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. The velocity analysis is an important step for the seismic processing. With the increase in the difficulty of work with specific conditions and complex geological structures, more complex travel-time approximations are developed to perform a better structural characterization. As the complexity increases, more approximations were developed aiming to characterize different factor responsible for the nonhyperbolicity, and using sometimes an additional parameter. Many nonhyperbolic multiparametric travel-time approximations were developed and their complexities vary strongly from one to other. In previous works, it was observed that some approximations present a unimodal behavior while other approximations showed a multimodal behavior. However, a specific kind of approximation showed both statistical distributions, the unimodal and the multimodal in distinct situations. To find out the factor responsible for this variation in the probabilistic distribution behavior of this kind of approximation, it was necessary to test different theoretical models to understand which variation in the structure interferes in the topography of the objective function. Keywords: Objective function, nonhyperbolic, probability distribution. RESUMO. A analise de velocidades e uma etapa importante para o processamento sismico. Com o aumento da dificuldade em se trabalhar com condicoes especificas e estruturas geologicas complexas, sao desenvolvidas aproximacoes de tempos de trânsito mais complexas para realizar uma melhor caracterizacao estrutural. Conforme a complexidade aumenta, mais aproximacoes sao desenvolvidas com o objetivo de caracterizar diferentes fatores responsaveis pela nao-hiperbolicidade, e usando parâmetros adicionais em alguns casos. Muitas aproximacoes nao-hiperbolicas multiparametricas de tempos de trânsito foram desenvolvidas e suas complexidades variam fortemente de uma para a outra. Em trabalhos anteriores foi observado quealgumas aproximacoes apresentam um comportamento unimodal enquanto outras aproximacoes mostraram um comportamento multimodal. Entretanto, um tipo especifico de aproximacoes mostrou ambas as distribuicoes estatisticas, a unimodal e a multimodal, em diferentes situacoes. Para encontrar o fator responsavel por esta variacao no comportamento da distribuicao probabilistica desse tipo de aproximacao, foi necessario testar diferentes modelos teoricos para entender qual variacao na estrutura interfere na topografia da funcao objetivo. Palavras-chave: Funcao objetivo, nao-hiperbolica, distribuicao probabilistica.

brazilian journal of geophysics

RELATION BETWEEN THE MODEL AND THE TOPOGRAPHY OF THE OBJECTIVE FUNCTION IN A VELOCITY ANALYSIS USING A NONHYPERBOLIC MULTICOMPONENT TRAVEL-TIME APPROXIMATION