Abstract: 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 orthogonal space. 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.

Abstract: Described herein is a framework for analyzing data in high-dimensional space. In accordance with one implementation, observed data and at least one input model parameter set is received. The input model parameter set serves as a solution candidate of a predefined problem (e.g., inverse or optimization problem) and is related to the observed data via a model. To provide enhanced computational efficiency, a reduced base with lower dimensionality is determined based on the input model parameter set. The reduced base is associated with a set of coefficients, which represents the coordinates of any model parameter set in the reduced base. Sampling is performed within the reduced base to generate an output model parameter set in the reduced base. The output model parameter set is compatible with the input model parameter set and fits the observed data, via the model, within a predetermined threshold.

Abstract: Described herein is a framework for analyzing data in high-dimensional space. In accordance with one implementation, observed data and at least one input model parameter set is received. The input model parameter set serves as a solution candidate of a predefined problem (e.g., inverse or optimization problem) and is related to the observed data via a model. To provide enhanced computational efficiency, a reduced base with lower dimensionality is determined based on the input model parameter set. The reduced base is associated with a set of coefficients, which represents the coordinates of any model parameter set in the reduced base. Sampling is performed within the reduced base to generate an output model parameter set in the reduced base. The output model parameter set is compatible with the input model parameter set and fits the observed data, via the model, within a predetermined threshold.

Abstract: 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.