A method comprising: obtaining geophysical data for a subsurface region; generating, with a computer, at least two subsurface property models of the subsurface region for at least two subsurface properties by performing an inversion that minimizes a misfit between the geophysical data and forward simulated data subject to one or more constraints, the inversion including generating updates to the at least two subsurface property models for at least two different scenarios that both fit the geophysical data with a same likelihood but have different values for model materiality, with the model materiality being posed as an equality constraint in the inversion, thereby the inversion being constrained by a predetermined range of values for the model materiality, wherein the model materiality is a functional of model parameters that characterize hydrocarbon potential of the subsurface region, and further wherein the model materiality weighs porosity of a hydrocarbon reservoir in the subsurface region against shale content of the hydrocarbon reservoir; analyzing a geophysical data misfit curve or geophysical data likelihood curve, wherein the geophysical data likelihood curve is the inverse of the data misfit curve, plotting model likelihood as a function of model materiality over the predetermined range of values of the model materiality to identify the at least two subsurface property models that correspond to a high-side and low-side, respectively, for each of the at least two subsurface properties, with the high-side and low-side quantifying uncertainties in the subsurface properties, and further with the high-side and low-side each determined at a respective upper or lower bound for model materiality; and prospecting for hydrocarbons in the subsurface region based on the at least two models that correspond to the high-side and the low-side for each of the at least two subsurface properties, wherein the at least two subsurface properties are the shale content (Vshale) and the porosity. obtaining geophysical data for a subsurface region; generating, with a computer, at least two subsurface property models of the subsurface region for at least two subsurface properties by performing an inversion that minimizes a misfit between the geophysical data and forward simulated data subject to one or more constraints, the inversion including generating updates to the at least two subsurface property models for at least two different scenarios that both fit the geophysical data with a same likelihood but have different values for model materiality, with the model materiality being posed as an equality constraint in the inversion, thereby the inversion being constrained by a predetermined range of values for the model materiality, wherein the model materiality is a functional of model parameters that characterize hydrocarbon potential of the subsurface region, and further wherein the model materiality weighs porosity of a hydrocarbon reservoir in the subsurface region against shale content of the hydrocarbon reservoir; analyzing a geophysical data misfit curve or geophysical data likelihood curve, wherein the geophysical data likelihood curve is the inverse of the data misfit curve, plotting model likelihood as a function of model materiality over the predetermined range of values of the model materiality to identify the at least two subsurface property models that correspond to a high-side and low-side, respectively, for each of the at least two subsurface properties, with the high-side and low-side quantifying uncertainties in the subsurface properties, and further with the high-side and low-side each determined at a respective upper or lower bound for model materiality; and prospecting for hydrocarbons in the subsurface region based on the at least two models that correspond to the high-side and the low-side for each of the at least two subsurface properties, wherein the at least two subsurface properties are the shale content (Vshale) and the porosity.