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 artifact related to a magnetic field variation in the volume of interest, the processor characterized by being 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 T 2 distribution, and detecting the motion artifact in response to determining that the differential echo-train includes a short-T 2 porosity fraction that is greater than a threshold value; and inverting two echo trains into two T 2 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 T 2 distributions, estimating a shift of a porosity amount between the at least two porosity fractions of each of the two T 2 distributions, and detecting the motion artifact based on the shift. 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 artifact related to a magnetic field variation in the volume of interest, the processor characterized by being 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 T 2 distribution, and detecting the motion artifact in response to determining that the differential echo-train includes a short-T 2 porosity fraction that is greater than a threshold value; and inverting two echo trains into two T 2 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 T 2 distributions, estimating a shift of a porosity amount between the at least two porosity fractions of each of the two T 2 distributions, and detecting the motion artifact based on the shift. 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 T 2 distribution, and detecting the motion artifact in response to determining that the differential echo-train includes a short-T 2 porosity fraction that is greater than a threshold value; and inverting two echo trains into two T 2 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 T 2 distributions, estimating a shift of a porosity amount between the at least two porosity fractions of each of the two T 2 distributions, and detecting the motion artifact based on the shift. <EOS>