Moments estimation of magnetic source terms from partial data

Laurent Baratchart (1) , Sylvain Chevillard (1) , Juliette Leblond (1) , Eduardo Andrade Lima (2) , Dmitry Ponomarev (3)

1 APICS - Analysis and Problems of Inverse type in Control and Signal processing
2 EAPS - Department of Earth, Atmospheric and Planetary Sciences [MIT, Cambridge]
3 POEMS - Propagation des Ondes : Étude Mathématique et Simulation

In this article, we give asymptotic formulas that link the (first and higher order) moments of the magnetic density distribution (also called magnetization) of a compactly supported magnetized sample with the 0-th and 1st order moments of the vertical component of the magnetic field it produces on a square piece of horizontal plane lying above it. Such a framework typically arises in geosciences when one measures the field generated by a small piece of (magnetized) rock with a magnetic microscope. In such a case, the magnetic moments of the sample are usually unknown and one is interested in recovering them from the data measured with the microscope, i.e. the vertical component of the magnetic field on a planar region above the sample. The formulas given in this article provide a practical way of recovering an estimate of the 0-th order moment of the magnetization (usually also called net moment) from simple computations with the measurements. This estimate is asymptotically exact when the square where the measurements are performed gets large. This allows one for implementing an actual "numerical magnetometer".

Domaines: Electromagnétisme

Laurent Baratchart, Sylvain Chevillard, Juliette Leblond, Eduardo Andrade Lima, Dmitry Ponomarev. Moments estimation of magnetic source terms from partial data. 2016. ⟨hal-01421157v1⟩