Systems and methods for calibrating a nuclear magnetic resonance tool

A system, comprising:

• a nuclear magnetic resonance (NMR) tool comprising an electromagnetic transmitter and an electromagnetic receiver configured to measure NMR responses;
• and
• a computing device coupled to the NMR tool, the computing device comprising one or more processors and one or more memories coupled to the one or more processors, wherein the one or more memories store instructions that, when executed by the one or more processors, cause the computing device to be configured to:
• receive N echo trains from a nuclear magnetic resonance (NMR) tool;
• perform a linear fit of the echo trains to determine an initial value of a parameter of an exponential decay curve based on the echo trains;
• generate a plurality of test sets, wherein each test set identifies a subset of the echo trains as test samples and identifies at least one of the echo trains as a control sample, wherein each test set comprises at most N−1 echo trains, and wherein the subset of echo trains in each test set is independent of subsets of echo trains in other test sets;
• perform, for each test set, a non-linear fit of the test samples of the test set based on the initial value of the parameter to determine a test value for the parameter for the test set;
• determine an error value for each test set based on a difference between a) an exponential decay curve based on the test value of the test set and b) values of the control sample(s) of the test set;
• select one of the test sets having an error value that is less than a predetermined error threshold;
• and
• calibrate the NMR tool based on the test value of the selected test set.

A non-transitory computer-readable medium storing instructions that, when executed by a processor, cause the processor to be configured to:

• receive N echo trains from a nuclear magnetic resonance (NMR) tool;
• perform a linear fit of the echo trains to determine an initial value of a parameter of an exponential decay curve based on the echo trains;
• generate a plurality of test sets, wherein each test set identifies a subset of the echo trains as test samples and identifies at least one of the echo trains as a control sample, wherein each test set comprises at most N−1 echo trains, and wherein the subset of echo trains in each test set is independent of subsets of echo trains in other test sets;
• perform, for each test set, a non-linear fit of the test samples of the test set based on the initial value of the parameter to determine a test value for the parameter for the test set;
• determine an error value for each test set based on a difference between a) an exponential decay curve based on the test value of the test set and b) the control sample(s) of the test set;
• select one of the test sets having an error value that is less than a predetermined error threshold;
• and
• calibrate the NMR tool based on the test value of the selected test set.