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ON THE SOLUTION OF THE GRAVITY DIRECT PROBLEM FOR A SPHERE WITH A SIMULATED ANNEALING APPROACH
Abstract
The solution of the gravity direct problems performs a crucial impact on the results of investigation of the gravity anomalies in oil and gas fields. The direct problem of gravimetry itself means that we have to determine the analytical characteristics of the gravitational field from a set of specified parameters of the geological medium (such as an average depth, an excess density, coordinates of anomaly sources, and other medium parameters). Evaluation of the distribution of similar parameters of anomalous bodies is extremely important for geodynamic monitoring of deposits. Within the framework of stochastic optimization techniques, a simulated annealing approach can be used to estimate the above-mentioned parameters distribution. This paper describes the implementation of the simulated annealing technique to solve a series of gravity direct problems based on gravity monitoring data. This method allows us to select the values simultaneously according to two parameters of the medium studied. The proposed method is developed as one of the subsystems of a special GIS for storing, processing, analysing, and visualizing of gravity monitoring data over the oil and gas field. The operation of the algorithm is characterized and the simulation results are given. For calculations a sequence of homogeneous spherical bodies was chosen, and their initial calculation parameters and the criterion to derive the optimal solutions are indicated. The initial parameters were the centre of the sphere x, its radius R, and the initial distribution of the gravity field ?g, and the parameters for finding the optimal values were the values of density ? and the average depth h. The obtained results of the system showed the acceptable accuracy of the algorithm for solution of the gravity direct problem by the proposed approach. The simulated annealing algorithm made it possible to increase the reliability of the model and reduce working time for the analysis of the measured gravitational field.
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