大地电磁响应数值计算中结点分布的最优化问题

首次提出用广义逆理论解决数值计算中结点分布的最优化问题。由于文章的目的仅在于提出和说明这种方法的概念,所以只考虑一种典型的一维大地模型,并叙述了广义逆理论在这种应用中的基本关系。结果表明这种算法可给出最佳的结点分布。雅可比矩阵,奇异值和对应的特征向量的分析,可以从本质上理解不同电性层中结点分布对数值计算精度的影响,对设计数值模型具有很重要的指导意义。本文的结果对二维和三维复杂模型的数值计算具有重要的参考意义。

OPTIMIZATION OF SPACING IN NUMERICAL MODELLING FOR MAGNETOTELLURIC RESPONSE

One of the possible error sources in implementing a finite difference algorithm for MT response might be the finite spacing between nodes in the model.lt is neccessary for the precision and the economic of computation to determine the spacing properly. The paper shows that generalized inverse theory can be used to optimize the distribution of nodal spacings in order to yield an effective computation with a required precision. Since the objective of this paper is to illustrate the concepts of the method at this point, a typical 1-D model is selected.And the basic relations for the inverse problem are developed. The results show that the inversion algorithm is quite robust for optimizing the distribution of nodal spacing and node density in the finite difference method, and much larger node spacing can be employed in resistive layers without suffering loss of accuracy. The analysis of the Jacobian matrix, eigenvectors and eigenvalues can aid in understanding which nodal spacings should be considered important for the numerical computation and which are non-important.lt is a guide to designing a numerical model. This method should be useful for the computation of MT response in numerical modelling.