Echo signals are acquired from operation of a nuclear magnetic resonance logging (NMR) tool in a borehole. The acquired echo signals are processed with respect to an inversion of each matrix in a plurality of matrices, wherein each matrix in the plurality of matrices accounts for motion of the NMR tool at a respective rate of penetration (ROP) of the NMR tool in the borehole, to produce respective spectrum coefficients for each ROP. Each spectrum is processed with respect to the respective matrices in the plurality of matrices to produce a test echo signal for each ROP. The acquired echo signals and the test echo signal for each ROP are processed to produce an error for each ROP. The ROP for the minimum of the errors is identified as the ROP of the NMR tool.