-
摘要:
地震波正演模拟是地震反演与成像的基础和关键，有限差分算法广泛应用于地震波数值模拟，差分算子的精度直接影响数值模拟的质量和效率.本文提出一种BFO-PSO算法下的有限差分算子优化方法，并应用其进行弹性波数值模拟.首先，将BFO算法中的趋化、复制、驱散三个步骤引入PSO算法，形成具有更好全局搜索能力和更快收敛速度的BFO-PSO混合优化算法；之后构造包含有限差分系数的目标函数，并应用BFO-PSO混合优化算法求取最优解，获得优化的有限差分算子；最后应用此优化的有限差分算子在不同模型上进行弹性波数值模拟.根据频散曲线及数值模拟结果，可以分析得出，BFO-PSO算法优化后的有限差分算子在保证计算效率的同时，具有更高的精度，可以有效压制数值频散，提高数值模拟的精度和效率.
Abstract:Forward modelling of elastic waves is the foundation and key of seismic inversion and imaging. The Finite-Difference (FD) method is one of the most popular means used in such numerical modelling, in which the accuracy of the difference operator affects the quality and efficiency of the modelling. In this paper, we propose an optimal FD method based on the BFO-PSO algorithm, and apply it to numerical modelling of elastic waves. First, the three steps of chemotaxis, replication and dispersal in the BFO algorithm are introduced into the PSO algorithm, and a new BFO-PSO hybrid optimization algorithm with better global searching ability and faster convergence speed is generated. Then, we construct the objective function containing the FD coefficients. The BFO-PSO algorithm is used to solve the object function and obtain the optimal FD method. Finally, numerical modelling of elastic waves is performed with this optimal FD method based on the BFO-PSO algorithm on some models. Numerical dispersion analysis and modelling results indicate that the optimal FD method based on the BFO-PSO algorithm has a high accuracy while ensuring calculation efficiency, and can efficiently suppress the numerical dispersion and improve the accuracy and efficiency of numerical modelling.
-
Key words:
- BFO-PSO algorithm /
- Finite-difference /
- Numerical modelling /
- Elastic waves
-
-
图 2
不同阶数的BFO-PSO算法下的优化有限差分算子的频散曲线
Figure 2.
Dispersion curves of the optimized FD operator based on the BFO-PSO algorithm for different values of N (different orders)
图 3
不同阶数的PSO算法下的优化有限差分算子的频散曲线
Figure 3.
Dispersion curves of the optimized FD operator based on the PSO algorithm for different values of N (different orders)
图 4
BFO-PSO算法与PSO算法优化的有限差分算子的频散曲线对比
Figure 4.
Comparison of numerical dispersion curves between optimized FD operator based on the BFO-PSO algorithm and the PSO algorithm
图 5
BFO-PSO算法与Remez交换算法(He et al., 2019)优化的有限差分算子的频散曲线对比
Figure 5.
Comparison of numerical dispersion curves between the optimized FD operator based on the BFO-PSO algorithm and the Remez algorithm (He et al., 2019)
图 7
应用不同有限差分算子得到的合成波场快照(X分量)
Figure 7.
Synthetic wavefield snapshots (X component) using different FD operators
图 8
应用不同有限差分算子得到的合成波场快照(Z分量)
Figure 8.
Synthetic wavefield snapshots (Z component) using different FD operators
图 10
在Marmousi模型应用不同有限差分算子进行弹性波数值模拟得到的合成地震记录(Z分量)
Figure 10.
Synthetic shot records (Z component) obtained by numerical modelling of elastic waves using different FD operators on Marmousi model
表 1
BFO-PSO算法下的优化有限差分算子系数
Table 1.
