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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 decompositionThe 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.

Introduction to Ground Penetrating Radar: Inverse Scattering and Data Processing

Foreword xiiiAcknowledgments xviiAbout the Author xixContributors xxi1 INTRODUCTION TO GPR PROSPECTING 11.1 What Is a GPR? 11.2 GPR Systems and GPR Signals 41.3 GPR Application Fields 51.4 Measurement Configurations, Bands, and Polarizations 61.5 GPR Data Processing 82 CHARACTERIZATION OF THE HOST MEDIUM 102.1 The Characteristics of the Host Medium 102.2 The Measure of the Propagation Velocity in a Masonry 112.3 The Measure of the Propagation Velocity in a Homogeneous Soil 132.3.1 Interfacial Data in Common Offset Mode with a Null Offset: The Case of a Point-like Target 132.3.2 Interfacial Data in Common Offset Mode with a Null Offset: The Case of a Circular Target 172.3.3 Interfacial Data in Common Offset Mode with a Non-null Offset: The Case of a Point-like Target 182.3.4 Noninterfacial Data in Common Offset Mode with a Null Offset: The Case of a Point-like Target 222.3.5 Interfacial Data in Common Midpoint (CMP) Mode 252.4 Lossy, Magnetic, and Dispersive Media 27Questions 313 GPR DATA SAMPLING: FREQUENCY AND TIME STEPS 323.1 Stepped Frequency GPR Systems: The Problem of the Aliasing and the Frequency Step 323.2 Shape and Thickness of the GPR Pulses 363.3 Stepped Frequency GPR Systems: The Problem of the Demodulation and the Frequency Step 403.4 Aliasing and Time Step for Pulsed GPR Systems 45Questions 474 THE 2D SCATTERING EQUATIONS FOR DIELECTRIC TARGETS 484.1 Preliminary Remarks 484.2 Derivation of the Scattering Equations Without Considering the Effect of the Antennas 514.3 Calculation of the Incident Field Radiated by a Filamentary Current 614.4 The Plane Wave Spectrum of an Electromagnetic Source in a Homogeneous Space 614.5 The Insertion of the Source Characteristics in the Scattering Equations 654.6 The Far Field in a Homogeneous Lossless Space in Terms of Plane Wave Spectrum 694.7 The Effective Length of an Electromagnetic Source in a Homogeneous Space 734.8 The Insertion of the Receiver Characteristics in theScattering Equations 75Questions 775 THE 2D SCATTERING EQUATIONS FOR MAGNETIC TARGETS 795.1 The Scattering Equations with Only Magnetic Anomalies 795.2 The Contribution of the x-Component of the Fitzgerald Vector 835.3 The Contribution of the z-Component of the Fitzgerald Vector 885.4 The Joined Contribution of Both the x- and z-Components of the Fitzgerald Vector 935.5 The Case with Both Dielectric and Magnetic Anomalies 94Questions 956 ILL-POSEDNESS AND NONLINEARITY 966.1 Electromagnetic Inverse Scattering 966.2 Ill-Posedness 976.3 Nonlinearity 976.4 The Ill-Posedness of the Inverse Scattering Problem 1006.5 The Nonlinearity of the Inverse Scattering Problem 103Questions 1037 EXTRACTION OF THE SCATTERED FIELD DATA FROM THE GPR DATA 1057.1 Zero Timing 1057.2 Muting of Interface Contributions 1067.3 The Differential Configuration 1107.4 The Background Removal 111Questions 1158 THE BORN APPROXIMATION 1168.1 The Classical Born Approximation 1168.2 The Born Approximation in the Presence of Magnetic Targets 1198.3 Weak and Nonweak Scattering Objects 120Questions 1219 DIFFRACTION TOMOGRAPHY 1229.1 Introduction to Diffraction Tomography 