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Introduction to Ground Penetrating Radar: Inverse Scattering and Data Processing

Introduction to Ground Penetrating Radar: Inverse Scattering and Data Processing

Raffaele Persico

ISBN: 978-1-118-30500-3

Jun 2014, Wiley-IEEE Press

392 pages

In Stock

$124.00

Description

A real-world guide to practical applications of ground penetrating radar (GPR)

The nondestructive nature of ground penetrating radar makes it an important and popular method of subsurface imaging, but it is a highly specialized field, requiring a deep understanding of the underlying science for successful application. Introduction to Ground Penetrating Radar: Inverse Scattering and Data Processing provides experienced professionals with the background they need to ensure precise data collection and analysis.

Written to build upon the information presented in more general introductory volumes, the book discusses the fundamental mathematical, physical, and engineering principles upon which GPR is built. Real-world examples and field data provide readers an accurate view of day-to-day GPR use. Topics include:

  • 2D scattering for dielectric and magnetic targets
  • 3D scattering equations and migration algorithms
  • Host medium characterization and diffraction tomography
  • Time and frequency steps in GPR data sampling
  • The Born approximation and the singular value decomposition

The six appendices contain the mathematical proofs of all examples discussed throughout the book. Introduction to Ground Penetrating Radar: Inverse Scattering and Data Processing is a comprehensive resource that will prove invaluable in the field.

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
Lorenzo 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 (Ilaria 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