Análise qualitativa do método de inversão completa das formas de onda no domínio do tempo

Abstract

One of the great challenges of modern science is to obtain good images of subsurfaces in an indirect way, since the direct way of observing such surface is often not feasible. We can cite some examples that use indirect processes of imaging, such as: Ultrasonography, Tomography, Seismic Imaging, among others. The similarity between these methods co- mes from the way used to obtain the image. In all the cited examples the region of interest is subjected to some kind of wave, which penetrates the middle (body) and undergoes reflections, refractions, etc. Such phenomena can be detected thanks to the reception of these waves by sensors. In this work we approach the problem of Seismic Imaging, detai- ling some of the most important steps in the technique, which is the most used by the Oil industry to image subsurface areas, in search of oil and gas reservoirs. This work deals with a general analysis of the FWI methodology in the time domain, from mathematical formulation to a computational application. In the development of this work the Finite Differences Method was used to discretize the acoustic wave equation, assuming the wave field to be exclusively acoustic. We also used the Descent Gradient Method to update the velocity model. We initially use a smooth velocity model that we assume to be close to the real model and reconstruct iteratively until a more realistic model is obtained. The Adjoint Method was used to calculate the objective function gradient. The analysis developed in this work was divided into three parts: analysis of the quality of the recons- tructed subsurface image due to a change in the number of shots; the same analysis, now considering the change in the number of iterations; and analysis of the execution time of each configuration. From this study, we can take a quantitative analysis of the parameters of the model, observing what we call the “optimal point”, the point where we find the solution m which minimizes our error function.