Euler Deconvolution in Cylindrical and Spherical Coordinate Systems

Euler deconvolution is a commonly used technique for the semi-automatic interpretation of potential field data. In the two dimensional case the known quantities are the field strength f, its horizontal and vertical gradients, and the structural index N. The unknown quantities are deltax and deltaz, the distance from a given point to the source location in the horizontal and vertical planes. Because the equation contains two unknown quantities is is usually solved in an overdetermined least-squares inverse manner using a window of data points. Although the use of large windows can reduce the effects of noise, it can also lead to the horizontal smearing of source locations, and if a window encompasses parts of more than one anomaly then interference problems can arise. This paper discusses the conversion of Eulers' equation from a Cartesian coordinate system to a cylindrical polar coordinate system, and then demonstrates that it can be solved at each point in space without the need for inversion. The method is then extended to the three dimensional case using a spherical coordinate system.