A novel methodology to quantify the spatial resolution in 2-D seismic surface wave tomographic problems is proposed in this study. It is based on both the resolving kernels computed via full resolution matrix and the concept of Full Width at Half Maximum (FWHM) of a Gaussian function. This method allows estimating quantitatively the spatial resolution at any cell of a gridded area. It was applied in the northeastern Brazil and the estimated spatial resolution range is in agreement with all previous surface wave investigations in the South America continent.

No abstract

SUMMARY The crustal structure of the south‐eastern Brazilian continental shelf has been investigated through the dispersion curves of seismic surface waves obtained at Brazilian seismological station RDJ. A set of eight continental‐shelf models has been tried, to obtain the best shear‐wave velocity structure. The inversion results suggest a sedimentary structure divided into two layers with shear‐wave velocities of 1.36 ± 0.10 km s−1 and 1.58 ± 0.10 km s−1, respectively. This is in agreement with preliminary results found by the Brazilian Petroleum Company Petrobras using seismic data in the area (O. R. Sá & L. P. A. Gamboa, private communication, 1994). The intermediate crustal layer has a shear‐wave velocity (3.26 ± 0.10 km s−1 typical of basement. An anomalous shear‐wave velocity of 3.98 ± 0.10 km s−1 has been determined for the lower crust. This suggests the existence of a transitional layer between lower crust and upper mantle, similar to that observed in both Mediterranean and Canadian passive continental margins. It was not possible to define precisely the crust‐mantle transition, but an analysis of the inversion results has shown that the Moho boundary is at around 40 ± 5 km depth.

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...