A method for processing nuclear magnetic resonance (NMR) measurement data includes receiving, with a processor, NMR measurement data obtained from an NMR tool, the NMR measurement data having an echo train affected by a motion artifact, wherein the motion artifact is related to a magnetic field magnitude that varies in a volume of interest due to a motion of the NMR tool. The method further includes reducing, with the processor, an effect on the NMR measurement data of the motion artifact by using a correcting inversion method that models the motion artifact to provide a corrected transverse relaxation time constant (T2) distribution, the correcting inversion method having a multiplicative term having a term that includes at least one local maximum and an optional decay term.