On the use of the gauss seidel method on linear parameter interpretation in magnetometry and gravimetry

Abstract

Listen

Translate article

Approximate magnetization and density distributions are found by dividing the ground into bodies with homogeneous properties. The resulting linear equation system for the material constants of the bodies are efficiently solved by the iterative Gauss—Seidel method, which has theoretically simple convergence criteria and small requirements on computer capacity. An efficient use of the method requires, that: 1. (1) The number of measurements equals the number of bodies. 2. (2) The bodies are placed so that the maximum influence of the body appears at corresponding field point. 3. (3) Bodies of similar size and with “narrow” anomalies should be preferred. 4. (4) The iteration converges from arbitrary starting values, if the horizontal distance between bodies of similar form exceeds a minimum value. This minimum value is approximately 1.5 times the depth for infinitely deep magnetic plates. The value depends on depth extent and it increases strongly when direction of magnetization differs more from the direction of the plate. Minimum distances between thin plates or cylinders are smaller than for thick plates, minimum distances for corresponding bodies in gravimetric interpretation are more than twice the minimum distances of magnetic bodies. 5. (5) Using starting values clearly less than the correct values gives convergent solutions for horizontal body distances a half to one quarter of the theoretical minimum values.