Higher derivatives analysis of 2-D magnetic data

This paper presents a new approach for determining the depth of a buried st ructure from numerical second-, third-, and fourth-horizontal-derivative an omalies obtained from 2-D magnetic data using filters of successive graticu le spacings. The problem of depth determination has been transformed into t he 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 de pths obtained from the second-, third-, and fourth-derivative anomaly value s can be used to determine simultaneously the actual depth to the buried st ructure and the optimum order of the regional magnetic field along the prof ile. 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 fiel d example from Arizona.