Groundwater is an important economic source of water supply for drinking water and irrigation water for agriculture. Surface nuclear magnetic resonance (SNMR) sounding is a relatively new geophysical method that can be used to determine the presence of culturally and economically important substances, such as subsurface water or hydrocarbon distribution. SNMR sounding allows the determination of water content and pore size distribution directly from the surface. The SNMR method is performed by stimulating an alternating current pulse through an antenna at the surface in order to confirm the existence of water in the subsurface. This paper reports the development of a 3-D forward modeling code for SNMR amplitudes and decay times, after which an improved 2-D and 3-D inversion algorithm is investigated, consisting of schemes for regularizing model parameterization. After briefly reviewing inversion schemes generally used in geophysics, the special properties of SNMR or magnetic resonance sounding (MRS) inversion are evaluated. We present an extension of MRS to magnetic resonance tomography (MRT), i.e. an extension for 2-D and 3-D investigation, and the appropriate inversions.