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. Many nonhyperbolic multiparametric travel-time approximations were developed in the last decades. As the seismic inversion became more popular, there were studies concerning the objective function of this kind of equations. Many of these approximations have a unimodal behavior where there is only the global minimum region while others have a multimodal statistical distribution with the global minimum region and one or more local minimum regions. However, two approximations showed both unimodal and multimodal behaviors to vary depending on the model. As the variation of the model generates only subtle distortions concerning the topology of the objective function, a method which can make this topology more abrupt is a solution to perform a more effective inversion. This kind of information can be reached using the L1-norm rather than the L2-norm, and with the comparison of the two norms for both reflection events (PP and PS) of the model and both approximations, it is possible to understand which kind of improvement it brings concerning the complexity and accuracy analysis. Keywords: objective function, nonhyperbolicity, probability distribution. RESUMO. Varias aproximacoes nao-hiperbolicas multiparametricas de tempos de trânsito foram desenvolvidas nas ultimas decadas. Com a inversao sismica se tornando cada vez mais popular, houve estudos relacionados a funcao objetivo desse tipo de equacao. Muitas dessas aproximacoes apresentam um comportamento unimodal, onde ha apenas uma regiao de minimo global, enquanto outras apresentam uma distribuicao estatistica multimodal, com a regiao de minimo global e uma ou mais regioes de minimos locais. Entretanto, duas aproximacoes mostraram ambos os comportamentos, unimodal e multimodal, variando a depender do modelo. Como a variacao do modelo gera apenas distorcoes sutis com relacao a topologia da funcao objetivo, um metodo no qual e capaz de tornar a topologia mais abrupta e uma forma de realizar a inversao de maneira mais efetiva. Este tipo de informacao pode ser obtido usando a norma L1 ao inves da norma L2, e com a comparacao das duas normas para ambos os eventos de reflexao (PP e PS) do modelo e para ambas as aproximacoes, e possivel entender qual tipo de melhoria e alcancada com relacao a analise de complexidade e de precisao. Palavras-chave: funcao objetivo, nao-hiperbolicidade, distribuicao probabilistica.

brazilian journal of geophysics

COMPARISON OF L2- AND L1-NORM TO PERFORM THE INVERSION OF TRAVEL-TIME CURVES USING NONHYPERBOLIC MULTIPARAMETRIC APPROXIMATIONS WITH UNIMODAL AND MULTIMODAL BEHAVIOR