2014-09-182014-09-181992-09-15MENDONÇA, Carlos Alberto. Interpolação de dados de campo potencial através da camada equivalente. 1992. 177 f. Tese (Doutorado) - Universidade Federal do Pará, Centro de Geociências, Belém, 1992. Curso de Pós-Graduação em Geofísica.https://repositorio.ufpa.br/handle/2011/5750The equivalent layer technique is an useful tool to incorporate (in the process of interpolation of potential field data) the constraint that the anomaly is a harmonic function. However, this technique can be applied only in surveys with small number of data points because it demands the solution of a least-squares problem involving a linear system whose order is the number of data. In order to make feasible the application of the equivalent layer technique to surveys with large data sets we developed the concept of equivalent data and the EGTG method. Basically, the equivalent data principle consists in selecting a subset of the data such that the least-squares fitting obtained using only this selected subset will also fit all the remaining data within a threshold value. The selected data will be called equivalent data and the remaining data, redundant data. This is equivalent to splitting the original linear systems in two sub-systems. The first one related with the equivalent data and, the second one, with the redundant data in such way that, the least-squares solution obtained by the first one, will reproduce all the redundant data. This procedure enables fitting all the measured data using only the equivalent data (and not the entire data set) reducing, in this way, the amount of operations and the demand of computer memory. The EGTG method optimizes the evaluation of dot products in solving least-squares problems. First, the dot product is identified as being a discrete integration of a known analytic integral. Then, the evaluation of the discrete integral is approximated by the evaluation of the analytic integral. This method should be applied when the evaluation of analytic integral needs less computational efforts than the discrete integration. To determine the equivalent data we developed two algorithms namely DOE and DOEg. The first one identifies the equivalent data of the whole linear systems while the second algorithm identifies the equivalent data in sub-systems of the entire linear systems. Each DOEg's iteration consists of one application of the DOE algorithm in a given subsystem. The algorithm DOE yields an interpolating surface that fits all data points allowing a global interpolation. On the other hand, the algorithm DOEg optimizes the local interpolation because it employs only the equivalent data while the other current algorithms for local interpolation employ all data. The interpolation methods using the equivalent layer technique was comparatively tested with the minimum curvature method by using synthetic data produced by prismatic source model. The interpolated values were compared with the true values evaluated from the source model. In all tests, the equivalent layer method had a better performance than the minimum curvature method. Particularly, in the case of bad sampled anomaly, the minimum curvature method does not recover the anomalies at the points where the anomaly presents high curvature. For data acquired at different levels, the minimum curvature method presented the worse performance while the equivalent layer produced very good results. By applying the DOE algorithm, it was possible to fit, using an equivalent layer model, 3137 gravity free-air data and 4941 total field anomaly data from the marine Equant-2 Project and the aeromagnetic Carauari-Norte Project, respectively. The DOEg algorithm was also applied in the same data sets optimizing the local interpolation. It is important to stress that none of these applications would have been possible without the concept of equivalent data. The ratio between CPU times (executing the programs with the same memory allocation) required by the minimum curvature method and the equivalent layer method in global interpolation was 1:31. This ratio was 1:1 in local interpolation.porAcesso AbertoInterpolaçãoAlgoritmosTeseCNPQ::CIENCIAS EXATAS E DA TERRA::GEOCIENCIAS::GEOFISICA::GRAVIMETRIA