A Least-squares Minimization Approach to Depth Determination from Magnetic Data

We have developed a least-squares minimization approach to depth determination from magnetic data. By defining the anomaly value T ð0Þ at the origin and the anomaly value T ðNÞ at any other distance ðNÞ on the profile, the problem of depth determination from magnetic data has been transformed into finding a solution to a nonlinear equation of the form f ðzÞ ¼ 0. Formulas have been derived for a sphere, horizontal cylinder, dike, and for a geologic contact. Procedures are also formulated to estimate the effective magnetization intensity and the effective magnetization inclination. A scheme for analyzing the magnetic data has been formulated for determining the model parameters of the causative sources. The method is applied to synthetic data with and without random errors. Finally, the method is applied to two field examples from Canada and Arizona. In all cases examined, the estimated depths are found to be in good agreement with actual value