航空瞬变电磁反演中灵敏度的快速高精度计算

Calculation of sensitivities for airborne electromagnetic inversion progress

为了满足在航空电磁反演迭代过程中灵敏度的计算要求,提出了多步长差分累加算法,以差分代替微分计算,用差分步长系数控制累加次数,通过多个步长中心差分结果的累加平均,实现了灵敏度的快速高精度计算。计算了多组大地模型灵敏度,结果表明:差分步长系数选取10,灵敏度矩阵元素的误差均可控制在0.1%以内。与传统中心差分方式和解析法进行对比分析,得到多步长差分累加算法在计算精度上优于中心差分方法;在计算速度上优于解析法,对于15层大地模型,计算速度提高5倍。最后,通过航空瞬变电磁反演仿真实例,证明了该算法能够满足航空电磁海量数据对反演精度和反演速度的要求。

To meet the requirements of the sensitivities during the airborne electromagnetic inversion iteration,a variable step size difference accumulation algorithm is proposed.Based on the idea of replacing the derivative by difference,and adjusting the accumulating time by difference step coefficient,a fast high-precision algorithm is realized.The sensitivity matrix of multi-group earth model is calculated.The results show that the error of the sensitivity matrix is within 0.1% when the coefficient of difference step is usually selected 10.Comparison with the routine center differential algorithm and the analytical method indicates that the variable step size difference accumulation algorithm is superior to center differential algorithm in calculation accuracy,and is better than analytical method in calculation speed.Finally,the proposed algorithm is applied to airborne inversion simulation to prove its effectiveness.