Global Optimization and Inital Models In Seismic Pre-Stack Inversion
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Abstract Pre stack inversion of seismic data consists of numerous difficulties. Two of the problems of greatest concern are the problems of non-uniqueness and non-linearity of the inversion. There may exist several solutions to any given inversion problem, and to be able to choose the correct solution we are dependent on a priori information. This thesis will explain how a priori information can be implemented with the seismic data using Bayesian modeling and fractal based initial methods in order to obtain the most likely solution for the inversion. This thesis will also explain the theory behind global optimization routines, such as the random walk Monte Carlo, the Metropolis algorithm and Simulated Annealing. A Simulated Annealing routine has been made, and this is used to solve optimization problems. The routine is analyzed for its capability of finding global optimums and the requirements for its success. It is then implemented to simulate the inversion of a seismic dataset. The solutions of the inverted data is then analyzed and compared to the actual solution. This is done for an uncontaminated dataset, and for a dataset containing noise. The work has shown that Simulated Annealing can be a good method for finding a global optimum, but that the global optimization routine is unable to produce good results without good constraints and a good initial model, due to the problem of non-uniqueness.