Motion detection and correction of magnetic resonance data

A nuclear magnetic resonance (NMR) apparatus for estimating properties of an earth formation, the apparatus comprising:

• a carrier configured to be deployed in a borehole in the earth formation;
• a nuclear magnetic resonance (NMR) measurement device including a transmitting assembly configured to emit one or more dual wait time pulse sequences, and a receiving assembly configured to detect a long-wait-time echo train and a short-wait-time echo train based on the one or more dual-wait-time pulses sequences;
• and
• a processor configured to analyze the long-wait-time echo train and the short-wait-time echo train to detect a potential motion artefact related to a magnetic field variation in the volume of interest, the processor configured to perform at least one of:
• estimating a difference between the long-wait-time echo train and the short-wait-time echo train to generate a differential echo-train, inverting the differential echo-train into a differential T2 distribution, and detecting the motion artefact in response to determining that the differential echo-train includes a short-T2 porosity fraction that is greater than a threshold value;
• and
• inverting two echo trains into two T2 distributions, the two echo trains selected from the long-wait-time echo train, the short-wait-time echo train and the differential echo train, calculating at least two porosity fractions for each of the two T2 distributions, estimating a shift of a porosity amount between the at least two porosity fractions, and detecting the motion artefact based on the shift.