Optimized FD coefficients based on the BFO-PSO algorithm
8阶 12阶 16阶 20阶 24阶 c1 0.84893502 0.91765515 0.94688314 0.96461796 0.97479403 c2 -0.25420642 -0.35256003 -0.40107190 -0.43249168 -0.45124395 c3 0.06597073 0.14837966 0.20125787 0.23962888 0.26412709 c4 -0.00974140 -0.05542580 -0.09962559 -0.13768333 -0.16450320 c5 0.01596538 0.04507117 0.07710039 0.10293941 c6 -0.00271980 -0.01745341 -0.04052505 -0.06281853 c7 0.00524544 0.01930171 0.03658504 c8 -0.00096164 -0.00794853 -0.01990991 c9 0.00260061 0.00986155 c10 -0.00054026 -0.00426879 c11 0.00149372 c12 -0.00034129 
下载: 导出CSV
-
Beheshti Z, Shamsuddin S M H. 2013. A review of population-based meta-heuristic algorithm. International Journal of Advances in Soft Computing and its Applications, 5(1): 1-35. http://www.researchgate.net/publication/270750820_A_review_of_population-based_meta-heuristic_algorithm
Chu C L, Stoffa P L. 2012. Determination of finite-difference weights using scaled binomial windows. Geophysics, 77(3): W17-W26. doi: 10.1190/geo2011-0336.1
Daryabeigi E, Dehkordi B M. 2014. Smart bacterial foraging algorithm based controller for speed control of switched reluctance motor drives. International Journal of Electrical Power & Energy Systems, 62: 364-373. http://www.sciencedirect.com/science/article/pii/S0142061514002506
Di Bartolo L, Dors C, Mansur W J. 2012. A new family of finite-difference schemes to solve the heterogeneous acoustic wave equation. Geophysics, 77(5): T187-T199. doi: 10.1190/geo2011-0345.1
Du Z Y, Wu G C, Li Y S. 2019. Three-dimensional elastic wave forward modeling in orthorhombic media based on least squares. Progress in Geophysics (in Chinese), 34(1): 69-79, doi: 10.6038/pg2019BB0566.
Hazra J, Sinha A K. 2011. A multi-objective optimal power flow using particle swarm optimization. European Transactions on Electrical Power, 21(1): 1028-1045. doi: 10.1002/etep.494
He Z, Zhang J H, Yao Z X. 2019. Determining the optimal coefficients of the explicit finite-difference scheme using the Remez exchange algorithm. Geophysics, 84(3): S137-S147. doi: 10.1190/geo2018-0446.1
Hussain K, Salleh M N M, Cheng S, et al. 2018. Metaheuristic research: a comprehensive survey. Artificial Intelligence Review, 52(4): 2191-2233. http://d.wanfangdata.com.cn/periodical/ChlQZXJpb2RpY2FsRW5nTmV3UzIwMjEwMzAyEiAxZDRkZWQyMDc3ZDExNDg3ZGFmOWRlMzIwNGE2Nzc5ZBoIamc3ZWkxYzY%3D
Jadoun V K, Gupta N, Niazi K R, et al. 2015. Modulated particle swarm optimization for economic emission dispatch. International Journal of Electrical Power & Energy Systems, 73: 80-88.
Kennedy J, Eberhart R. 1995. Particle swarm optimization.//Proceedings of ICNN′95-International Conference on Neural Networks. Perth, WA, Australia: IEEE, 4: 1942-1948.
Lei X J. 2012. Swarm Intelligent Optimization Algorithms and Their Applications (in Chinese). Beijing: Science Press.
Li J, Dang J W, Bu F. 2013. Research and improvment of bacteria foraging optimization algorithm. Computer Simulation (in Chinese), 30(4): 344-347, 415. http://en.cnki.com.cn/Article_en/CJFDTOTAL-JSJZ201304081.htm
Li M D, Zhao H, Weng X W, et al. 2016. A novel nature-inspired algorithm for optimization: Virus colony search. Advances in Engineering Software, 92: 65-88. doi: 10.1016/j.advengsoft.2015.11.004
Liang W Q, Wu X, Wang Y F, et al. 2018. A new staggered grid finite difference scheme optimised in the space domain for the first order acoustic wave equation. Exploration Geophysics, 49(6): 898-905. doi: 10.1071/EG17088
Lines L R, Slawinski R, Bording R P. 1999. A recipe for stability of finite-difference wave-equation computations. Geophysics, 64(3): 967-969. doi: 10.1190/1.1444605
Liu L B, Duan P R, Zhang Y Y, et al. 2020. Overview of mesh-free method of seismic forward numerical simulation. Progress in Geophysics (in Chinese), 35(5): 1815-1825, doi: 10.6038/pg2020DD0117.
