A minimization approach to depth and shape determination of mineralized zones from potential field data using the Nelder-Mead simplex algorithm

Abstract We have developed a generalized minimization approach to depth and shape determination from potential field data (gravity, self-potential, or magnetic) due to sources of simple geometry (e.g., spheres, cylinders, dikes, contacts) that resemble mineralized bodies. The Nelder-Mead simplex algorithm is applied to solve a nonlinear equation in depth for each fixed shape factor using the anomaly values at few points on anomaly profile. The algorithm is achieved through two steps. First, it computes the standard deviation of the depths determined using different characteristic distances for each value of the shape factor. Second, it chooses the optimum shape and depth with minimum standard deviation. Procedures are also formulated to determine the other model parameters. The technique is applied to noisy synthetic data as well as three real cases of different mineralization from Sweden, Germany, and Canada.