A new inversion method for NMR signal processing

We present a new, semi-analytic inversion method for nuclear magnetic resonance (NMR) log measurements. Our method represents multiwait-time measurements via short sums of exponentials. The resulting sparse T₂ distribution requires fewer T₂ relaxation times than present in linearized inversion methods. The T₁ relaxation times, and corresponding amplitudes are estimated via convex optimization and a semi-analytic algorithm. We obtain an efficient way to represent the NMR data that can be utilized to estimate petrophysical properties and for compression in logging-while-drilling applications.