Genetic Simulated Annealing Inversion Method Research Based On Bayes Theory

With the development of the oil and gas exploration, the precision requirement greatly in reservoir description, which is gradually beyond the capacity of the conventional seismic inversion method. The Bayes stochastic inversion method is adopt in this paper to solve the inversion problem through the genetic simulated annealing method. The genetic algorithm and the simulated algorithm are improved in this paper to be feasible under the theory of Bayes stochastic inversion method.Studies and analysis of the classic GA are proceeded in this paper to research and demonstrate its convergence. Each operation in GA is studied in detail to present its physical background, contribution, and influence, including encoding, selection, crossover operation and mutation. On the basis of schemata theorem and building block hypothesis, the performance of GA are analyzed and evaluated. Through the model test, the search ability of GA is analyzed.Studies and analysis of the classic SA are proceeded in this paper. Compared with the annealing process in physical system, the simulated annealing process and each parameter in it are studied and analysis for their influence and contribution. The key parameter, temperature, is thoroughly discussed and analyzed. The convergence of the algorithm is proved on statistics. The characters of the convergence process are presented in the model test.These two methods, GA and SA, have their own advantages in optimization:GA has strong global search capability that make it hard to get trapped in local minimum or maximum, S A has higher precision in the process of convergence. It will be trapped in local minimum or maximum but it can jump out commonly. The precision of SA is exhibited by the highly concentration result in the later stages of the convergence process.These two methods above are adopt into the Bayes inversion method with some improvement. When the optimization problem is mapped into the background of probability and statistics, according to the Bayes theory, the probabilistic model should be established after the analysis of the complex high dimension problems. Through the combination of the GA and SA, the optimization process begins from the probabilistic model. The GA algorithm is embedded in the SA algorithm in this paper. By this way, the outstanding global research capability of GA and the high precision of SA are effectively combined. Before the embedding operation, the GA algorithm need some modification, which is designed in this paper as a new step after the mutation operation. Here the genetic code of every individuals in the population will be partitioned into fragments and evaluated separately. According to the evaluation result, the best genetic fragment of each locus will be picked out and concatenated. Therefore, a new individual called "King" is generated. The "King" individual indicates the pinnacle of current population or an index of the evolution degree. What’s more important is the "King" individual act as the joint point between the inner loop (GA) and external loop (SA).Due to the influence of the genetic simulated annealing method, the whole process chain constructed by the MCMC algorithm is no longer a standard Markov chain, it turns into a non-time-homogeneous Markov chain concatenated by a series of time homogenous Markov chain. The two nested methods proposed two independent loops which decompose the optimization process into two simultaneous process with different search parameters including walking radius, search direction.etc.The Bayes theory set the whole implementation process of optimization into the probability and statistics background, thus the evaluation of the target parameter is no longer a determined, single value. The Bayes inversion method attempts to establish a distribution which the parameter may satisfy. The function of the implementation method, which we choose the combination of GA and S A in this paper, is to reduce the variance of the distribution (the posterior distribution). The final distribution obtained through all the steps genetic simulated annealing, Metropolis-Hastings algorithm shows the expectation and the variance of the target parameter. The expectation can be used as the final result and the variance indicates the certainty of the result.The application on actual seismic data shows that the Bayes inversion method have better results than the conventional constrained sparse pulse inversion method.