Inversão da forma de onda completa baseada em mecânicas estatísticas generalizadas

• Ano de defesa: 2021
• Autor(a) principal: Silva, Sérgio Luiz Eduardo Ferreira da
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal do Rio Grande do Norte; Brasil; UFRN; PROGRAMA DE PÓS-GRADUAÇÃO EM FÍSICA
• Palavras-chave em Português: Problemas inversos; FWI; Estatística de Tsallis; Estatística de Kaniadakis; q-Gaussiana; -Gaussiana; Máxima entropia; Entropias generalizadas
• Link de acesso: https://repositorio.ufrn.br/handle/123456789/32249

The subsurface imaging is a central procedure in seismic exploration and, consequently, a topic of great economic interest. In general, the seismic data inversion process is employed to estimate the physical parameters of the subsurface. In geophysical applications, seismic inversion is usually formulated as an optimization problem that aims to minimize the difference between the modeled data and the observed data through the Gauss’ law of error, which is closely linked to the Boltzmann-Gibbs statistical mechanics. In this approach, errors are assumed to be distributed according to a Gaussian distribution. However, in practice, especially in non-linear problems, errors are seldom Gaussian and, therefore, this approach may fail to reconstruct physical models, especially when there are outliers in the data set. Thus, the error laws determined by non-Gaussian statistics are essential for a robust seismic inversion. In this way, we present in this work new methodologies for the execution of seismic inversions based on non-Gaussian statistics. In particular, the generalized statistics in the sense of Tsallis and Kaniadakis are considered to solve a challenging problem of seismic inversion, called, Full-Waveform Inversion. In this work, we present the foundation and formalism of the FWI based on generalized statistical mechanics, as well as the results of several numerical tests carried out on two different subsurface models: (i) we consider a very dense seismic acquisition geometry in a Marmousi case study; and then, (ii) we employ an OBN acquisition in a case study with a representative model of the Brazilian pre-salt field. At the end, we compare the conventional FWI with the FWI based on Tsallis and Kaniadakis statistics. The results suggest that the FWI based on generalized statistical mechanics is a powerful methodology, especially in noisy environments. In addition to the proposed methodology to provide better reconstruction of the subsurface models, no computational cost is added compared to the conventional approach.