| Abstract: | A method to determine the position and magnetization vector of buried objects producing a magnetic anomaly is described. The data used were collected in boreholes. Since the anomaly is due to a number of objects, a ‘stripping’ procedure is employed for finding them, and therefore the process of inversion for finding all objects causing the anomaly consists of a few inversion steps. In each inversion step, two dipoles are considered as a model which approximates an object. The position and magnetic moments of the dipoles are the unknown parameters. The initial parameters are optimized by minimization of an objective function. The optimization procedure consists of a combination of linear and non-linear inversion. The solution of the linear inversion is obtained by singular value decomposition and that of the non-linear inversion by a six-dimensional simplex method (polytope algorithm). After finding one object, its effect is subtracted (‘stripped’) from the data and a new inversion step is started with new initial models and with a reduced data set. The inversion steps for finding different objects are continued until the absolute norm of the data becomes less than some adjustable value. The data will also be inverted assuming a three-dipole model in order to find the effect of using a more complex model in the inversion. The efficiency of the method is demonstrated using synthetic and real borehole data. |
