Magnetic Resonance Imaging for Groundwater

This book presents the basics of the non-invasive geophysical method for groundwater investigation, called Magnetic Resonance Sounding (MRS) or Surface Nuclear Magnetic Resonance (SNMR), and its practical application to the problems of groundwater localization and aquifer characterization. The method is based on the nuclear magnetic resonance (NMR) phenomenon and is selectively sensitive to groundwater. The main aims of the author are to teach the reader the basic principles of the method as well as to formulate consistent approximate models, leading to reasonably simple inverse problems.

Containing an extensive bibliography, numerous practical and numerical examples as well as a detailed presentation of the nuts and bolts of the method based on the long-term experience of SNMR development and practical use, this book is useful for students, scientists and professional engineers working in the field of hydrogeophysics and hydrogeology.

Contents

1. SNMR Imaging for Groundwater.
2. The Basics of NMR.
3. Forward Modeling.
4. Inversion.
5. Link Between SNMR and Aquifer Parameters.

PREFACE vii

ACKNOWLEDGEMENTS ix

CHAPTER 1. SNMR IMAGING FOR GROUNDWATER 1

1.1. Brief history of SNMR development 1

1.2. The basic principles 2

1.3. Magnetic Resonance Sounding 5

1.4. Measuring setup 8

1.5. Geophysical tool for hydrogeologists 12

CHAPTER 2. THE BASICS OF NMR 15

2.1. NMR phenomenon 15

2.1.1. Precession of free spins 15

2.1.2. Macroscopic spin magnetization 16

2.2. NMR relaxation 22

2.2.1. Longitudinal relaxation 22

2.2.2. Transverse relaxation 24

2.2.3. Diffusion in non-homogeneous magnetic field 26

2.3. NMR measurements 31

2.3.1. Free induction decay (FID) 31

2.3.2. Spin echo (SE) 38

CHAPTER 3. FORWARD MODELING 45

3.1. The imaging equation 45

3.2. The Earth’s magnetic field 54

3.3. Modeling typical SNMR signals 59

3.4. 3-D sensitivity of the SNMR loop 68

3.5. Experimental verification 76

CHAPTER 4. INVERSION 85

4.1. The SNMR inverse problem 85

4.2. Linearization. 89

4.3. Discretization 92

4.3.1. The 1-D inverse problem 92

4.3.2. The 3-D inverse problem 105

4.4. Linear inverse problems 113

4.5. Nonlinear inverse problems 115

4.5.1. Inversion of the geomagnetic field variations 116

4.5.2. Inversion of the resistivity distribution 118

CHAPTER 5. LINK BETWEEN SNMR AND AQUIFER PARAMETERS 121

5.1. Parameters used for characterizing an aquifer 122

5.2. Available SNMR estimates on aquifer parameters 126

5.2.1. Detection of groundwater 126

5.2.2. Aquifers and geometry 128

5.2.3. Storage-related parameters 131

5.2.4. Flow-related parameters 134

5.3. Joint use of SNMR and resistivity data 138

BIBLIOGRAPHY 143

INDEX 155