An adaptive finite difference method for traveltime and amplitude
An adaptive finite difference method for traveltime and amplitude
复制标题
DOI：
--
复制
发表时间：
1999
期刊：
影响因子：
--
通讯作者：
J. Qian;W. Symes
中科院分区：
文献类型：
--
作者：
J. Qian;W. Symes
点源程函方程由于其解在源处的奇异性，难以高精度求解。所有形式上的高阶格式都被证明是一阶精度的，而无需对该奇异性进行特殊处理。基于高阶ENO（Essentially NonOscillatory）Runge-Kutta差分格式的近轴程函方程自适应迎风差分方法克服了这一困难。该方法通过基于后验误差估计的自动网格细化和粗化来控制误差。它以比固定网格方法低得多的成本达到规定的精度。可靠的辅助量，如起飞角和几何扩展因子，是副产品。
The eikonal equation with point source is difficult to solve with high order accuracy because of the singularity of the solution at the source. All the formally high order schemes turn out to be first order accurate without special treatment of this singularity. Adaptive upwind finite difference methods based on high order ENO (Essentially NonOscillatory) Runge-Kutta difference schemes for the paraxial eikonal equation overcome this difficulty. The method controls error by automatic grid refinement and coarsening based on an a posteriori error estimation. It achieves prescribed accuracy at far lower cost than fixed grid methods. Reliable auxiliary quantities, such as take-off angle and geometrical spreading factor, are by-products.