The ellipsoidal magnetization model has a wide range of application scenarios. For example, in aviation magnetic field prospecting, mineral prospecting, seabed prospecting, and UXO (unexploded ordnance) detection. However, because the existing ellipsoid magnetization formula is relatively complicated, the detection model is usually replaced by a dipole. Such a model increases the error probability and poses a significant challenge for subsequent imaging and pattern recognition. Based on the distribution of ellipsoid gravity potential and magnetic potential, the magnetic anomaly field distribution equation generated by the ellipsoid is deduced by changing the aspect ratio, making the ellipsoid equivalent to a sphere. The result of formula derivation shows that the two magnetic anomaly fields are consistent. This paper uses COMSOL finite element software to model UXO, ellipsoids, and spheres and analyzes magnetic anomalies. The conclusion shows that the ellipsoid model can completely replace the UXO model when the error range of 1nT is satisfied. Finally, we established two sets of ellipsoids and calculated the magnetic anomalous field distributions on different planes using deduction formulas and finite element software. We compared the experimental results and found that the relative error of the two sets of data was within [Formula: see text]‰. Error analysis found that the error distribution is standardized and conforms to the normal distribution. The above mathematical analysis and finite element simulation prove that the calculation method is simple and reliable and provides a magnetic field distribution equation for subsequent UXO inversion.
Practical analysis of 3-D dynamic nonlinear magnetic field using time-periodic finite element method
