Local homogeneity of potential fields and fractional homogeneous functions: a new theory for improved source parameter estimation

Summary We describe a multiscale method for source parameter estimations (depth to the source, homogeneity degree) based on a new theory, which we propose for studying explicitly inhomogeneous field. The theory consists in enlarging the set of homogeneous fields with those having a fractional homogeneity-degree and in relaxing the standard homogeneous equation to a local homogeneity equation. We show the validity of the method as applied to the inhomogeneous-degree gravity fields of a finite vertical cylinder.