Chaos Annealing Algorithm And Its Application In Seismic Inversion

Bayesian inference is a valid approach used in geophysical problems. Bayesian inference is a very convenient mathematical tool to update our current knowledge when new algorithms become available. If Bayesian inference used to describe the problem, the posterior probability density function of earth model describes the solution of a geophysical inverse problem. Monte Carlo method is used to sample geophysical model according to Bayesian inference. Monte Carlo method can generate a large collection of models according to the posterior probability distribution and analyses and display the models with relative likelihood of model properties.To derive correct medium velocity from pre-stack seismic data is very significant to complicated structure imaging. The complexity solution of the above problem needs a good optimization method. A new successive overall optimization calculation method-chaotic annealing will be used in the solution and non-linear velocity inversion calculation. The method only uses objective function value, without solving for the derivative directions. The method is different from random methods (such as analog annealing, genetic algorithm), and it applies a dynamic equation to control optimizing computation process. The dynamic equation make the solution fast approximate the minimum point. At the same time it can make the solution escape local extreme value and cause the overall optimization capacity when the solution approximates the minimum point. For a given energy or cost function, a chaotic evolution system in which chaos provides a scheme for searching the minima of the energy function in the state space can be constructed easily. By controlling a bifurcation parameter from the chaotic dynamics regime to the fixed-point regime gradually the system may eventually reach the global optimum state or its good approximation with very high probability.