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Introduction to Ground Penetrating Radar:Inverse Scattering and Data Processing

Cover Image Copyright Year: 2014
Author(s): Persico, R.
Publisher: Wiley-IEEE Press
Content Type : Books & eBooks
Topics: Aerospace ;  Communication, Networking & Broadcasting ;  Components, Circuits, Devices & Systems ;  Fields, Waves & Electromagnetics
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      Front Matter

      Persico, R.
      Introduction to Ground Penetrating Radar:Inverse Scattering and Data Processing

      DOI: 10.1002/9781118835647.fmatter
      Copyright Year: 2014

      Wiley-IEEE Press eBook Chapters

      The prelims comprise:
      Half-Title Page
      Series Page
      Title Page
      Copyright Page
      Dedication Page
      Table of Contents
      Foreword
      Acknowledgments
      About the Author
      Contributors View full abstract»

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      Introduction to GPR Prospecting

      Persico, R.
      Introduction to Ground Penetrating Radar:Inverse Scattering and Data Processing

      DOI: 10.1002/9781118835647.ch1
      Copyright Year: 2014

      Wiley-IEEE Press eBook Chapters

      This book focuses on ground-penetrating radar (GPR) data processing based on the Born approximation. In particular, the core of the processing dealt in the book is the migration and the linear Born model-based inversion algorithms, both of which considered either in a 2D or in a 3D framework. The book focuses on some of the theoretical aspects important for an aware execution of a GPR measurement campaign, followed by a proper processing and, when possible, a reasonable interpretation. There are essentially two kinds of GPR systems: the pulsed one and the stepped-frequency one. Whatever the system, the GPR signal can be regarded as a function of the spatial point and of the time or the frequency indifferently. In several GPR application fields, it can be particularly useful to make use of advanced GPR systems equipped with a large array of antennas. View full abstract»

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      Characterization of the Host Medium

      Persico, R.
      Introduction to Ground Penetrating Radar:Inverse Scattering and Data Processing

      DOI: 10.1002/9781118835647.ch2
      Copyright Year: 2014

      Wiley-IEEE Press eBook Chapters

      For a correct interpretation of the ground-penetrating radar (GPR) signal, it is important to have some estimation of the electromagnetic characteristics of the background medium. A complete characterization theoretically means a measure of the dielectric permittivity and of the magnetic permeability, both meant as complex quantities to account for losses and variables versus the frequency. In many cases, the propagation medium is a low-lossy medium; that is, the real part of the wavenumber is much larger than the imaginary part. The electromagnetic characteristics of the propagation medium depend on its chemical composition, its water content, its porosity, its mineralogy, and possibly its temperature. The measure of the propagation velocity of the electromagnetic waves in a homogeneous soil might be done, in principle, with a buried marker, similarly to what is described for the case of a wall. View full abstract»

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      GPR Data Sampling

      Persico, R.
      Introduction to Ground Penetrating Radar:Inverse Scattering and Data Processing

      DOI: 10.1002/9781118835647.ch3
      Copyright Year: 2014

      Wiley-IEEE Press eBook Chapters

      It is possible to transmit a train of harmonic signals instead of a pulse. This procedure essentially involves transmitting the harmonic components of the pulse sequentially. The systems that do that are the stepped frequency ground-penetrating radars (GPRs). The theoretical advantages of a stepped frequency system with respect to a pulsed one are essentially based on the possibility to have a trade-off between the duration of the harmonic signals and the noise on the data. This chapter discusses the shape and thickness of the GPR pulses, and the problem of the Hermitian images, which arises from the possibility of an imprecise demodulation of the received signal. The effects of aliasing for a stepped frequency system are more easily recognizable from the achieved data. After transformation in time domain and processing, aliased data provides duplications of the actual targets along the depth and at a fixed distance from the real objects. View full abstract»

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      The 2D Scattering Equations for Dielectric Targets

      Persico, R.
      Introduction to Ground Penetrating Radar:Inverse Scattering and Data Processing

      DOI: 10.1002/9781118835647.ch4
      Copyright Year: 2014

      Wiley-IEEE Press eBook Chapters

      The behavior of the electromagnetic signal radiated by a ground-penetrating radar (GPR) and scattered by buried targets is governed by Maxwell's equations. So, in order to provide hopefully deep enough and self-consistent discussion of GPR data processing, this chapter starts from the beginning and provides the derivation of the whole formulation up to the migration and the linear inversion. This chapter describes the derivation of the scattering equations without considering the effect of the antennas, and the calculation of the incident field radiated by a filamentary current. It discusses plane wave spectrum and effective length of an electromagnetic source in a homogeneous space. The chapter considers the problem of inserting the source and receiver characteristics into the scattering operator. It calculates the far field in a homogeneous lossless space in terms of plane wave spectrum. View full abstract»

