论文详情
提高波动方程有限差分数值模拟的精度和效率对于地震勘探有着重要意义。基于频散关系保持的思想,利用最小平方法和拉格朗日乘数法,对二阶导数的五对角紧致有限差分格式进行了差分系数优化,并对优化前后的模拟精度、频散关系及稳定性条件进行了分析和对比。研究结果表明,对于同样的差分精度,优化格式具有更小的截断误差和更低的数值频散以及更高的计算精度,适用于更粗的空间网格。对简单的均匀介质模型和复杂的Marmousi模型进行了声波方程数值模拟,结果表明,2N阶优化格式在压制数值频散方面优于2N阶原格式,也优于2N+2阶原格式,这意味着在对同一模型进行数值模拟时,可以使用更大的空间步长和更少的计算节点,从而减少计算内存和时间,提高计算效率。
Improving the accuracy and efficiency of finite difference numerical simulations of wave equations is important in seismic exploration.In this paper,least square method and Lagrange multiplier method are used to perform differential coefficient optimization for pentadiagonal compact finite difference scheme of second derivatives,which is based on dispersion relationship preservation.Theoretical analysis indicates that,compared with traditional schemes,the proposed optimized scheme is more suitable for coarse grid computing due to its smaller truncation error and lower numerical dispersion.Test results on simple homogeneous model and Marmousi model showed that 2N-order optimization scheme was superior to both the 2N-order and 2N+ 2-order original scheme in suppressing numerical dispersion.Larger space steps can be set using the proposed scheme,which reduce computational memory and increase computational efficiency.
国家自然科学基金青年科学基金项目(41604099)和油气资源与勘探技术教育部重点实验室(长江大学)开放基金项目(K2018-1)共同资助。