Rapid computation of magnetic anomalies with demagnetization included, for arbitrarily shaped magnetic bodies

Summary. The potential function ø for a magnetic body of susceptibility μ in a medium of susceptibility μ* satisfies the integral equation
Here Φ* is the potential function for the region without the heterogeneity and R is the distance from the point of observation to the point on the surface, s , of the body. δΦ /δn is the normal derivative, in the direction of the outward normal. The equation allows for the effects of demagnetization. For numerical purposes the surfaces can be divided into N facets over which δΦ/δ n is a constant. The unknown quantities δΦ/δn_j can be found from the system of equations defined by:
The prime on the summation sign denotes that the summation does not include the i th element. The magnetic field in the direction of the unit vector P( P ₁, P ₂, P₃ ) is given by: