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. Seismic tomography is used in reservoir geophysics as an important method for high-resolution imaging. The classical Born approach, which is used in single-frequency diffraction tomography under the condition of weak scattering, is limited by the requirement to know the background velocity in advance. We propose tomographic inversion approaches within matrix formalism and the Born approximation conditions. These approaches are iterative (in the sense that the background velocity field is updated at each iteration) and do not require knowledge of the true background velocity. In the first approach, a single-frequency that is kept constant is used. In the second approach, several frequencies are also kept constant and are used simultaneously. In the third approach, in addition to the background velocity, the working frequency is also updated. Finally, in the last approach, the multiple frequencies used simultaneously are updated throughout the iteration. The proposed approaches were tested on a synthetic model containing a dipping layer and a paleochannel, with cross-well acquisition geometry, and the data were contaminated with Gaussian noise. When compared to the standard, single-frequency non-iterative approach, the iterative process with the use of multiple frequencies generated results with smaller RMS errors for model parameter, velocity and data. Keywords: seismic inversion, seismic tomography, wave numerical modeling, reservoir characterization. RESUMO. A tomografia sismica e usada na geofisica de reservatorios como um metodo importante para obtencao de imagens de alta resolucao. A abordagem classica de Born, usada na tomografia de difracao de unica frequencia sob a condicao de espalhamento fraco, e limitada pela necessidade de se conhecer antecipadamente a velocidade do fundo homogeneo. Propomos abordagens iterativas de inversao tomografica dentro do formalismo matricial e sob a condicao da aproximacao de Born. Essas abordagens tem uma natureza iterativa, onde o campo de velocidade de fundo e atualizado em cada iteracao, sendo que o conhecimento da velocidade verdadeira do fundo homogeneo nao e necessario. Na primeira abordagem e usada uma unica frequencia mantida constante. Na segunda abordagem sao usadas simultaneamente varias frequencias tambem mantidas constantes. Na terceira abordagem, alem da velocidade do fundo homogeneo, a frequencia de trabalho tambem e atualizada. Finalmente, na ultima abordagem, as multiplas frequencias usadas simultaneamente sao atualizadas durante a iteracao. As abordagens propostas foram testadas em um modelo sintetico contendo uma camada inclinada e um paleocanal, com geometria de aquisicao poco a poco, sendo os dados contaminados com ruido gaussiano. Quando comparado com a abordagem padrao nao-iterativa de unica frequencia, o processo iterativo com o uso de multiplas frequencias gerou resultados com erros menores de RMS para o parâmetro de modelo, a velocidade e o vetor de dados. Palavras-chave: inversao sismica, tomografia sismica, modelagem numerica de ondas, caracterizacao de reservatorios.

NEW ITERATIVE AND MULTIFREQUENCY APPROACHES IN GEOPHYSICAL DIFFRACTION TOMOGRAPHY