1. A magnetic resonance imaging (MRI) system comprising: an assembly of gantry components including static and gradient magnetic field generators and at least one radio frequency (RF) coil defining an imaging volume; an MRI control system, connected to control said gantry components, including at least one RF transmitter, at least one RF receiver and computer control circuits configured to effect specified MRI data acquisition sequences of RF and gradient magnetic pulses which acquire, from an object located within said imaging volume, RF nuclear magnetic resonance (NMR) spin responses emanating from different spatially located volumes of NMR nuclei respectively corresponding to different positions in k-space as a function of a magnetic field experienced by the nuclei; said computer control circuits being configured to effect: (A) for each of a series of slices j, a data acquisition sequence using (a) RF and slice select magnetic gradient pulses followed by (b) at least one magnetic gradient pulse, having a same magnitude if more than one and being in a same direction as said slice select magnetic gradient pulse but under a predetermined stress condition, located at least partly within an analog-to-digital converter (ADC) window providing successive temporal samples i of NMR phase responses Φ i,j , (B) determining magnetic field temporal variations at each sample point i based on the slope of the phase difference ΔΦ between plural slices j at temporal sampling time i, and (C) storing representations of the determined temporal magnetic field variations for subsequent use in MRI system operations.