强磁性体ΔT异常计算的误差分析研究

Error analysis of calculation of total field anomaly due to highly magnetic bodies

本文主要针对当前磁法勘探中高精度处理解释的需求,对强磁性体ΔT异常计算存在的误差进行分析研究.我们首先通过理论模型计算试验,证明常规计算采用的投影关系的ΔT与实际测量的模量差ΔT之间的误差E在磁异常幅值大时是明显存在的,其影响不容忽视.其次,当磁性强且剩磁存在时,投影ΔT曲线及其误差曲线在磁化方向与地磁场方向改变时具有一定的对称性;地磁场T0、磁性体形态（如二度水平圆柱体模型的半径r、柱体埋深R）和磁性参数（如磁化率κ）等参数确定的情况下,最大误差值出现在磁性体正上方,且其大小与磁性参数（κ）和模型体规模（如r/R）之间皆是指数关系;另外,研究还发现ΔT的计算误差曲线的一些其他规律特点,如在各纬度带上,ΔT计算误差的最大值Emax曲线的极值主要分布在中纬度地区;磁异常矢量Ta与地磁场T0的夹角θ逐渐变化时,随θ变化Emax曲线的极值分布在θ=90°~120°范围内;当磁异常幅值小于10000nT时,最大误差近似为磁异常矢量垂直于地磁场方向的测点附近的误差值;另外,磁性体（圆柱体为例）的半径（即尺度）与埋深的比值r/R超过0.5,且磁化率超过0.1SI时误差已达到3.9nT,磁化率增大与对应的Emax的值呈指数增长特点.因此,我们的研究表明,在强磁性体、磁异常幅值大的数据处理、反演及解释时,现有方法会产生较大的误差,应该基于严格的模量差ΔT,完善相应的处理以及反演方法.

Currently,the magnetic prospecting has a great demand for high-precision processing and interpretation.In order to meet this requirement,we studied the approximate error E betweenΔTact（the total-field anomaly）andΔTpro（the projection of anomalous field vector onto the direction of geomagnetic field）.Generally speaking,the error Eis extremely small when the bodies have weakly magnetic susceptibilities.However,when the bodies have highly magnetic susceptibilities,the error E might be large.This will lead to significant effects on subsequent quantitative inference.Therefore,we investigated the error Edue to highly magnetic bodies.In this paper,a systematic error analysis was made by using a 2-D elliptic cylinder model.We investigated the error Ethrough numerical experiments of magnetic anomalies produced by highsusceptibility bodies.Normally,for high susceptibilities,we found that the existed remanencesignificantly affected the error E.The error analysis showed that the magnitude ofΔTact was usually larger than that ofΔTpro.This implied that a theoretical anomaly computed without accounting for the error E would overestimate the anomaly associated with the body.we used the 2-D elliptic cylinder model to illustrate the importance of the error analysis when the bodies were highly magnetic.Firstly,we demonstrated through numerical experiments that the error E was obvious and should not be ignored.Secondly,we showed that the curves ofΔTpro and the error E had a certain symmetry when the directions of magnetization and geomagnetic field changed.And we also displayed that the Emax（the maximum value of the error E）appeared above the center of the magnetic body when the parameters such as the vector of geomagnetic field T0,the geometric form（e.g.,the radius r and the depth R of the 2Dhorizontal cylinder body）and the magnetic parameters（e.g.,the susceptibilityκ）are determined,and that the relationship between the Emax and magnetic parameters or size of the model（e.g.,r/R）is exponential.Then we discovered some other characteristics about the error E.For instance,the curve of Emax with respect to the latitude was symmetrical on both sides of magnetic equator,and the extremum of the Emaxcan always be found in the mid-latitudes.When T0 was perpendicular to Ta（the vector of the anomaly）,the error Erised with the increase of Ta.Whenθ（the included angle between Taand T0）changed,the Emaxdue to the cylinder model is found inθ=90°~120°.When r/Ris larger than 0.5and the susceptibility is larger than 0.1SI,the Emaxreaches to 3.9nT.As a result of the numerical experiments,we concluded that when the bodies have highly magnetic susceptibilities,the error E may be great and will affect the subsequent magnetic processing and inversion.Therefore,the error Ecannot be ignored when the magnetic data are processed,inverted,and interpreted in highly magnetic environments.