On analytic formulas useful to solve the inverse magnetization problem

Overview & Synopsis

This work takes its roots in the inverse magnetization problem, where the magnetization properties of rocks are sought from measurements of the magnetic field they generate, taken on a horizontal plane at some height above the rocks. The Poisson kernel being at the core of the corresponding magnetic potential, double integrals of functions over the cube of a distance are ubiquitous in this context. We present explicit formulas for the particular case when the numerator of the integrand is a polynomial of two variables and show how these formulas can be useful to address the inverse magnetization problem.