Numerical computation of the Green′s function of a layered media with rough interfaces

IEEE Trans. Geosci. Remote Sensing

Soldovieri

Erricolo

et al. 2012

Radio-frequency (RF) tomography is extended for imaging underground structures and tunnels assuming rough terrain. The theory of RF tomography described in an earlier paper remains applicable, provided that a numerical Green's function is computed. An FFT-based and intrinsically parallel method for obtaining numerical Green's functions is described. This method is corroborated with explicit formulas and implemented for RF tomography. Simulated data computed using a finite-difference time-domain code are used to demonstrate performance.

Section: Numerical Green's Functionmentioning

confidence: 53%

Section: Numerical Green's Functionmentioning

confidence: 99%

Imaging Below Irregular Terrain Using RF Tomography

IEEE Trans. Geosci. Remote Sensing

Soldovieri

Erricolo

et al. 2012

“…We assume the air-earth interface to be flat; however, the problem of non-flat surfaces can be solved as well (at additional complexity [7]). In this context, the air half-space is modeled as free-space medium, while the ground halfspace is modeled as an homogeneous medium with background relative dielectric permittivity D  , background conductivity D  , and magnetic permeability 0  .…”

Section: Forward Modelmentioning

confidence: 99%

Sparse reconstruction methods in RF Tomography for underground imaging

2010 International Waveform Diversity and Design Conference

Parker

2010

Underground imaging involving RF Tomography is generally severely ill-posed posed. Tikhonov Regularization is perhaps the most common method to address this ill-posedness. The proposed methods are based upon the realistic assumptions that targets (e.g. tunnels) are sparse and clustered in the scene, and have known electrical properties. Therefore, we explore the use of alternative regularization strategies leveraging sparsity of the signal and its spatial gradient, while also imposing physically-derived amplitude constraints. By leveraging this prior knowledge, cleaner scene reconstructions are obtained.I.

“…Unfortunately, the Green dyad for a general irregular surface cannot be represented in analytic form, but must be computed numerically. The computation of the numerical Green dyad is derived by extending the method proposed in [2]. In this section, we assume that the terrain model is described by an indicator function ( ) Γ r that designates the presence/absence of the background soil in a particular point r , both inside and outside D , i.e.…”

Section: Irregular Surface: Numerical Green Dyadmentioning

confidence: 99%

Imaging under irregular terrain using RF tomography and numerical green functions

2010 IEEE Antennas and Propagation Society International Symposium

Soldovieri

Akduman

et al. 2010

Self Cite

IntroductionRF tomography has been proposed to localize and image man-made underground structures and tunnels using a set of arbitrarily distributed narrowband electromagnetic sensors placed above or below the ground. Basically, a set of s transmitters emit a monochromatic signal into the ground; waves impinge upon dielectric anomalies (e.g. tunnels) thus generating a scattered field. Finally, distributed receivers sample the scattered field and relay this information to a base station for post processing. For a deeper understanding of the principles of RF tomography for belowground imaging, see [1]. Currently, RF tomography is based upon the knowledge of the Green function of the scattering problem: analytic expressions are limited only to layered media with planar interfaces [5]. For irregular terrains, a numerical Green function has to be evaluated and here we show a proper reformulation of RF tomography that accounts for numerical Green function that describes the spatial impulse response of the terrain shape. This improvement lead to more reliable reconstructions compared to the case of a planar interface. Figure 1: Geometry RF Tomography Assuming Flat SurfaceWe consider the 3D transmitter-receiver geometry depicted in Fig. 1. The n-th electrically small dipole (length l ) acting as transmitter is located at position a n r , with moment direction ˆn a and current intensity n I , and the m-th electrically small dipole acting as receiver is located at position b m r , with moment direction ˆm b . Each transmitter emits a monochromatic signal with frequency f . We first assume the air-earth interface to be flat: in the next section, we will address the problem of non-flat interface. The air half-space is modeled as free-space medium, while the ground half-space is modeled as an homogeneous medium with background relative dielectric permittivity D ε , 978-1-4244-4968-2/10/$25.00 ©2010 IEEE background conductivity D