有限长圆柱体磁异常场全空间正演方法  

Forward modeling of magnetic anomalies of finite-length cylinder in 3D space

作　　者：郭志馗 陈超[1] 陶春辉[2] 胡正旺[1] 

机构地区：[1]中国地质大学(武汉)地球物理与空间信息学院地球内部多尺度成像湖北省重点实验室,武汉430074 [2]国家海洋局第二海洋研究所海底科学重点实验室,杭州310012

出　　处：《地球物理学报》2017年第4期1557-1570,共14页Chinese Journal of Geophysics

基　　金：国家自然科学基金项目(41574070);国际海域资源调查与开发"十二五"重大项目(DY125-11-R-01;DY125-11-R-05);国家重点基础研究发展计划(2012CB417305)资助

摘　　要：在经典位场理论中,许多简单形体位场异常难以通过积分得到全空间的解析式.圆柱体是一类很重要的理论模型体,常用于模拟圆柱状地质体或非地质体(如管线),但目前还不能用解析公式正演有限长圆柱体在三维空间里的磁异常,而多是采用近似简化为有限长磁偶极子或线模型代替.对于有限长圆柱体,特别是半径相对于上顶埋深较大时,这种近似的误差不可忽略.本文利用共轭复数变量替换法,推导出有限长圆柱体在全空间的引力位一阶、二阶导数,利用Poisson关系得到磁异常正演公式,进而利用有限长圆柱体磁异常正演公式求解管状体的磁异常,得到不同磁化方向、不同大小的管线产生的磁场的特征,并将其推广到截面为椭圆的情况.最后通过模拟计算定量给出了将圆柱体近似为线模型的条件.In the classical theory of potential fields, potential field anomalies caused by individual bodies in simple shapes is generally difficult to be expressed by an analytic formula in 3D space. Cylinder, as a significate theoretical model type, is generally used to model cylindrical-like geological bodies and non-geological bodies such as pipelines. However, we cannot use any analytic formula to calculate the magnetic anomalies of a finite-length cylinder in 3D space, except for approximating it as a magnetic dipole or dipole-line. But error due to the approximation cannot be ignored while the radius is larger than the top buried depth. In this study, we propose an approach to calculate the magnetic anomalies of a finite-length cylinder in 3D space. The expressions for calculating gravity and its gradients of a finite-length cylinder are derived using conjugate-complex variables substitution, and then the formula to calculate magnetic anomaly in 3D space is obtained based on the Poisson relationship between the gravity and magnetic fields. We present magnetic anomalies of synthetic models with various radii of cylinders and pipes in different placement patterns and magnetization directions. Meanwhile, the approach is extended to calculate magnetic anomalies of an elliptic cylinder. Finally, we show the conditions for replacing a cylinder by a dipole-line through quantitative modeling.

关 键 词：有限长圆柱体 磁异常正演 共轭复变量替换 三维空间 

分 类 号：P631[天文地球—地质矿产勘探]