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.

Table of Contents:
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