1. A computer-implemented method for quantitatively estimating uncertainty in a model of a subsurface physical property inferred by inversion of measured geophysical data, comprising: performing, with a computer, a principal component decomposition of the model by transforming the model to a principal component domain, using a computer; reducing, with a computer, the principal component domain to an N-dimensional reduced domain by selecting N, less than all, principal components, based on a criterion favoring larger principal components over smaller principal components; defining, with a computer, an D-dimensional perturbation space within the N-dimensional reduced domain, where D<N; generating, with a computer, perturbed models by perturbing the model within the perturbation space and interpolation within the perturbation space; applying, with a computer, a statistical analysis technique to the perturbed models to compute the uncertainty in said model inferred by inversion of measured geophysical data, or compute a statistically updated model and associated uncertainty; performing a computer simulation with the perturbed models, wherein the simulation includes generating simulated geophysical data from the perturbed models, comparing the simulated geophysical data to the measured geophysical data, and transforming a misfit between the simulated geophysical data and the measured geophysical data to an uncertainty in the subsurface property inferred by the inversion of the measured geophysical data; and prospecting for hydrocarbon in a subsurface region, wherein a hydrocarbon exploration decision is based on the subsurface property inferred by the inversion of the measured geophysical data and the uncertainty in the subsurface property.