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对于时间域航空电磁法二维和三维反演来说,最大的困难在于有效的算法和大的计算量需求.本文利用非线性共轭梯度法实现了时间域航空电磁法2.5维反演方法,着重解决了迭代反演过程中灵敏度矩阵计算、最佳迭代步长计算、初始模型选取等问题.在正演计算中,我们采用有限元法求解拉式傅氏域中的电磁场偏微分方程,再通过逆拉氏和逆傅氏变换高精度数值算法得到时间域电磁响应.在灵敏度矩阵计算中,采用了基于拉式傅氏双变换的伴随方程法,时间消耗只需计算两次正演,从而节约了大量计算时间.对于最佳步长计算,二次插值向后追踪法能够保证反演迭代的稳定性.设计两个理论模型,检验反演算法的有效性,并讨论了选择不同初始模型对反演结果的影响.模型算例表明:非线性共轭梯度方法应用于时间域航空电磁2.5维反演中稳定可靠,反演结果能够有效地反映地下真实电性结构.当选择的初始模型电阻率值与真实背景电阻率值接近时,能得到较好的反演结果,当初始模型电阻率远大于或远小于真实背景电阻率值时反演效果就会变差.
For the two-dimensional and three-dimensional inversion of the time-domain aeromagnetic method, the biggest difficulty lies in the effective algorithm and the large amount of computational requirements.In this paper, the 2.5-D inversion method of the time-domain electromagnetism method is realized by the nonlinear conjugate gradient method, We focus on solving the problems of calculation of sensitivity matrix, calculation of optimal iterative steps and selection of initial model in iterative inversion.In the forward calculation, we use the finite element method to solve the electromagnetic field partial differential equations Time-domain electromagnetic response is obtained by high-precision numerical algorithm of inverse Laplace transform and inverse Fourier transform.In the calculation of sensitivity matrix, a companion equation method based on pull Fourier double transform is adopted, time consumption only needs to be calculated twice forward Which saves a lot of computation time.For the calculation of the optimal step size, the quadratic interpolation backward tracking method can guarantee the stability of the inversion iteration.We design two theoretical models to test the validity of the inversion algorithm, and discuss the choice of different initial models And the effect on the inversion results.The model shows that the nonlinear conjugate gradient method is stable and reliable in time domain aeromagnetic 2.5D inversion and the inversion results can effectively reflect Under the real electrical structure, when the initial model resistivity value is close to the real background resistivity value, good inversion results can be obtained. When the initial model resistivity is much larger or smaller than the true background resistivity value The effect will be worse.