On an Analytical Orthonormal Multipolar Basis for Magnetic Anomaly Detection

Magnetic anomaly detection aims to find hidden ferromagnetic masses by estimating the weak perturbation they induce on local Earth's magnetic field. Classical detection schemes rely on signals recorded on a moving sensor, and the modeling of the source as a function of unknown parameters. These are eased if the source field along the magnetometer trajectory decomposes over an orthonormal basis. Usually, spherical harmonics are used for determining the general multipolar basis functions that describe the anomaly signal. A new analytical set of functions (multipolar orthonormal basis functions - MOBF) that spans the space of the noise-free measured signal is introduced in this paper. The sampled MOBF are shown to satisfy quasi orthonormality, providing fairly equivalent performances than those obtained after a Gram-Schmidt orthonormalization on the sampled initial basis.