摘要
地质勘探中的全波形反演模型可以转化为一个求解带微分方程约束的最小二乘问题,这类模型通过扩大了搜索区域,减少了变量的储存,提高了计算效率.基于上述模型,采用有限差分方法离散Helmholtz方程,提出一类预处理共轭梯度法求解地震波场,并交替更新地层信息.数值实验中测试和比较了对角预处理、Gauss-Seidel预处理和不完全LU分解三种预处理方法,实验结果表明这类预处理方法应用到共轭梯度法中能够减少迭代步数、改善实验精度,加快反演迭代效率.
The full-waveform inversion method in frequency domain can be trans- formed into a least squares problem constrained by a partial differential equation, which is widely used in geological exploration. The inversion model with a penalty term expands searching domain and reduces variable storage, thus improving com- putational efficiency. Based on this model, a class of preconditioned conjugate gradient methods are used to solve the seismic wave field. The Holmholtz equation is discretized by using finite difference method, and the stratigraphic model is up- dated alternatively. Numerical experiments show that the preconditioning process in the conjugate gradient method can reduce iteration steps, improve precision, and increase efficiency. In the last part, we find the optimal tolerance of incomplete LU decomposition through experiments.
出处
《应用数学与计算数学学报》
2016年第1期71-80,共10页
Communication on Applied Mathematics and Computation
基金
国家自然科学基金资助项目(11271289)
中央高校基础研究经费资助项目(1390219158)
