Foreword xiii

Acknowledgments xvii

About the Author xix

Contributors xxi

1 INTRODUCTION TO GPR PROSPECTING 1

1.1 What Is a GPR? 1

1.2 GPR Systems and GPR Signals 4

1.3 GPR Application Fields 5

1.4 Measurement Configurations, Bands, and Polarizations 6

1.5 GPR Data Processing 8

2 CHARACTERIZATION OF THE HOST MEDIUM 10

2.1 The Characteristics of the Host Medium 10

2.2 The Measure of the Propagation Velocity in a Masonry 11

2.3 The Measure of the Propagation Velocity in a Homogeneous Soil 13

      2.3.1 Interfacial Data in Common Offset Mode with a Null Offset: The Case of a Point-like Target 13

      2.3.2 Interfacial Data in Common Offset Mode with a Null Offset: The Case of a Circular Target 17

      2.3.3 Interfacial Data in Common Offset Mode with a Non-null Offset: The Case of a Point-like Target 18

      2.3.4 Noninterfacial Data in Common Offset Mode with a Null Offset: The Case of a Point-like Target 22

      2.3.5 Interfacial Data in Common Midpoint (CMP) Mode 25

2.4 Lossy, Magnetic, and Dispersive Media 27

      Questions 31

3 GPR DATA SAMPLING: FREQUENCY AND TIME STEPS 32

3.1 Stepped Frequency GPR Systems: The Problem of the Aliasing and the Frequency Step 32

3.2 Shape and Thickness of the GPR Pulses 36

3.3 Stepped Frequency GPR Systems: The Problem of the Demodulation and the Frequency Step 40

3.4 Aliasing and Time Step for Pulsed GPR Systems 45

      Questions 47

4 THE 2D SCATTERING EQUATIONS FOR DIELECTRIC TARGETS 48

4.1 Preliminary Remarks 48

4.2 Derivation of the Scattering Equations Without Considering the Effect of the Antennas 51

4.3 Calculation of the Incident Field Radiated by a Filamentary Current 61

4.4 The Plane Wave Spectrum of an Electromagnetic Source in a Homogeneous Space 61

4.5 The Insertion of the Source Characteristics in the Scattering Equations 65

4.6 The Far Field in a Homogeneous Lossless Space in Terms of Plane Wave Spectrum 69

4.7 The Effective Length of an Electromagnetic Source in a Homogeneous Space 73

4.8 The Insertion of the Receiver Characteristics in the Scattering Equations 75

      Questions 77

5 THE 2D SCATTERING EQUATIONS FOR MAGNETIC TARGETS 79

5.1 The Scattering Equations with Only Magnetic Anomalies 79

5.2 The Contribution of the x-Component of the Fitzgerald Vector 83

5.3 The Contribution of the z-Component of the Fitzgerald Vector 88

5.4 The Joined Contribution of Both the x- and z-Components of the Fitzgerald Vector 93

5.5 The Case with Both Dielectric and Magnetic Anomalies 94

      Questions 95

6 ILL-POSEDNESS AND NONLINEARITY 96

6.1 Electromagnetic Inverse Scattering 96

6.2 Ill-Posedness 97

6.3 Nonlinearity 97

6.4 The Ill-Posedness of the Inverse Scattering Problem 100

6.5 The Nonlinearity of the Inverse Scattering Problem 103

      Questions 103

7 EXTRACTION OF THE SCATTERED FIELD DATA FROM THE GPR DATA 105

7.1 Zero Timing 105

7.2 Muting of Interface Contributions 106

7.3 The Differential Configuration 110

7.4 The Background Removal 111

      Questions 115

8 THE BORN APPROXIMATION 116

8.1 The Classical Born Approximation 116

8.2 The Born Approximation in the Presence of Magnetic Targets 119

8.3 Weak and Nonweak Scattering Objects 120

      Questions 121

9 DIFFRACTION TOMOGRAPHY 122

9.1 Introduction to Diffraction Tomography 122

9.2 Diffraction Tomography for Dielectric Targets 123

9.3 Diffraction Tomography for Dielectric Targets Seen Under a Limited View Angle 130

9.4 The Effective Maximum and Minimum View Angle 140

9.5 Horizontal Resolution 142

9.6 Vertical Resolution 145

9.7 Spatial Step 147

9.8 Frequency Step 148

9.9 Time Step 149

9.10 The Effect of a Non-null Height of the Observation Line 150

9.11 The Effect of the Radiation Characteristics of the Antennas 156

9.12 DT Relationship in the Presence of Magnetic Targets 158

9.13 DT Relationship for a Differential Configuration 160

9.14 DT Relationship in the Presence of Background Removal 163

      Questions 168

10 TWO-DIMENSIONAL MIGRATION ALGORITHMS 169

10.1 Migration in the Frequency Domain 169

10.2 Migration in the Time Domain (Raffaele Persico and Raffaele Solimene) 175

      Questions 181

