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INTERPRETATION OF GRAVITY ANOMALIES BY NON‐LINEAR OPTIMISATION *
Author(s) -
ALCHALABI MAHBOUB
Publication year - 1972
Publication title -
geophysical prospecting
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.735
H-Index - 79
eISSN - 1365-2478
pISSN - 0016-8025
DOI - 10.1111/j.1365-2478.1972.tb00616.x
Subject(s) - gravity anomaly , interpretation (philosophy) , anomaly (physics) , linear programming , density contrast , function (biology) , regional geology , mathematics , environmental geology , mathematical optimization , hyperspace , geology , computer science , algorithm , telmatology , hydrogeology , physics , artificial intelligence , paleontology , geotechnical engineering , condensed matter physics , astronomy , evolutionary biology , oil field , biology , programming language
A bstract The interpretation of a gravity anomaly in terms of the shape of the anomalous body is a non‐linear problem and may, therefore, be carried out using non‐linear optimisation techniques. The formulation is extended to include cases where the density contrast and the regional background are also unknown. For a given model the objective function is provided by the discrepancy between the observed anomaly and the calculated anomaly due to the model. Given an initial model, the optimisation procedure searches for a minimum of the objective function by an iterative adjustment of the parameters. A number of suitable objective functions is given. The behaviour of these functions in the parameter hyperspace is quite complex. Accordingly, direct search methods should be employed at the early stages of the search, changing to gradient methods at later stages. The use of constraints is also necessary to ensure the geological feasibility of the model. The required computer time may be largely reduced by careful programming. Two examples of interpretation by optimisation methods are given.