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Stochastic simulation and inversion method based on random medium theory and gradual deformation algorithm



Stochastic inversion is an inversion method using logging data and constrained by seismic data. In order to use the known prior information more comprehensively, we propose a stochastic inversion method based on the random medium theory and the gradual deformation algorithm. Firstly, we use seismic data to estimated the autocorrelation parameters of random medium. The mean and standard deviation of the inversion parameters are obtained from the log data. Then we select a mixed ellipse autocorrelation function to simulate a prior model of statistical characteristic parameters which conforms to the inversion parameter spatial correlation. After that, the gradual deformation algorithm is applied to update the random phase information and the random simulation is carried out. A new objective function is constructed by combining autocorrelation parameters with inversion parameters. Combining with the objective function, the iteration is stopped when the convergence condition is reached. The validity of the method is verified by the actual data test.