1. A method for uncertainty estimation for nonlinear inverse problems related to determining spatial distribution of a physical property of subsurface formations, comprising: obtaining an inverse model of spatial distribution of the physical property of the subsurface formations made using measurements from sensors deployed proximate the subsurface formations; obtaining a set of possible models of spatial distribution based on the measurements; obtaining a set of model parameters; reducing a number of model parameters in the set by a covariance-free compression transform; mapping upper and lower limits of a value of the physical property bounds to orthogonalspacedefining a model polytope including a geometric region of feasible models; performing at least one of random and geometric sampling of the model polytope in a reduced-dimensional space to generate an equi-feasible ensemble of models, the reduced-dimensional space consisting of a hypercube approximation; evaluating probable model samples based on misfits from among an equi-feasible model ensemble determined by forward simulation and data misfit rejection; computing final uncertainties from the equivalent model ensemble; and displaying the final uncertainties in at least one map.