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 a principal component decomposition of the model by transforming the model to a principal component domain, using a computer; reducing the principal component domain to an N-dimensional reduced domain by selecting N, less than all, of the principal components, based on a criterion favoring large principal components over small principal components; defining an D-dimensional perturbation space within the reduced domain, where D<N; generating one or more perturbed models by perturbing the model within the perturbation space; and applying a statistical analysis technique to some or all of the one or more 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.