A New Data Processing Method for Magnetic Anomaly Detection and Localization Based on 2-D Orthonormal Basis Functions

This work proposes a new processing method based on orthonormal basis functions (OBFs) for two-dimensional (2-D) magnetic anomaly data, which is an innovative extension of one-dimensional (1-D) OBFs. In most surveys, ferromagnetic targets are usually regarded as magnetic dipoles. The magnetic anomaly field of a dipole in a horizontal plane is essentially a linear combination of linearly independent basis functions, which are then transformed into a set of 2-D orthonormal basis functions (2-D-OBFs) using the Gram-Schmidt algorithm. On the basis of the 2-D-OBFs, a processing procedure for 2-D magnetic anomaly data is established and named the 2-D-OBF method. This method converts magnetic anomaly maps to energy maps, in which there is only one positive peak corresponding to the horizontal location of a magnetic dipole. As a consequence, the detection and localization are significantly simplified. To verify this new method, a total of 3000 Monte Carlo simulations were carried out, and the synthetic data were also processed using the traditional 1-D-OBF method. The statistics of the 2-D-OBF results showed that the localization accuracy and false alarm rate are 0.34 m and 1.9%, respectively, at a data noise level of 10 nT, which was much better than the 1-D-OBF method. Another synthetic data experiment verified the reliability of the 2-D method for handling multiple targets simultaneously, even when the magnetic anomalies of adjacent targets are severely superimposed. For the measured aeromagnetic data, the 2-D-OBF method also works well. Additionally, this method exhibits outstanding noise immunity in all tests. The signal-to-noise ratios (SNRs) of the energy data are improved by approximately 14 dB compared to that of the magnetic anomaly data within the signal bandwidth. Developed from rigorous mathematical physics definitions, the 2-D-OBF method is more conducive to the implementation of automatic data processing programs and has considerable practical promise.