Magnetic resonance signal moment determination using the Earth’s magnetic field

[Display omitted] •Under-sampled k-space data used to obtain NMR signal moments.•Method and analysis demonstrated on a fouling reverse osmosis membrane module.•Measurements demonstrated on the module as a function of radial angle.•Measurements using Earth’s field NMR in agreement with high field measurements.•Method more sensitive to module biofouling than conventional pressure drop. We demonstrate a method to manipulate magnetic resonance data such that the moments of the signal spatial distribution are readily accessible. Usually, magnetic resonance imaging relies on data acquired in so-called k-space which is subsequently Fourier transformed to render an image. Here, via analysis of the complex signal in the vicinity of the centre of k-space we are able to access the first three moments of the signal spatial distribution, ultimately in multiple directions. This is demonstrated for biofouling of a reverse osmosis (RO) membrane module, rendering unique information and an early warning of the onset of fouling. The analysis is particularly applicable for the use of mobile magnetic resonance spectrometers; here we demonstrate it using an Earth’s magnetic field system.