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UNCERTAINTY ESTIMATION FOR LARGE-SCALE NONLINEAR INVERSE PROBLEMS USING GEOMETRIC SAMPLING AND COVARIANCE-FREE MODEL COMPRESSION
UNCERTAINTY ESTIMATION FOR LARGE-SCALE NONLINEAR INVERSE PROBLEMS USING GEOMETRIC SAMPLING AND COVARIANCE-FREE MODEL COMPRESSION
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机译:基于几何采样和无协方差模型压缩的大型非线性逆问题的不确定度估计
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摘要
A method for uncertainty estimation for nonlinear inverse problems includes obtaining an inverse model of spatial distribution of a physical property of subsurface formations. A set of possible models of spatial distribution is obtained based on the measurements. A set of model parameters is obtained. The number of model parameters is reduced by covariance free compression transform. Upper and lower limits of a value of the physical property are mapped to orthogonalspace. A model polytope including a geometric region of feasible models is defined. At least one of random and geometric sampling of the model polytope is performed in a reduced-dimensional space to generate an equi-feasible ensemble of models. The reduced-dimensional space includes an approximated hypercube. Probable model samples are evaluated based on data misfits from among an equi-feasible model ensemble determined by forward numerical simulation. Final uncertainties are determined from the equivalent model ensemble and the final uncertainties are displayed in at least one map.
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