飞行高度同时反演的固定翼航空瞬变电磁一维反演

Research on 1D inversion method of fix-wing airborne transient electromagnetic record with flight altitude inversion simultaneously

航空电磁测量记录中,不仅感生电动势测最数据有观测误差,而且高度计测量数据也有误差,直接进行常规反演往往导致反演结果不可靠,研究飞行高度数据有误差下的反演算法具有实际意义.本文以层状模型的固定翼时间域航空电磁多分量理论响应数据为例,提出了两种针对飞行高度计记录数据有误差时的正则化反演算法,一个是自适应正则化反演方法,另一个是约束优化反演方法,结合光滑化模型约束方式,将飞行高度作为一个待反演参数与电阻率参数一并反演,以获得更可靠的解释结果.第一种算法侧重于已知的地电信息相对较少的一般情况下的反演,只要给定初始飞行高度值和初始均匀半空间模型的电阻率值,即可稳定地同时重构地下介质电阻率和飞行高度.反演中正则因子由自适应的方式获得,并用奇异值分解法解反演方程.而第二种算法则用于先验信息较多的特殊场合,可事先设定反演模型参数及飞行高度参数的上下限范围,并通过有限内存拟牛顿约束优化方法搜索可行域里的最优解.用多层介质模型的理论响应数据加入不同水平噪声后进行反演试算,对使用不同飞行高度初值和不同约束参数时的反演结果作对比分析.结果表明,无论飞行高度值偏高或偏低,两种算法均能稳定有效地重构地下介质电导率分布和飞行高度值,但飞行高度初值不准会降低反演的收敛速度;文章的一个算例显示,在飞行高度初值偏低15 m下,第一种算法在第10次迭代后的解释高度与真值的误差小于0.3 m,第二种算法在参数约束下,第6次迭代以后的各次迭代的飞行高度值在119.4～121 m之间,其平均值与真值的误差不足0.2 m.

In the record of airborne electromagnetic survey, not only the measured voltage data but also the altimeter data have observation error; the results of conventional inversion are badly affected particularly in middle/shallow layer if inaccurate flight altitude was used in inversion. Therefore, it＇s a significant thing to research the inversion algorithm using observation data with inaccurate flying altitude. In this paper, the fix-wing airborne electromagnetic multi-component responses data in time domain of layered model is used as an example and two regularized inversion algorithms are presented to invert for earth resistivity and the flying altitude simultaneously aiming at the inversion problem of inaccurate flying altitude. One is the adaptive regularized inversion method and the other is constrained optimization inversion method. Combined with the restraint technique of smoothing inversion model, the flight altitude, seen as an inversion parameter in both methods, is determined along with the earth resistivity in the inversion to obtain a better interpretation result. The first algorithm is mainly used on the common occasion, for example there is little known geoelectricity information beforehand. Given the initial flight altitude （for instance, the measurement of altimeter） and the resistivity of initial half-space model, the algorithm can reconstruct the resistivity and the flight altitude steadily and reliably. The regularizing factor used in inversion is obtained adaptively and the singular value decomposition （SVD） method is used to resolve the inversion equations. The second inversion algorithm makes use of the bound constraints of the model resistivity and the flight altitude determined by the known geoelectricity information to accomplish the constrained inversion. The regularizing factor is set beforehand based on the smooth degree of the model and the optimal result of model resistivity and flight altitude is searched in the feasible region by limited-memory quasi-Newton （LMQN） optimization method. The inversion method is tested using the synthetic data of multi-layered model with noises added. The iterative process of the regularized inversion is analyzed and shown in this paper. The inversion results of different initial value of flight altitudes and different constraints of inversion parameters used in inversion are compared in this paper. It shows that both the resistivity distribution and the flight altitude are reconstructed well whatever the initial flight altitude is higher or lower; the inaccurate flight altitude data used as initial value in inversion, however, might lower the velocity of convergence of the inversion. According to the result of an example in the paper, when the given flight altitude initial value has a lower error of 15 m compared to the true flight altitude, the errors of flight altitude value from the first inversion algorithm are all less than 0.3 m after the 10^th iteration, and for the second method, the flight altitude values of the inversion after 6^th iteration vary from 119.4 m to 121 m, whose mean has an error of 0.2 m.