Inversion of NMR echo trains using a supplementary nonlinear equality constraint

A system for estimating properties of a resource bearing formation, the system comprising:

• an input device configured to receive a measured echo train generated by a nuclear magnetic resonance (NMR) measurement device deployed in a region of interest, and a measured noise of the measured echo train;
• and
• a processing device configured to perform:
• calculating a T2 distribution subject to a nonlinear equality constraint, the nonlinear equality constraint dependent on the measured noise and a fitting error between the measured echo train and a modeled echo train, wherein calculating the T2 distribution includes estimating a solution for the T2 distribution that is closest to satisfying the nonlinear equality constraint, wherein estimating the solution includes minimizing an objective function.