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      The 2D Scattering Equations for Magnetic Targets

      Persico, R.
      Introduction to Ground Penetrating Radar:Inverse Scattering and Data Processing

      DOI: 10.1002/9781118835647.ch5
      Copyright Year: 2014

      Wiley-IEEE Press eBook Chapters

      This chapter first considers two dimensional (2D) scattering equations for magnetic targets with only magnetic anomalies. Due to the linearity of the relationships between the magnetic fields and the Fitzgerald vector, the X-component and the Z-component, of the Fitzgerald vector, are considered as two separated potentials. Each of them is associated with an electromagnetic field, and the final solution is given by the sum of these two electromagnetic fields. The chapter then considers the joined contribution of both the X- and Z-components of the Fitzgerald vector. It presents the comprehensive scattered field due to the buried magnetic anomalies. Finally, the chapter presents the internal and external scattering equations in the case of both dielectric and magnetic anomalies, or (which is the same) in the presence of targets with both dielectric and magnetic properties different from those of the embedding soil. View full abstract»

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      Ill-Posedness and Nonlinearity

      Persico, R.
      Introduction to Ground Penetrating Radar:Inverse Scattering and Data Processing

      DOI: 10.1002/9781118835647.ch6
      Copyright Year: 2014

      Wiley-IEEE Press eBook Chapters

      The direct scattering problem consists of the calculation of the scattered field if we know the underground scenario, whereas the inverse scattering problem consists in the reconstruction of the underground scenario if we know the scattered field. In both the direct and the inverse problem the characteristics of the antennas and of the soil are assumed to be known. Customarily the inverse problems present some additional difficulties with respect to the corresponding direct ones. In particular, unlike the direct ones, the inverse problems are usually ill-posed. Moreover, if the direct problem is nonlinear, also the corresponding inverse problem is nonlinear. In particular, the electromagnetic inverse scattering problem is both ill-posed and nonlinear. View full abstract»

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      Extraction of the Scattered Field Data from The GPR Data

      Persico, R.
      Introduction to Ground Penetrating Radar:Inverse Scattering and Data Processing

      DOI: 10.1002/9781118835647.ch7
      Copyright Year: 2014

      Wiley-IEEE Press eBook Chapters

      Before extracting the scattered field data, the problem of the zero timing is to be addressed. In particular, the choice of the zero time is a problem arising from a physical constraint, namely the fact that any ground penetrating radar (GPR) system has a finite band and, consequently, it cannot radiate or receive correctly an impulse with an immediate rising up. After the preliminary zero timing, the datum observed in the observation point is the voltage related to the total field in that point, which is roughly proportional to the total field in that point. An important difference between the differential datum and the background removal (BKGR) datum is that the first one is conceived as associated to a specific hardware, whereas BKGR is a procedure that can be applied on the usual common offset data. View full abstract»

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      The Born Approximation

      Persico, R.
      Introduction to Ground Penetrating Radar:Inverse Scattering and Data Processing

      DOI: 10.1002/9781118835647.ch8
      Copyright Year: 2014

      Wiley-IEEE Press eBook Chapters

      Born series for the scattered field is achieved by substituting Born series for the internal field into the external scattering equation. Analogously to the Born series for the internal field there is no general guarantee for the convergence of the Born series for the scattered field. In any case, the first term of this sequence provides the first-order Born Approximation (BA) for the scattered field. The weakness, in a weak scatterer, is a feature related to the maximum level of the contrast and the electrical size of the buried target, its shape, and the nature of the background medium. It is important to emphasize that, independently from the validity of the BA in the current situation, an aspect worth emphasizing is that the secondary sources that generate the scattered field under BA have the same support of secondary sources. This support is just the extension of the buried targets. View full abstract»

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      Diffraction Tomography

      Persico, R.
      Introduction to Ground Penetrating Radar:Inverse Scattering and Data Processing

