Aplicação de eficientes técnicas computacionais a problemas de tomografia sísmica com ondas superficiais

Abstract

ABSTRACT. In order to save computational resources, a non-iterative algorithm based on both Horowitz-Sahni scheme (to manage sparse matrix) and the Ohio State University (OSU) algorithm (to compute matrix inversion) is proposed. The algorithm deals with least-squares solution characteristics, by structuring data for speeding up access. It is applied to the unsymmetric rectangular system matrix, which compaction improves both time and memory requirements up to 98% for only the matrix.Afterwards, symmetrical matrices are compressed and the OSU algorithm is modified in order to save additional demand in about 50%. In all cases, removal of redundant elements yields a significative reduction in access, and consequently, in the overall time and memory requirements. The algorithm was tested in a 2,000 Rayleigh wave paths dataset for various grid cell sizes, and the results were compared with both full storage and Singular Value Decomposition (SVD) techniques. Those tests showed that the economy varies from 65% to 98%. It was also applied in two real cases in Southeastern and Northeastern Brazil, using a standalone Personal Computer (PC), which demand was reduced by a factor of sixteen, with no loss of accuracy. Although the algorithm is intended to a specific problem in Seismology (surface wave tomography), it also allows to whichever is the sparse system solution, including the rigorous computation of resolution and covariance matrices.Keywords: Group-velocity tomography, Damped least-squares, Sparse system, Full resolution and covariance matrices, Speeding up processing. RESUMO.Com o objetivo de economizar recurso computacional,é proposto um algoritmo não-iterativo baseado nos esquemas de Horowitz-Sahni, para gerenciamento de matriz esparsa, e da Ohio State University, para inversão matricial. O algoritmo explora as características da solução por MMQ, estruturando os dados de forma a gerenciá-los eficientemente. Primeiramente, o esquemaé aplicadoà matriz dos coeficientes (retangular, não simétrica), cuja compactação pode reduzir a demanda em até 98%, na matriz. Posteriormente, matrizes simétricas são também comprimidas, e o algoritmo OSUé modificado, contribuindo para otimizar recursos em adicionais 50%. Em todos os casos, a remoção de elementos redundantes implica na redução nos tempos de acesso e memória exigida. A rotina foi submetida a testes de desempenho envolvendo 2.000 trajetórias de ondas Rayleigh, para várias dimensões de células da grade, cujos resultados foram comparados com as técnicas, tradicional e SVD, e comprovaram uma economia de recursos que varia entre 65% e 98%. O esquema foi, também, utilizado em dois casos reais, no Sudeste e Nordeste do Brasil, empregando-se, exclusivamente, um computador do tipo PC, cuja demanda foi reduzida em dezesseis vezes, sem perda de exatidão nos cálculos. Embora o algoritmo seja aplicado, neste contexto, a um problema específico naárea de Sismologia (tomografia com ondas superficiais), ele pode ser usado em quaisquer ocorrências de sistema esparso, sobretudo quandoé e...

A Method to Estimate Spatial Resolution in 2-D Seismic Surface Wave Tomographic Problems

“…In general, those studies use a different approach, called checkerboard tests, which are based on the inversion of synthetic data constructed as from subjective assumptions about input and output models [9] According to [9], in such analysis the quality criterion is the similarity between both final and initial models used to calculate the synthetics. In this study, we calculated the exact resolution matrix (Equation (4)), by using some efficient computational techniques into a Personal Computer [10]. It is fundamental to observe that the computation of the resolution matrix through Equation (4) is based only on the surface wave paths distributions of the target area.…”

“…The Multiple-Filter Technique [20] was applied in the digital seismograms selected for this study. Twenty two periods, ranging from 10 to 102 s (i.e., 10 , were selected to compose the source-station dispersion curves. This computation produced 3134 source-station Rayleigh wave group velocity dispersion curves and all details about the surface wave data processing can be found in [16].…”