On analytic formulas useful to solve the inverse magnetization problem

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.