Effective algorithm for determination of the intersection points of geophysical line networks

Abstract

An algorithm is presented for the determination of the intersection points of arbitrary lines, going in two perpendicular directions. The solution does not depend on any hypothesis about the type of the line and is directly obtained from the coordinates of the points which surround the intersection point, irrespective of whether the coordinates are determined by means of some kind of positioning system or by computerization. The lines most frequently used in the surveys can be enclosed by a rectangle whose sides are defined by the minimum and the maximum coordinates of the observation points. The intersection point belongs to the overlap of the two rectangles which enclose respectively the traverse and the base line. Thus the problem is reduced to the following two sub-problems. The first subproblem consists of the creation of a sequence of contractive overlaps such that the last has minimum dimensions. The second sub-problem consists of determination of the coordinates of the intersection point. It is shown that for data obtained from an aerogeophysical survey 2 to 3 iterations are necessary for the determination of one intersection point. The algorithm can be used to determine the sections of random quasilinear objects, for example, between boreholes and a given horizon, whose data are stored on a data base.