基于最小均方误差的磁场反演及磁场评估算法研究

Research on magnetic field inversion and magnetic field evaluation algorithm based on minimum mean square error

为了保证反演模型的稳定性,基于点磁荷理论,改进磁场反演建模的数学模型.针对固定式南北航向测量中磁场y分量较小容易造成拟合效果不佳的问题,提出一种自适应权重的基于最小均方根误差(MMSE)的反演算法,通过实测磁场数据进行验证,能保证磁场三分量皆能实现较高精度的深度换算,在加入10 dB噪声后仍能保证误差皆小于10%,符合工程实际,证明了模型算法的稳定性;同时,为了评估反演输入磁场数据的正确性,提出一种基于T分布原理的磁场评估方法,结果显示:该方法能获得磁场置信区域,在95%置信度下,实现对原始样本中符合要求的磁场数据进行筛选,筛选有效率为20%,提高了反演输入数据正确性的概率,实现了对多组磁场数据的有效评估.

In order to ensure the stability of the inversion model,the mathematical model of magnetic field inversion modeling was improved based on the point magnetic charge theory.Aiming at the problem of poor fitting effect caused by small y component of magnetic field in fixed north-south course measurement,an inversion algorithm based on minimum root-mean-square error(MMSE)with adaptive weights was proposed,which was verified by measured magnetic field data to ensure that all three components of magnetic field could achieve relatively high precision depth conversion.After adding 10 dB noise,the error is still less than 10%,which accords with the engineering practice,and proves the stability of the model algorithm.At the same time,in order to evaluate the correctness of inversion input magnetic field data,a magnetic field evaluation method based on T-distribution principle was proposed.The results show that the magnetic field confidence region can be obtained by this method,and the magnetic field data meeting the requirements in the original sample can be screened with 95% confidence,and the screening efficiency is 20%,which improves the probability of the correctness of the inversion input data and realizes the effective evaluation of multiple groups of magnetic field data.