航空磁探中水下目标三维积分方程磁场建模

Magnetic Field Modeling of Underwater Target Using 3D Integral Equation for Aeromagnetic Anomaly Detection

为获取航空磁探中水下铁磁性目标的空间磁场分布,通过三维积分方程法的基本原理推导出空间磁场的解析式,根据矢量恒等式和高斯散度定理简化空间磁场计算式,建立水下铁磁性目标空间磁场预测模型。通过铁磁性长方体对模型进行理论验证,使用铯光泵磁力仪测量铁磁性长旋转椭球体的高空磁场;然后,基于预测模型推算铁磁性长旋转椭球体的磁场,根据实际测量的磁场数据和预测值进行比较。结果表明,预测模型的推算精度较高,平均绝对误差为0.320 5 nT,平均相对误差为12.368%。

To obtain the spatial distribution of the magnetic field of underwater ferromagnetic target in the aeromagnetic anomaly detection, the analytical equation of spatial magnetic field of the underwater ferromagnetic target was derived based on the fundamentals of the three dimensional integral equations method. The analytical equation of spatial magnetic field was simplified by the vector identity and the Gaussian divergence theorem, and the prediction model of the magnetic field of the underwater ferromagnetic target was established. The theoretical validation of the prediction model was performed using the ferromagnetic cuboid. The magnetic field of the ferromagnetic ellipsoid at high altitude was measured by the cesium vapour optically pumped magnetometer. Then the magnetic field of the ferromagnetic ellipsoid was calculated by the proposed prediction model. The prediction values and the measurement values were compared. The results showed that the prediction accuracy of the prediction model was good enough. The mean absolute error was 0.3205 nT, and the mean relative error was 12.368%.