A New Method for Depth and Shape Determinations from Magnetic Data

We present in this paper a new formula representing the magnetic anomaly expressions produced by most geological structures. Using the new formula we developed a simple and fast numerical method to determine simultaneously the depth and shape of a buried structure from second-horizontal derivative anomalies obtained from magnetic data with filters of successive window lengths. The method involves using a nonlinear relationship between the depth to the source and the shape factor and a combination of observations at four points with respect to the coordinate of the source center with a free parameter (window length). The relationship represents a parametric family of curves (window 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 window curves. This method can be applied to residuals as well as to the observed magnetic data consisting of the combined effect of a local structure and a second-order regional or less. The method is applied to synthetic data with and without random errors and tested on three field examples from India, Brazil and the USA. In all cases the shape and depth of the buried structures are in good agreement with the actual ones.