Direction of polarization determined from magnetic anomalies

Abstract

In traditional methods of interpretation of the results of magnetic surveys the effects due to permanent magnetization are neglected. Recent geomagnetic research on the remanent magnetization of rocks has shown this neglect to be unjustified. Moreover, techniques now being employed provide better measurements of magnetic-field variations than have ordinarily been available in the past. With most of the newer methods components of the field are measured in directions other than those generally treated in the earlier methods of interpretation. In order to take advantage of the new developments, equations for the magnetic field over a point dipole, a horizontal line of dipoles, a thin, dipping sheet, a thick, dipping sheet, and a sloping step are derived in the case where both the directions of measurement and polarization are arbitrary. It is found that these directions combine with other properties of the bodies to form parameters from which various features of the magnetic anomalies over the bodies can be determined. In terms of these combined parameters it is possible to obtain the higher derivatives of the expressions for the fields over these bodies and to develop methods of determining the unknown parameters of the bodies, including the direction of polarization, when magnetic profiles over them are given. Further, it is shown that the fields over four of the bodies treated can be obtained by successive differentiation of a single function. This fact is used in drawing charts for computing values of the fields and their derivatives at points along profiles over any of these bodies. Graphs are given, showing the position of special points such as peaks and inflection points on the profiles for any direction of polarization and measurement. Methods of calculation of the unknown parameters of the line of dipoles and the thin, dipping sheet when their anomalies are given, are outlined, followed by examples of calculation in the case of theoretically calculated sample profiles.