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

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.