Water Content and Relaxation Time Estimation Using Full-Wave Form Inversion of MRS Signal

The magnetic resonance sounding (MRS) method is a relatively novel geophysical method, which allows for the estimation of hydrogeophysical parameters due to the direct sensitivity of hydrogen molecules of water. The use of this method makes it possible to determine the presence or absence of water below the surface more precisely and to determine the important characteristics of the hydrogeology parameters of the aquifer layer such as water content and hydraulic conductivity. The MRS technique is based on the Nuclear Magnetic Resonance (NMR) principles to determine the subsurface distribution of hydrogen protons. MRS field measurements are mostly carried out with a surface antenna as transmitter/receiver of electromagnetic signals. However novel instruments utilize a number of reference loops to mitigate noise in MRS signals. It enables us to use more sophisticated noise canceling strategies and it is possible to overwhelm the drawbacks from the single-channel MRS filtering techniques (Ghanati and Hafizi, 2017; Ghanati, et al, 2016b). To obtain depth information, a series of measurements at different pulse moments,  (where  is current amplitude and τ is pulse duration) are passed through the loop. The larger the pulse moment, the larger the penetration depth. By varying the pulse moment, a spatial distribution of aquifer properties with respect to the depth can be obtained from the MRS data inverse problem.
From data space point of view, in the inversion of magnetic resonance sounding data, two types of algorithms have been presented: 1) Initial Amplitude Inversion (IAI) and 2) Time Step Inversion (TSI). Given that in the above-mentioned methods only a portion of the data is used for inversion, it is not possible to provide a stable solution with a suitable depth resolution in the inversion process, while the use of the full waveform inversion of the magnetic resonance signal (i.e., using whole data space) increases the stability and resolution of water content and relaxation time models. Magnetic resonance signals naturally show a multi-exponential behavior that is due to the suppression of signals from layers or sub-volumes that have different relaxation times. In this method, the concept of multi-exponential behavior is considered for magnetic resonance signal data due to the non-uniform distribution of relaxation time at sub-surface pores. The proposed algorithm is evaluated using some synthetic examples and a real data set with the assumption of multi-exponential regime. From the numerical experiments, it is clearly observed that the presented method obtains a more realistic distribution of relaxation time versus the depth of the survey compared to the IAI algorithm with the assumption of the mono-exponential behavior. Furthermore, since the amplitude of the magnetic resonance signal is related to the sub-surface water content directly, the theory of multi-dimensional behavior in the inversion of the magnetic resonance signal provides a significant improvement in the fitting of the signals, which makes it possible a more accurate and reliable estimate of sub-surface water content. Finally, to evaluate the accuracy of the algorithm assuming multi-exponential behavior of signals, Bootstrap uncertainty analysis is performed on the field data. Given the results of the uncertainty analysis and its comparison with the geological model obtained from the borehole results, the power of the proposed approach in estimating the position and water content of subsurface aquifers is clearly visible.