Nuclear magnetic resonance measurement of a medium are made using a tool with a static magnetic field having a gradient. The nuclear spins of the medium are magnetically polarized using the static magnetic field. Data are acquired from at least three sensitive volumes of the medium using an interleaved sequence of pulses at three different non-overlapping frequencies. At each frequency, a number of sub-sequences of a saturation pulse, a recovery pulse and at least one refocusing pulse are used. The saturation times between the saturation pulse and the recovery pulse for the sub-sequences are selected from a distribution of values between a minimum time to a maximum time to enable determination of T1 and T2 spectra over a wide range of values. Repetitions of sub-sequences having the same saturation at one or more frequencies may be carried out with phase alternation of the recovery pulse phases.