The magnetic anomaly of a two-dimensional body of uniform magnetization and arbitrary shape can be expressed compactly in terms of the vertical and horizontal derivatives of the corresponding gravity anomaly and an angle p which incorporates both the direction of magnetization and the direction in which the observed magnetic anomaly component is measured. The formula is useful for computing families of curves. By an extended use of the formulation, computation of the conjugate harmonic function to the observed magnetic anomaly makes it possible to compute the anomaly for different values of p without knowledge of the shape of the body. The simplicity of the formulation cannot be extended to bodies of three-dimensional shape but computational short cuts are nevertheless available.
The basic formulaIspir & KolCak (1969) have described a useful short cut in computing families of magnetic anomaly curves for two-dimensional bodies. A compact formula of similar type which relates the magnetic anomaly to the derivatives of the gravity anomaly is given here.The formula presented is most obviously useful for calculating families of magnetic anomaly curves over two-dimensional bodies with minimum computational effort, by computer or otherwise. It is a somewhat more general and more simple formulation than that given by Ispir and Kokak. It gives a much simplified approach to the evaluation of analytical expressions for magnetic anomalies caused by geometrical two-dimensional bodies, based only on differentiation of the corresponding gravity anomaly formulae. It also provides a useful starting point in the development of direct methods of magnetic interpretation, and is particularly well suited to the application of complex variable to interpretation theory.Let us consider a magnetic anomaly component produced by a two-dimensional body of uniform magnetization and arbitrary cross-section (Fig. I). The horizontal x-axis is chosen to be perpendicular to the strike of the body and lies entirely above the body. The y-axis points vertically downwards and the z-axis is parallel to the strike. Let the magnetization be J(J,, J,, JJ, its dip I,, its azimuth o r , measured from the x-axis in either sense, and the unit vector in the direction of the component of magnetization in the xy-plane m(cos p, sin p). Let the magnetic anomaly A(x, y ) be measured in the direction F(F,, F,,, FZ). 251
