Quantitative investigation of effective parameters on resolution and penetration depth of magnetic resonance sounding data using singular value decomposition of forward function

Due to the direct sensitivity to the hydrogen of water molecules, magnetic resonance sounding (MRS) provides estimate of hydro-geophysical parameters such as water content and hydraulic conductivity. 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 principles to determine the subsurface distribution of hydrogen protons. MRS measurements are carried out with a surface antenna as transmitter/receiver of electromagnetic signals. To obtain depth information, a series of measurements at different pulse moments, are passed through the loop. By varying the pulse moment, a spatial distribution of aquifer properties with respect to the depth can be obtained from the MRS data inversion. From data space point of view, in the inversion of magnetic resonance sounding data, three types of algorithms have been presented:  Initial Amplitude Inversion, Time Step Inversion, and Full waveform inversion. Given that in the two first 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.
    One of the important issues to be considered in the inversion of geophysical data is the evaluation of the quality of inverted models. This means that using mathematical tools, the degree of certainty or uncertainty of the models obtained from solving the inverse problem is determined quantitatively, and this helps to better interpret geophysical models. Evaluating the quality of water content and relaxation time models resulting from the inversion of surface nuclear magnetic resonance data is also essential.
In this research, we extract the model resolution matrix using singular value analysis of the leading MRS function. This method consists of evaluating the components of loop size, maximum moment pulse, distribution of subsurface layers as well as ambient noise level conditions as inputs on the resolution and depth of MRS data. The effect of each of these components on the resolution of magnetic resonance sounding data is measured through artificial models and field data. The results show that the loop size increases the penetration and also increases the vertical resolution if the maximum moment pulse is constant. This is also true if the loop size is constant and the maximum moment pulse is increasing. Increasing the noise level reduces the resolution and is managed through depth. The results of this dissertation will be an important step in optimizing measurement components to improve vertical resolution in water content and relaxation time models and also increase the penetration depth in magnetic resonance sounding studies. The hydro-geophysical sources of water and relaxation time are reviewed in the inversion of the polynomial using the GSVD method.