1229.2 Diffraction Tomography for Dielectric Targets 1239.3 Diffraction Tomography for Dielectric Targets Seen Under a Limited View Angle 1309.4 The Effective Maximum and Minimum View Angle 1409.5 Horizontal Resolution 1429.6 Vertical Resolution 1459.7 Spatial Step 1479.8 Frequency Step 1489.9 Time Step 1499.10 The Effect of a Non-null Height of the Observation Line 1509.11 The Effect of the Radiation Characteristics of the Antennas 1569.12 DT Relationship in the Presence of Magnetic Targets 1589.13 DT Relationship for a Differential Configuration 1609.14 DT Relationship in the Presence of Background Removal 163Questions 16810 TWO-DIMENSIONAL MIGRATION ALGORITHMS 16910.1 Migration in the Frequency Domain 16910.2 Migration in the Time Domain (Raffaele Persico and Raffaele Solimene) 175Questions 18111 THREE-DIMENSIONAL SCATTERING EQUATIONS 182Lorenzo Lo Monte, Raffaele Persico, and Raffaele Solimene11.1 Scattering in Three Dimensions: Redefinition of the Main Symbols 18211.2 The Scattering Equations in 3D 18411.3 Three-Dimensional Green's Functions 18411.4 The Incident Field 18511.5 Homogeneous 3D Green's Functions 18711.6 The Plane Wave Spectrum of a 3D Homogeneous Green's Fucntion 19211.7 Half-Space Green's Functions 197Questions 20412 THREE-DIMENSIONAL DIFFRACTION TOMOGRAPHY 20512.1 Born Approximation and DT in 3D 20512.2 Ideal and Limited-View-Angle 3D Retrievable Spectral Sets 21012.3 Spatial Step and Transect 21212.4 Horizontal Resolution (Raffaele Persico and Raffaele Solimene) 21312.5 Vertical Resolution, Frequency and Time Steps 217Questions 21813 THREE-DIMENSIONAL MIGRATION ALGORITHMS 21913.1 3D Migration Formulas in the Frequency Domain 21913.2 3D Migration Formulas in the Time Domain 22213.3 3D Versus 2D Migration Formulas in the Time Domain 226Questions 22814 THE SINGULAR VALUE DECOMPOSITION 22914.1 The Method of Moments 22914.2 Reminders About Eigenvalues and Eigenvectors 23114.3 The Singular Value Decomposition 23414.4 The Study of the Inverse Scattering Relationship by Means of the SVD 238Questions 24115 NUMERICAL AND EXPERIMENTAL EXAMPLES 24215.1 Examples with Regard to the Measure of the Propagation Velocity 24215.1.1 Common Offset Interfacial Data with Null Offset on a Homogeneous Soil 24215.1.2 Common Offset Interfacial Data on a Wall, Neglecting the Offset Between the Antennas 24515.1.3 Interfacial Common Offset Data on a Homogeneous Soil: The Effect on the Offset Between the Antennas 24715.1.4 Noninterfacial Common Offset Data with a Null Offset Between the Antennas 24915.1.5 Common Midpoint Data 25015.2 Exercises on Spatial Step and Horizontal Resolution 25215.3 Exercises on Frequency Step and Vertical Resolution 26415.4 Exercises on the Number of Trial Unknowns 27115.5 Exercises on Spectral and Spatial Contents 27415.6 Exercises on the Effect of the Height of the Observation Line 28015.7 Exercises on the Effect of the Extent of the Investigation Domain 28415.8 Exercises on the Effects of the Background Removal 29515.9 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) 30415.10 2D and 3D Inversion Examples (Ilaria Catapano and Raffaele Persico) 311APPENDICES 327APPENDIX A (Raffaele Persico and Raffaele Solimene) 329APPENDIX B 334APPENDIX C 335APPENDIX D 337APPENDIX E 340APPENDIX F (Raffaele Persico and Raffaele Solimene) 346APPENDIX G: ANSWERS TO QUESTIONS 349References 358Index 365