基于电导率加权平均法的频率域航空电磁三维谱元正演模拟研究

3D AEM forward modeling based on the poly-grid spectral-elementmethod with average weighted conductivity

三维电磁正演算法的精确性和有效性对于实测电磁数据的反演和解释至关重要。近年来,谱元法逐渐被应用于三维电磁正演中,其中基于规则/形变六面体网格的谱元法在航空电磁正演模拟中的效果已得到了验证。然而,常规谱元法在处理每个离散单元时,通常赋予其单一的物理属性,导致在模拟复杂模型时仍需采用精细网格以满足模型离散需求,对复杂模型的适用性存在不足。鉴于谱元法基函数的高阶性,提出了一种基于电导率体积加权平均的谱元法。该方法将物理模型离散化与数值网格离散化相分离,实现了对单元内物理属性变化的精细描述,同时避免了正演方程未知数数量的增加。以频率域航空电磁三维正演为例,对改进的谱元法的精度与效率进行了分析。数值算例结果表明,改进的谱元正演算法能够在保证不低于常规正演算法精度的前提下,减少所需的自由度,从而提高计算效率。

The accuracy and effectiveness of 3D EM forward modeling are two key points that affect inversion and data interpretation.AEM forward modeling based on the spectral-element(SE)method using regular/deformed hexahedral cells has been verified to be feasible.However,a conventional SE method with a certain physical property assigned to each discrete element still cannot avoid fine grids to discretize a complex model,leading to poor adaptability to complicated earth model.To address this issue,we take into account the nature of the high-order basis functions of the SE method and develop a modified SE method with average volume-weighted conductivity.Physical model discretization is separated from numerical grid discretization,so as to realize the detailed description of physical property change within each element and meanwhile avoid an increase in the number of the equation unknowns in forward modeling.We perform^(3)D frequency domain AEM forward modeling to examine the accuracy and efficiency of the modified SE method.Numerical tests demonstrate that the modified algorithm can achieve an accuracy not less than that of conventional modeling methods while using fewer degrees of freedom,thus improve the forward modeling efficiency.