Magnetic Resonance Imaging for Groundwater

<p>PREFACE vii</p>
<p>ACKNOWLEDGEMENTS ix</p>
<p>CHAPTER 1. SNMR IMAGING FOR GROUNDWATER 1</p>
<p>1.1. Brief history of SNMR development 1</p>
<p>1.2. The basic principles 2</p>
<p>1.3. Magnetic Resonance Sounding 5</p>
<p>1.4. Measuring setup 8</p>
<p>1.5. Geophysical tool for hydrogeologists 12</p>
<p>CHAPTER 2. THE BASICS OF NMR 15</p>
<p>2.1. NMR phenomenon 15</p>
<p>2.1.1. Precession of free spins 15</p>
<p>2.1.2. Macroscopic spin magnetization 16</p>
<p>2.2. NMR relaxation 22</p>
<p>2.2.1. Longitudinal relaxation 22</p>
<p>2.2.2. Transverse relaxation 24</p>
<p>2.2.3. Diffusion in non–homogeneous magnetic field 26</p>
<p>2.3. NMR measurements 31</p>
<p>2.3.1. Free induction decay (FID) 31</p>
<p>2.3.2. Spin echo (SE) 38</p>
<p>CHAPTER 3. FORWARD MODELING 45</p>
<p>3.1. The imaging equation 45</p>
<p>3.2. The Earth s magnetic field 54</p>
<p>3.3. Modeling typical SNMR signals 59</p>
<p>3.4. 3–D sensitivity of the SNMR loop 68</p>
<p>3.5. Experimental verification 76</p>
<p>CHAPTER 4. INVERSION 85</p>
<p>4.1. The SNMR inverse problem 85</p>
<p>4.2. Linearization. 89</p>
<p>4.3. Discretization 92</p>
<p>4.3.1. The 1–D inverse problem 92</p>
<p>4.3.2. The 3–D inverse problem 105</p>
<p>4.4. Linear inverse problems 113</p>
<p>4.5. Nonlinear inverse problems 115</p>
<p>4.5.1. Inversion of the geomagnetic field variations 116</p>
<p>4.5.2. Inversion of the resistivity distribution 118</p>
<p>CHAPTER 5. LINK BETWEEN SNMR AND AQUIFER PARAMETERS 121</p>
<p>5.1. Parameters used for characterizing an aquifer 122</p>
<p>5.2. Available SNMR estimates on aquifer parameters 126</p>
<p>5.2.1. Detection of groundwater 126</p>
<p>5.2.2. Aquifers and geometry 128</p>
<p>5.2.3. Storage–related parameters 131</p>
<p>5.2.4. Flow–related parameters 134</p>
<p>5.3. Joint use of SNMR and resistivity data 138</p>
<p>BIBLIOGRAPHY 143</p>
<p>INDEX 155</p>