11 THREE-DIMENSIONAL SCATTERING EQUATIONS 182

orenzo Lo Monte, Raffaele Persico, and Raffaele Solimene

11.1 Scattering in Three Dimensions: Redefinition of the Main Symbols 182

11.2 The Scattering Equations in 3D 184

11.3 Three-Dimensional Green's Functions 184

11.4 The Incident Field 185

11.5 Homogeneous 3D Green's Functions 187

11.6 The Plane Wave Spectrum of a 3D Homogeneous Green's Fucntion 192

11.7 Half-Space Green's Functions 197

      Questions 204

12 THREE-DIMENSIONAL DIFFRACTION TOMOGRAPHY 205

12.1 Born Approximation and DT in 3D 205

12.2 Ideal and Limited-View-Angle 3D Retrievable Spectral Sets 210

12.3 Spatial Step and Transect 212

12.4 Horizontal Resolution (Raffaele Persico and Raffaele Solimene) 213

12.5 Vertical Resolution, Frequency and Time Steps 217

Questions 218

13 THREE-DIMENSIONAL MIGRATION ALGORITHMS 219

13.1 3D Migration Formulas in the Frequency Domain 219

13.2 3D Migration Formulas in the Time Domain 222

13.3 3D Versus 2D Migration Formulas in the Time Domain 226

      Questions 228

14 THE SINGULAR VALUE DECOMPOSITION 229

14.1 The Method of Moments 229

14.2 Reminders About Eigenvalues and Eigenvectors 231

14.3 The Singular Value Decomposition 234

14.4 The Study of the Inverse Scattering Relationship by Means of the SVD 238

      Questions 241

15 NUMERICAL AND EXPERIMENTAL EXAMPLES 242

15.1 Examples with Regard to the Measure of the Propagation Velocity 242

      15.1.1 Common Offset Interfacial Data with Null Offset on a Homogeneous Soil 242

      15.1.2 Common Offset Interfacial Data on a Wall, Neglecting the Offset Between the Antennas 245

      15.1.3 Interfacial Common Offset Data on a Homogeneous Soil: The Effect on the Offset Between the Antennas 247

      15.1.4 Noninterfacial Common Offset Data with a Null Offset Between the Antennas 249

      15.1.5 Common Midpoint Data 250

15.2 Exercises on Spatial Step and Horizontal Resolution 252

15.3 Exercises on Frequency Step and Vertical Resolution 264

15.4 Exercises on the Number of Trial Unknowns 271

15.5 Exercises on Spectral and Spatial Contents 274

15.6 Exercises on the Effect of the Height of the Observation Line 280

15.7 Exercises on the Effect of the Extent of the Investigation Domain 284

15.8 Exercises on the Effects of the Background Removal 295

15.9 2D and 3D Migration Examples with a Single Set and Two Crossed Sets of B-Scans (Marcello Ciminale, Giovanni Leucci, Loredana Matera, and Raffaele Persico) 304

15.10 2D and 3D Inversion Examples (Ilari Catapano and Raffaele Persico) 311

APPENDICES 327

APPENDIX A (Raffaele Persico and Raffaele Solimene) 329

APPENDIX B 334

APPENDIX C 335

APPENDIX D 337

APPENDIX E 340

APPENDIX F (Raffaele Persico and Raffaele Solimene) 346

APPENDIX G: ANSWERS TO QUESTIONS 349

References 358

Index 365

Raffaele Persico was born in Napoli, Italy in 1969. After humanistic secondary school studies, he achieved his degree in Electronic Engineering from the University of Napoli Federico II and then his Ph. D. in Information Engineering from the Second University of Napoli. He has been Fellow Student at the Second University of Napoli, Research Sci-ent istat the Consortium CO. RI. S. T. A. , and then Research Scientist at the Institute for the Electromagnetic Sensing of the Environment IRE A-CNR. Since 2007, he has been affil-i ated with the Institute for Archaeological and Monumental Heritage I BAM-CNR. problems, GPR data processing, and GPR systems. He has co-authored about 150 papers in international journals and conference proceedings and holds an Italian patent on the reconfigurability of the GPR systems. He is reviewer for several international journals and is Associate Editor of Near Surface Geophysics. He chaired the 13th International Conference on Ground Penetrating Radar, held in Lecce, Italy in 2010, and has devised a proto typ al reconfigurable stepped-frequency GPR system together with the IDSC or-PA\Dr. Persico's research activity has been devoted to microwave imaging, inverse poration and the University of Florence. Since 2009hehasbeena Member of the Euro GPR Association.

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