered grid to obtain the wave extrapolation operator for second-order decoupled elastic wave propagation. The mixed-domain symbol incorporates the accurate spectral evaluation of spatial derivatives and the time-marching adjustment to ensure that the solution is exact for homogeneous wave propagation for time steps of arbitrarily large size. Considering its straightforward implementation in heterogeneous media, it's necessary to do N times inverse fast Fourier transform (FFT) every time step, where N is the total size of the model grids. In order to reduce computational cost, we apply low-rank finite difference to approximate the symbol without any FFT involved. The 2D numerical experiments demonstrate that our SGLFD method has improved the accuracy of modeling results compared with the ordinary staggered-grid finite difference method (SGFD).
This paper has been withdrawn from the Technical Program and will not be presented at the 87th SEG Annual Meeting.