有限长导线源频率测深有限内存拟牛顿一维反演

本文采用有限内存拟牛顿法实现有限长导线源频率测深阻抗响应数据的一维反演。水平层状介质有限长导线源阻抗频率响应由基于虚界面法获得的地表水平正交电场和磁场计算得到;一维反演优化问题的求解利用有限内存拟牛顿法,结合光滑模型约束,直接对阻抗的频率响应数据进行反演。在反演过程中,正则化参数的调整采用目标函数自适应技术。反演模型剖分为多层,各层厚度自地表按比例增加。反演从均匀半空间开始,终止条件为目标函数相对变化小于10~(-4)。分别对理论模型和实际数据进行了反演模拟。为考察反演的稳定性,还对理论数据添加10%随机噪声后进行了反演。数值计算结果表明:有限内存拟牛顿方法可以用于有限长导线源频率测深阻抗频率响应的反演;该反演方法对初始模型的依赖性弱,从均匀半空间模型出发基本可以恢复到真实模型;反演初期收敛较快,后期收敛速度变慢,反演结束一般需要迭代40次左右。噪声数据反演结果表明,随机噪声对反演结果影响不大,说明有限内存拟牛顿法具有较好的抗干扰能力。本文研究成果给出了可控源电磁数据反演的一种新方法;同时,利用本文的研究成果,可以为二维或三维反演建立合适的初始模型。

1-D Inversion for Controlled Source Electromagnetic Sounding Using Limited Memory Quasi-Newton Method

This paper uses limited memory quasi-Newton method to solve 1-D inversion for impedance response of long wire source frequency sounding.Impedance response of a long wire source in horizontal layered earth model is calculated from the ground level orthogonal electromagnetic fields,and the fields are obtained by the virtual interface method.To solve optimization problems of one dimensional inversion,limited memory quasi-Newton method is adopted.Furthermore,it uses smoothness constrains for model and inverses impedance response directly.Adaptive method of target function is used for adjusting regularization parameter in the process of inversion.The inversion model is divided into many layers that scale up the thickness.It's inversed from homogeneous half-space model until the fitting error is less than 10 4.We inverse theoretical model and actual data respectively,and then the data with 10％ random noise are tested in order to investigate the stability.The numerical results show that the method of limited memory quasi-Newton is feasible for 1-D inversion for impedance response of long wire source frequency sounding;The method has little dependence on initial model,and inversion from homogeneous half-space model can still restore the true model;The objective function converges quickly at first and the speed slows down gradually later,and it takes about 40 iterations generally;The inversion results of noise data show that random noise has little effect,it also demonstrates the limited memory quasi-Newton method has certain anti-interference ability.This paper presents a new inversion method for controlled source electromagnetic data,meanwhile,the results can provide initial model for 2-D and 3-D inversion.