      DOI: 10.1002/9781118835647.ch9
      Copyright Year: 2014

      Wiley-IEEE Press eBook Chapters

      There are several kinds of diffraction tomography (DT) relationships in relationship with the measurement configuration, but this chapter focuses on the common offset configuration. In general, a DT relationship requires more approximations than does the linearization provided by the BA. The effective maximum view angle is difficult to be predicted in a theoretical way, but in general it can be heuristically evaluated from the data. The chapter demonstrates the calculation of the available horizontal resolution, although the horizontal resolution cannot be separated from the vertical one, because the two quantities are correlated within the DT relationships. DT also provides an approximated but powerful tool to calculate the spatial step needed for taking GPR measurements correctly. The chapter also shows that GPR data can be processed either in the frequency domain or in the time domain. View full abstract»

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      Two-Dimensional Migration Algorithms

      Persico, R.
      Introduction to Ground Penetrating Radar:Inverse Scattering and Data Processing

      DOI: 10.1002/9781118835647.ch10
      Copyright Year: 2014

      Wiley-IEEE Press eBook Chapters

      This chapter focuses on data in the frequency domain and the time domain. In both cases, the chapter focuses on the case of common offset data gathered at the air-soil interface, as well as to the case of only dielectric soils and dielectric targets. The migration formula in frequency domain essentially consists in an interpolation of the spectrum of the data multiplied times a known function and then back Fourier transformed in the spatial domain. It has the drawback that it requires some interpolation of the spectrum of the data, but has the computational advantage that it is a two-dimensional (2D) inverse Fourier transform and therefore can be implemented by means of computationally effective IFFT algorithms. Several commercial codes for ground penetrating radar (GPR) data processing allow us to choose the number of traces to be taken into account when performing the Kirchhoff's migration. View full abstract»

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      Three-Dimensional Scattering Equations

      Persico, R.
      Introduction to Ground Penetrating Radar:Inverse Scattering and Data Processing

      DOI: 10.1002/9781118835647.ch11
      Copyright Year: 2014

      Wiley-IEEE Press eBook Chapters

      2D inverse scattering is the most common model in ground penetrating radar (GPR) data processing. However, recent advances in distributed GPR, coherent GPR, HF GPR, and RF tomography led to an extension of classical 2D work in a more proper 3D scenario. This chapter discusses 3D scattering equations. Specifying the 3D scattering equations, means finding the expressions of Green's functions and (for a given and characterized source) of the incident field. Due to the increased complexity of the 3D dealing, it is useful to generalize the definition of Green's function. In 3D, any Green's function is dyadic and thus can be expressed by means of a general matrix scheme. The chapter discusses retrieval of expressions of the homogeneous Green's functions. The calculation of the homogeneous Green's functions is a preliminary step for the calculation of the half-space Green's functions. View full abstract»

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      Three-Dimensional Diffraction Tomography

      Persico, R.
      Introduction to Ground Penetrating Radar:Inverse Scattering and Data Processing

      DOI: 10.1002/9781118835647.ch12
      Copyright Year: 2014

      Wiley-IEEE Press eBook Chapters

      The (first-order) Born approximation (BA) in 3D can be introduced in the same way as done in 2D, namely approximating the internal field with the incident one. It is important to outline that the spectral weight tends to zero all over the bound of the visible circle, so that the actual retrievable spectral set is never equal to the ideal one, in the sense that it would not be equal to the ideal set even if the measurement plane surface were unlimited, analogously to what happened in 2D. The spatial step and the transect or, in other terms, the spatial needed steps along the direction of the movement of the antennas and along the horizontal direction orthogonal to this are driven by the Nyquist criterion. In order to estimate the horizontal (and then the vertical) resolution, the same steps as implemented in the 2D case can be followed. View full abstract»

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      Three-Dimensional Migration Algorithms

      Persico, R.
      Introduction to Ground Penetrating Radar:Inverse Scattering and Data Processing

      DOI: 10.1002/9781118835647.ch13
      Copyright Year: 2014

      Wiley-IEEE Press eBook Chapters

      This chapter provides three-dimensional (3D) migration formulas, namely for the data gathered at the air-soil interface in common offset on a nonmagnetic soil and without magnetic targets. The source is assimilated to a Hertzian dipole, and the received signal is approximated as the projection of the field along the direction of the receiving dipole in the observation point. The chapter exposes the physical reason why in the formulas of the 2D migration in the time domain, the datum is integrated versus the time, whereas in the homologous 3D formulas the integration along the time disappears. View full abstract»

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      The Singular Value Decomposition

      Persico, R.
      Introduction to Ground Penetrating Radar:Inverse Scattering and Data Processing

