论文详情
在有限差分方法中,利用优化算法来优化差分系数进而压制数值频散是一种直接且高效的策略。在常用的优化算法中,雷米兹交换算法相比于其它算法在拓宽差分系数有效带宽方面具有更显著的效果,但是该方法在低波数段会产生强烈的频散误差。为了压制雷米兹交换算法在低波数段的频散误差,且保留较宽的有效带宽的特点,提出了一种基于雷米兹交换算法和拉格朗日乘数法耦合的优化差分系数方法。首先根据雷米兹交换算法计算差分系数,再计算该差分系数频散曲线的零点,之后利用频散关系和零点构建约束条件,最后用拉格朗日乘数法求解二范数目标函数和约束条件并得到优化差分系数。频散测试和数值模拟结果表明,该方法具有较宽的有效带宽和低频散误差的优点。复杂模型试验表明该方法在空间步长较小的情况下,对频散的压制效果优于雷米兹交换算法和最小二乘算法。
The use of the finite-difference (FD) optimized coefficients algorithm to suppress numerical dispersion is a straightforward and efficient strategy in the field of FD forward modeling.For the current optimal algorithms,Remez exchange algorithm (REA) has a broader effective bandwidth than other methods,but suffers stronger numerical dispersion in low-wavenumber regions.To reduce the numerical dispersion in low-wavenumber region and maintain the characteristic of broad effective bandwidth,an optimized FD coefficients method coupled with REA and Lagrange algorithm (LA) was proposed.First,the FD coefficients are obtained using the REA,and the zero points of the curve are then derived using the dispersion relation curve of the FD coefficients.Subsequently,the zero points and dispersion relation curve are used to construct the restricted condition.Finally,the optimized FD coefficients are obtained using the LA to solve the L2-norm objective function and the restricted condition.Theoretical analysis and numerical experiment reveal that the proposed method has a low dispersion error in low-wavenumber regions and wide effective bandwidth.Under a low space step,the numerical experiment of modified Marmousi model demonstrated that the proposed method has a lower numerical dispersion compared with that of the REA and least square methods.
国家自然科学基金优秀青年基金项目(41922028)、国家重点研发计划项目(2019YFC0605503)和中国石油科技重大专项(ZD2019-183-003)共同资助。