A least-squares minimization approach to depth determination from numerical horizontal magnetic gradients

We have developed a least-squares minimization approach to depth determination of a buried structure from numerical horizontal gradients obtained from magnetic data using filters of successive window lengths. The problem of depth determination from magnetic gradients has been transformed into the problem of finding a solution to a non-linear equation of the form f(z)=0. The method involves using simple models convolved with the same horizontal gradient filter as applied to observed magnetic data. As a result, the method can be applied not only to the magnetic effect due to a purely local structure but also to measured magnetic data. Formulas have been derived for thin dikes, horizontal cylinders, spheres, and geologic contacts. Procedures are also formulated to estimate the amplitude coefficient and the index parameter. The method is applied to synthetic data with and without random noise. Finally, the validity of the method is tested on two field examples from Canada and India. In both cases, the depth obtained is found to be in a very good agreement with the actual depth