Numerical study of the variations of magnetic resonance signals caused by surface slope

When performing forward modelling and inversion of Magnetic Resonance Sounding (MRS) data, the water-content distribution is typically assumed to be horizontal (1D case). This assumption is fully justified because MRS is often used for characterizing continuous aquifers in a nearly flat environment. However, MRS can also be used in areas with sharp topographical variations. Following a review of the standard MRS equations when using a coincident transmitter/receiver loop, the mathematical terms potentially affected by tilting of the loop are discussed. We present the results of a numerical modelling exercise, studying a case where the surface is not horizontal and the loop cannot be considered to be parallel to the top of the aquifer. This shows that maximum variations in the MRS-signal amplitude are caused mainly by north- or south-dipping slopes. Slope effects depend on the loop size (a larger loop produces a larger error) especially in the presence of shallow water. With a geomagnetic-field inclination of 65° and a slope angle ≤ 10°, the topography causes a maximum variation in amplitude of less than 10%. Near magnetic poles and equator, the slope effect is lower and undetectable in most cases. It was found that within a 10% range of variation in the amplitude, errors introduced into inversions are within the typical uncertainty for MRS inversion and hence no topographic corrections are necessary. Thus, a significant effect from non-horizontal topography might be expected only when data uncertainty is lower than the slope effect (the slope effect is lower than equivalence when data quality is poor). Today, most field data sets are inverted using the modulus of the MRS signal, but some new developments consider the complex signal (both modulus and phase). However, inversion of complex MRS signals, which would provide a higher sensitivity to groundwater distribution, may be affected by slope effect. Thus, the slope orientation and dip angle should be accurately measured in the field when the phase of MRS signals is inverted too.