1. A computer-implemented method for modeling a subsurface anomalous density zone comprising: i. forming a density model; ii. computing a response to said density model; iii. inverting said response to arrive at a geometric model of the anomalous density zone; iv. applying a sharpening function to boundary regions of said geometric model to distinguish between the anomalous density zone and a surrounding region; and wherein said step of inverting comprises the sub-steps of (a) creating a measure of data misfit; (b) creating a measure of a desired model characteristic; and, (c) minimizing the model measure subject to the fitting of the data to the desired level; wherein said step of inverting is carried out using the set of formulae: Given d obs = g ⁡ ( m ) + ɛ solve min m ⁢ ( m - m 0 ) T ⁢ C 0 - 1 ⁡ ( m - m 0 ) such ⁢ ⁢ that χ 2 = ( d obs - g ⁡ ( m ) δ ⁢ ⁢ d 0 ) 2 = χ 0 2 where d obs is the observed gravity response, ε is the unknown error inherent in an observed response, m is a density model being recovered, m 0 is a target model, g( ) is a mathematical embodiment of the geophysical gravity measurement, T is a transpose operator, χ 2 is a direct measure of the data misfit, χ 0 2 is the misfit of target model, C 0 is a target model covariance, and δd 0 is an estimate of the true error.