基于收缩二叉树结构网格剖分的大地电磁二维有限单元法正演研究

2D MT numerical simulation using FEM based on bi-tree grid

在大地电磁的正演计算中,通常采用不断增加垂向步长以减少垂向剖分节点数,以提高计算效率。本文针对规则网格剖分无法实现随深度增加横向变步长剖分的实际情况,提出了一种基于二叉树结构的收缩网格剖分算法。该算法利用二叉树结构在实现四边形剖分的基础上,通过四边形三角形化实现三角剖分;利用对边的访问实现快速的双二次插值;利用带二次插值节点的三角形再剖分实现网格细化,同时引入缓冲层解决二叉树收缩过快问题。试算结果表明,采用这种收缩结构的二维大地电磁正演精度与规则剖分下的计算精度相当,同时大大减少了节点数,提高了计算效率。

The computation efficiency of numerical simulation depends directly on the number of nodes created by the discrete model.Usually the magnetotelluric forward modeling increases the vertical steps and reduces the vertical discrete nodes.But it is difficult to increase the horizontal steps with the depth by the regular discrete method.In view of this situation,we propose a model discrete algorithm based on the binary tree structure.Using bi-tree,the algorithm calculates quadrilaterals,and then performs triangulation on the quadrilaterals.It is easy to achieve double quadratic interpolation by inserting the middle point at side of triangle.The triangle with middle points can be triangulated into four sub-triangles.The numerical simulations demonstrate that this method greatly improves computation efficiency with fewer nodes while the forward modeling accuracy matches with that of the regular discrete method.