If anomalies of gravity or of the terrestrial magnetic field are to be interpreted, methods are required which enable us to evaluate the gravitational or the magnetic field of bodies of any given shape quickly. Since limited accuracy is sufficient, graphical methods are suitable. This paper deals with such a graphical method. It consists in carrying out the required triple integrations in two steps, the first step being a simple, the second a double integration. By aid of graphs the integrations are reduced to simple counting operations.
Pour interpréter des anomalies de la gravité ou du champ magnétique terrestre, il faut des méthodes permettant d'évaluer rapidement le champ de gravité ou magnétique de corps de n'importe quelle forme. Etant donné qu'une précision limitée suffit, les méthodes graphiques conviennent.
La présente contribution traite d'une telle mé- thode graphique. Elle consiste à pratiquer les intégrations triples requises en deux étages, le premier étage étant constitué par une intégration simple, le deuxième par une intégration double.
A l'aide de graphiques, les intégrations sont ré- duites à de simples opérations de comptage. $ 1. Let G be a body of constant density p. The gravity anomaly K, at a point A of space, due to G, is given by the well-known formula G * Swiss Federal Institute of Technology, Head of Department of Geophysics. cm3, = constant of gravity k, = 6.67, < - - gr sed (q! 10-8) x, y, z = rectangular coordinates of A (z - axis pointing vertically downward) $, y, t = coordinates of a point Q of G r = Q A = + ~ X-E)? + (Y-s)~ + (z-<)~ I/($ 2. Let G' be a model of G of linear scale 1: L. (Fig. 1) At the model-space, we introduce spherical coordinates p, 4, $ with the centre A' (A' being the point of the model-space, corresponding to A) by the equations t-x = Lp sin 4 cos Q v-y = Lp sin 3 sin $. .. (2) sy-z=Lpcos3. p, 4 and $ determine the position of the model Q' of Q. (Fig. 2) Denoting the equation r=Lp. .. .. (3) and introducing the spherical coordinates at (i), we get K, = k, p Ljjscos 4 sin 4 dp d 3 d Q. (4) G' $ 3. We first integrate in (4) with respect to c$: dQ = @ (p, 8). ... (5) The geometrical significance of 8 is the following: The vertical line Z through A' is the axis 5 = o of the system of spherical coordinates (Fig. 2). All s 614 PROCEEDINGS THIRD WORLD PETROLEUM CONGRESS-SECTION I i I l ! l Fig. 1 615 F. GASSMANN-GRAPHICAL EVALUAT1ON OF THE ANOMALIES A' z+ Fig. 2 points with a definite value of 8 and of 1, on a horizontal circle with the centre on Z. The length of arc, covered by all points of the circle, belonging to G', is (p, 9) times the radius of the circle. In order to evaluate (P graphical
