This letter presents a magnetic target inversion method that does not vary with changes in the coordinate system and is based on the cross-product of the intermediate eigenvectors of any two points in the dipole field which is in the same/opposite direction as the magnetic moment vector. We used tensor geometric invariants to interpret this new physical property and obtain the unit magnetic moment vector. Using this, the unit vector of the measurement point-source displacement vector was derived. The distance between the measurement point and the source was obtained via the Frobenius norm of the gradient tensor matrix. Simulations verified that the proposed method is unaffected by attitudes and yields unique inversion results, and the results revealed that the inversion accuracy of the proposed method is high. The simulation results also show that conditional cosine and measurement noise have considerable influence on the inversion accuracy in the proposed method.

Currently, when the existing magnetic dipole inversion methods are used, the classification process heavily relies on the localization results, and the localization error can significantly deteriorate the classification results. In order to address this problem, the present study proposes a novel magnetic dipole inversion method based on tensor geometric invariants, in which localization and classification processes are mutually independent. First, based on tensor geometric invariants, it was proved that the cross product between the intermediate eigenvectors at any two measurement points in the dipole magnetic field is either in the same direction as the magnetic moment vector or in the opposite direction. Accordingly, the direction of the magnetic moment vector could be directly obtained. Next, based on tensor geometric invariants, nonlinear equations including the position parameters of the dipole were constructed so as to derive the position of the dipole. By employing the proposed method, localization and classification were found to be two mutually independent processes, both of which are relatively insensitive to attitude changes of the measurement system. The present simulation results demonstrate that the proposed method is superior to the scalar triangulation and ranging (STAR) method, the Nara improved method, and the STAR improved method in both classification and localization performance. Moreover, the proposed method exhibits the strongest noise immunity and can be effectively used for real-time inversion.

The magnetic moment measurement method based on magnetic sensor array is proposed to solve the problems of cumbersome calculation process and low inversion accuracy in the current magnetic moment calculation methods. Based on the concepts of magnetic field intensity, magnetic gradient tensor and Frobenius norm, this method can use the magnetic field information collected by magnetic sensor array to calculate the magnetic moment vector. The factors that may affect the measurement effect, such as sensor array structure, sensor precision and baseline size, are analyzed by simulation, and the advantages and disadvantages of three magnetic moment measurement methods based on magnetic sensor array are compared. Simulation results show that the proposed method is flexible in use, convenient in measurement, accurate in results, and has strong feasibility and reliability in geological survey and other applications.