Euler inversion of magnetic anomalies using analytical continuation

Abstract

Some properties of the analytical expressions of potential fields as homogeneous functions allow the inverse problem for magnetic anomalies, caused by simple sources, to be solved in a direct way, without use of derivatives and a system of equations. The tool in the proposed here new inversion technique is the finite‐difference similarity transform (FDST). FDSTs are generated from a set of central points of similarity (CPS). These transforms are sensitive to the distance between a chosen CPS and the source. The CPS and the degree of homogeneity that give minimal values of the respective FDST indicate the source position and shape. The technique requires calculation of an upward analytical continuation of the inverted field, or measured field at two height levels. The approach shows possibilities for obtaining stable solutions in an automated inverse procedure. 2D model and field examples illustrate the effectiveness of inversion using FDST. 2D gravity, as well as 3D magnetic and gravity inversions, are possible on the same theoretical base.