This paper presents a new approach for determining the depth of a buried structure from numerical second-, third-, and fourth-horizontal-derivative anomalies obtained from 2-D magnetic data using filters of successive graticule spacings. The problem of depth determination has been transformed into the problem of finding a solution to a nonlinear equation of the form z = f(z). Formulas have been derived for a horizontal cylinder and a dike. The depths obtained from the second-, third-, and fourth-derivative anomaly values can be used to determine simultaneously the actual depth to the buried structure and the optimum order of the regional magnetic field along the profile. This powerful technique can solve two major potential field problems: regional residual separation and depth determination. The method is applied to theoretical data with and without random errors and is tested on a field example from Arizona.