Shape and depth solutions from magnetic data using a parametric relationship

Abstract

We have developed a simple method to simultaneously determine the shape (shape factor) and the depth of a buried structure from magnetic data. The method is similar to Euler deconvolution, but it solves for shape and depth independently. The method involves using a relationship between the shape factor, the depth to the source, and a combination of observations at symmetric points with respect to the coordinate of the source center with a free parameter (graticule spacing). The relationship represents a parametric family of curves. For a fixed free parameter, the depth is determined for each shape factor. The computed depths are plotted against the shape factors representing a continuous monotonically increasing curve. The solution for the shape and depth of the buried structure is read at the common intersection of the parametric curves. The parametric curves method is applied to two theoretical magnetic anomaly profiles due to a thin dike and a horizontal cylinder. The method is also tested on a field example from Brazil. In all cases, the shape and depth solutions obtained are in good agreement with the actual ones.