      DOI: 10.1002/9781118835647.ch14
      Copyright Year: 2014

      Wiley-IEEE Press eBook Chapters

      The kind of method of moments (MoM) used in this chapter is based on point matching in both spatial and frequency domains. The singular value decomposition (SVD) of a rectangular matrix is introduced in the chapter as an extension of the basic theory of the eigenvalues and eigenvectors of a square matrix. So, preliminarily, some reminders about the eigenvalues and eigenvectors are provided in relationship to matrix inversions. The problem of solving rectangular linear algebraic systems can be dealt with in a regularized way, which requires an extension of the eigenvalue theory; this extension is the SVD. The SVD provides not only a method for the solution of the problem but also a possible method for the analysis the problem. In particular, even if numerically, the SVD can help us to understand the characteristics of the scattering operator. View full abstract»

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      Numerical and Experimental Examples

      Persico, R.
      Introduction to Ground Penetrating Radar:Inverse Scattering and Data Processing

      DOI: 10.1002/9781118835647.ch15
      Copyright Year: 2014

      Wiley-IEEE Press eBook Chapters

      This chapter provides some numerical examples of measure of propagation velocity based on the diffraction curves. The real ground penetrating radar (GPR) pulses cannot have zero duration, because the band of the system (in particular the band of the antennas) is never infinite. In the real word, the diffraction curves have some thickness, and this constitutes an unavoidable source of uncertainty, both with regard to the propagation velocity of the waves and with regard to the depth of the buried targets. The chapter describes some examples about the needed spatial step, frequency step and the correlated achievable horizontal and vertical resolutions. It shows some examples regarding the effect of the height of the observation domain and background removal. The chapter demonstrates application of 2D and 3D migration algorithms to field data. View full abstract»

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      Appendix A

      Persico, R.
      Introduction to Ground Penetrating Radar:Inverse Scattering and Data Processing

      DOI: 10.1002/9781118835647.app1
      Copyright Year: 2014

      Wiley-IEEE Press eBook Chapters

      No abstract. View full abstract»

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      Appendix B

      Persico, R.
      Introduction to Ground Penetrating Radar:Inverse Scattering and Data Processing

      DOI: 10.1002/9781118835647.app2
      Copyright Year: 2014

      Wiley-IEEE Press eBook Chapters

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      Appendix C

      Persico, R.
      Introduction to Ground Penetrating Radar:Inverse Scattering and Data Processing

      DOI: 10.1002/9781118835647.app3
      Copyright Year: 2014

      Wiley-IEEE Press eBook Chapters

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      Appendix D

      Persico, R.
      Introduction to Ground Penetrating Radar:Inverse Scattering and Data Processing

      DOI: 10.1002/9781118835647.app4
      Copyright Year: 2014

      Wiley-IEEE Press eBook Chapters

      No abstract. View full abstract»

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      Appendix E

      Persico, R.
      Introduction to Ground Penetrating Radar:Inverse Scattering and Data Processing

      DOI: 10.1002/9781118835647.app5
      Copyright Year: 2014

      Wiley-IEEE Press eBook Chapters

      No abstract. View full abstract»

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      Appendix F

      Persico, R.
      Introduction to Ground Penetrating Radar:Inverse Scattering and Data Processing

      DOI: 10.1002/9781118835647.app6
      Copyright Year: 2014

      Wiley-IEEE Press eBook Chapters

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      Appendix G

      Persico, R.
      Introduction to Ground Penetrating Radar:Inverse Scattering and Data Processing

      DOI: 10.1002/9781118835647.app7
      Copyright Year: 2014

      Wiley-IEEE Press eBook Chapters

      No abstract. View full abstract»

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      References

      Persico, R.
      Introduction to Ground Penetrating Radar:Inverse Scattering and Data Processing

      DOI: 10.1002/9781118835647.refs
      Copyright Year: 2014

      Wiley-IEEE Press eBook Chapters

      No abstract. View full abstract»

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      Index

      Persico, R.
      Introduction to Ground Penetrating Radar:Inverse Scattering and Data Processing

      DOI: 10.1002/9781118835647.index
      Copyright Year: 2014

      Wiley-IEEE Press eBook Chapters

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      Supplemental Images

      Persico, R.
      Introduction to Ground Penetrating Radar:Inverse Scattering and Data Processing

      DOI: 10.1002/9781118835647.ins1
      Copyright Year: 2014

      Wiley-IEEE Press eBook Chapters

      No abstract. View full abstract»




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