Full FID Inversion of MRS Data

The Magnetic Resonance Sounding (MRS) method, also known as surface NMR, is a non-invasive geophysical method which directly studies groundwater reservoirs from surface measurements. It is capable of direct estimating of water content distribution (from initial amplitudes) and indirect information on pore sizes (from relaxation time). The purpose of this paper is to introduce a new inversion scheme for the full MRS data set. The multi-exponential behaviour of the NMR signal is taken into account and estimated by the Stretched-Exponential model (Hilfer, 2002), in which the time constant and stretching exponent determine the centre and the width of the distribution. The model space is then described with much less parameters, compared with the multi-exponential description. The FID time series are logarithmically gated and the discretization in the z-direction in the forward algorithm is decoupled from discretization of the inversion model. The inversion routine supports smooth and block inversion of the data and a full linear model parameter sensitivity analysis can be calculated (Tarantola and Valette, 1982), an essential criteria for evaluation of the inversion results.