Inversão sísmica das formas de onda baseada em otimização híbrida

Abstract

The Oil today is a vital resource for society. Besides being a great player in the energy sector, it is also a raw material for many products that are essential in our daily lives. However, the increase of its production is a consequence of the technological advance we have had over the last decades. This advance in data storage and processing has greatly favored an important step in reservoir characterization: subsurface imaging. The purpose of this work is to use Full Waveform Inversion with a hybrid inversion methodology that extracts advantages from two optimization classes, Derivative Free Optimization and Gradient Based Optimization, to obtain an estimate of the model. In practice we use an adaptation of Particle Swarm Optimization, where we add two new terms, the first one is a gradient that it serves as a guide and the second a bond term, which guarantees smoothness in the inversion. The gradient leads us to a derivative-based inversion, while the Particle Swarm Optimization leads us to a naturalistic approach, so we have a hybrid strategy. In the modeling step we use an acoustic approach doing a fourth order finite difference discretization in space and second in time, the gradient term was computed with the adjoint method to approximate the objective function gradient using the image condition and the adjoint field. Another feature of the method proposed in this work is that we use a Progressive Matching inversion strategy in order to reduce the processing and storage cost, so it is necessary to evaluate only the inversion spatial window parameters at each step only, instead of involving all parameters of the model. To evaluate the accuracy of the method we compared our hybrid inversion with a derivative based inversion, using a Quasi-Newton low memory (LBFGS-B). This comparison was made by analyzing the model reconstructed in both methodologies and also through of the correlation between them and the real model. In all numerical experiments we use a re-sampled cut of the Marmousi model. In the traditional inversion we use a initial model gradient type. In the hybrid method, an initial model is not necessary, but we have a constant speed model. The results obtained by the proposed method in this work brought a better estimate of the model, but there is a disadvantage in the working time compared to traditional inversion.