Simultaneous computation of gravity and magnetic anomalies resulting from a 2-D object

This paper presents a new algorithm for the simultaneous computation of gravity and magnetic anomalies resulting from an infinitely long (2-D) body with an arbitrary polygonal cross-section. With the assumption of uniform volume density and magnetization, the gravity or magnetic field may be expressed as the field resulting from an equivalent distribution of surface mass density or surface pole density, respectively, over the surface of the source body. The resulting surface integrals are reduced to new line integrals using Stokes' theorem. The components of the fields for each bounding surface are expressed in terms of a now line integral and the solid angle subtended by the surface at the point of observation. Since these analytical solutions are similar in form, a direct relation is derived between gravity and magnetic fields, which allows their simultaneous computation. Hence, the same computer program can be used to compute the gravity field, the magnetic field, or both fields simultaneously. This new approach will find wide applications in the joint inversion of potential field data, as it will make the numerical computations much faster.