Depth and shape solutions from second moving average residual magnetic anomalies

We have developed a simple and fast numerical method to simultaneously determine the depth and shape of a buried structure from second moving average residual anomalies obtained from magnetic data with filters of successive window lengths. The method is similar to Euler deconvolution, but it solves for depth and shape independently. The method involves using a nonlinear relationship between the depth to the source and the shape factor, and a combination of observations at five points with respect to the coordinate of the source centre with a free parameter (window length). The method is based on computing the standard deviation of the depths determined from all second moving average residual anomalies for each value of the shape factor. The standard deviation may generally be considered a criterion for determining the correct depth and shape of the buried structure. When the correct shape factor is used, the standard deviation of the depths is less than the standard deviation using incorrect values of the shape factor. This method can be applied to residuals, as well as the observed magnetic data consisting of the combined effect of a residual component due to a purely local structure and a regional component represented by a polynomial of up to fourth-order. The method is applied to synthetic data, with and without random errors, and tested on a field example from Brazil. In all cases, the shape and depth of the buried structures are found in good agreement with the actual ones.