Euler deconvolution in a radial coordinate system

This paper introduces the conversion of Euler's equation from a Cartesian coordinate system to a radial coordinate system, and then demonstrates that for sources of the type 1/r^N (where r is the distance to the source, and N is the structural index) it can be solved at each point in space without the need for inversion, for a known structural index. It is shown that although the distance to the source that is obtained from Euler's equation depends on the structural index used, the direction to the source does not. For some models, such as the gravity and magnetic response of a contact, calculation of the analytic signal amplitude of the data is necessary prior to the application of the method. Effective noise attenuation strategies, such as the use of moving windows of data points, are also discussed. The method is applied to gravity and magnetic data from South Africa, and yields plausible results.