Inversions of surface-NMR signals using complex kernels

Surface Nuclear Magnetic Resonance (SNMR) is used for groundwater exploration and aquifer characterization (e.g. [1]). The NMR-Experiment is conducted by a coincident transmitter and receiver loop at the surface exciting the protons of water molecules underground with the Larmor frequency of the earth's magnetic field. Performing a SNMR measurement with increasing excitation intensity (pulse moment) yields a complex sounding curve, where the amplitude of the relaxation signal is determined by the numbers of protons i.e. the water content. The subsurface electrical conductivity affects both the amplitude and especially the phase [2,3].