Liu Y. 2013. Globally optimal finite-difference schemes based on least squares. Geophysics, 78(4): T113-T132. doi: 10.1190/geo2012-0480.1
Miao Z Z, Zhang J H. 2020. Reducing error accumulation of optimized finite-difference scheme using the minimum norm. Geophysics, 85(5): T275-T291. doi: 10.1190/geo2019-0758.1
Passino K M. 2002. Biomimicry of bacterial foraging for distributed optimization and control. IEEE Control Systems Magazine, 22(3): 52-67. doi: 10.1109/MCS.2002.1004010
Pillay N. 2016. A review of hyper-heuristics for educational timetabling. Annals of Operations Research, 239(1): 3-38. doi: 10.1007/s10479-014-1688-1
Qu R, Pham N, Bai R B, et al. 2015. Hybridising heuristics within an estimation distribution algorithm for examination timetabling. Applied Intelligence, 42(4): 679-693. doi: 10.1007/s10489-014-0615-0
Ren Y J, Huang J P, Yong P, et al. 2018. Optimized staggered-grid finite-difference operators using window functions. Applied Geophysics, 15(2): 253-260. doi: 10.1007/s11770-018-0668-7
Wang J, Meng X H, Liu H, et al. 2017. Cosine-modulated window function-based staggered-grid finite-difference forward modeling. Applied Geophysics, 14(1): 115-124. doi: 10.1007/s11770-017-0596-y
Wang Z Y, Liu H, Tang X D, et al. 2015. Optimized finite-difference operators based on Chebyshev auto-convolution combined window function. Chinese Journal of Geophysics (in Chinese), 58(2): 628-642, doi: 10.6038/cjg20150224.
Yan H Y, Yang L, Li X Y. 2016. Optimal staggered-grid finite-difference schemes by combining Taylor-series expansion and sampling approximation for wave equation modeling. Journal of Computational Physics, 326: 913-930. doi: 10.1016/j.jcp.2016.09.019
Yang L, Yan H Y, Liu H. 2017. Optimal staggered-grid finite-difference schemes based on the minimax approximation method with the Remez algorithm. Geophysics, 82(1): T27-T42. doi: 10.1190/geo2016-0171.1
Zhang J H, Yao Z X. 2013. Optimized finite-difference operator for broadband seismic wave modeling. Geophysics, 78(1): A13-A18. doi: 10.1190/geo2012-0277.1
杜泽源, 吴国忱, 李雨生. 2019. 基于最小二乘的三维正交介质弹性波高精度正演模拟. 地球物理学进展, 34(1): 69-79, doi: 10.6038/pg2019BB0566.
雷秀娟. 2012. 群智能优化算法及其应用. 北京: 科学出版社.
李珺, 党建武, 卜锋. 2013. 细菌觅食优化算法的研究与改进. 计算机仿真, 30(4): 344-347, 415. doi: 10.3969/j.issn.1006-9348.2013.04.078
刘立彬, 段沛然, 张云银等. 2020. 基于无网格的地震波场数值模拟方法综述. 地球物理学进展, 35(5): 1815-1825, doi: 10.6038/pg2020DD0117.
王之洋, 刘洪, 唐祥德等. 2015. 基于Chebyshev自褶积组合窗的有限差分算子优化方法. 地球物理学报, 58(2): 628-642, doi: 10.6038/cjg20150224.
-
图(10)
表(1)
计量
- 文章访问数: 2841
- PDF下载数: 222
- 施引文献: 0