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132 CHAPTER 3. TERRESTRIAL SYSTEMS 3.1.11 Efficient reconstruction of dispersive dielectric profiles using TDR Student assistant Patrick Leidenberger, Benedikt Oswald, Kurt Roth Abstract Time Domain Reflectometry (TDR) has become an indispensable technique for measuring the water content of soils. We use a numerical model for TDR signal propagation in dispersive dielectric materials. We couple this model with a genetic algorithm to invert measured TDR traces. To make this approach more efficient we use hierarchical spatial resolution. Figure 3.11: Reconstruction of a measured TDR trace (Grenzhof test site, Heidelberg; 30cm three-rod probe); reflection coefficient ρ vs. time. The ohmic and dispersive dielectric profiles (spatial resolution 3.75cm) for the calculated trace are generated with a hierarchical genetic algorithm. Background A TDR instrument transmits a fast rise time pulse on a TDR probe. The probe usually consists of parallel conductors. Variations of impedance along the probe causes a partial reflection of the signal, which is measured. Furthermore the conductivity and the frequencydependent dielectric properties between the conductors of the probe have an affect on the measured signal. In this study we want to extract the dielectric parameters from TDR traces measured at the Grenzhof test site at Heidelberg to get the water content. Therefore we reconstruct hierarchical the spatial distributed dielectric parameters along the probe with a genetic algorithm. Funding Deutsche Forschungsgemeinschaft (Project No. 1080-8/2) Methods and results We have implemented a explicite time domain solver for the transmission line equations (3.3) and (3.4) that uses Debye model for dispersive media. ∂v ∂x ∂i ∂x � = − R ′ � ′ ∂ + L i (3.3) ∂t � = − G ′ � ′ ∂ + C v (3.4) ∂t The transmission line equations with piecewise constant parameters describes a TDR probe. We couple this solver with a genetic algorithm, in order to reconstruct the dispersive dielectric and ohmic profiles along the TDR probe. The genetic algorithm generates a population with different individuals (a number of different sets of profiles). For every individual we calculate a synthetic TDR trace and compare it with the measured trace. Then the new population is created from the old one by crossing the best individuals and random mutation. We use the genetic approach here, because the error landscape contains a lot of local minima. We implement a hierarchical spatial reconstruction of the profiles for more efficiency. Therefor we start with a coarse spatial resolution of the parameter profile. If the calculated TDR traces from new individuals do not match better to the measured trace for a while we increase the spatial resolution, by cutting old intervals into halves. This method does not only speed up the profile reconstruction process but also leads to a smoother parameter profile. Outlook/Future work The code will be tested on TDR traces measured with long probes (1m or more). Such a long, vertical installed TDR probe will provide a lot of informations about grounds properties in a simple way. Main publication Leidenberger, P., Oswald, B. and Roth, K. (2005). Efficient reconstruction of dispersive dielectric profiles using time domain reflectometry (TDR). Hydrology and Earth System Sciences Discussions, 2 (4), 1449-1502.
3.1. SOIL PHYSICS 133 3.1.12 3D Full-wave, electromagnetic model of ground penetrating radar systems Participating scientist Benedikt Oswald Abstract Ground penetrating radar (GPR) has been increasingly used in hydrological applications for subsurface structure investigation. The size of structures that can be resolved is intimately related to the relevant wavelength of the GPR signal. A finite element time domain 3-dimensional electrodynamics code has been implemented for studying GPR signal propagation. +Y[m] +Y[m] 3 3 2 2 1 1 +Z[m] 2 1 0 0 +Z[m] 2 1 0 0 1 1 2 2 3 +X[m] -6.08 -12.83 -19.59 -26.34 -33.10 +X[m] 3 -39.85 -46.61 -53.36 pdelta_310_340tsno1400.job.cmp Figure 3.12: An electromagnetic wave is launched from a horizontal dipole antenne on the soil surface (upper side of green regon) and scattered off 2 dielectric objects (2 yellow regions) buried in the underground (inside green region); lower plot: dielectric parameter distribution modeling two spheres; upper plot: contour plot of the normalized electric field intensity [dB] for timestep 1400 of the simulation. Background Increasing GPR resolution requires shorter wavelength λ which demands higher frequency f. Due to attenuation of the GPR signal proportional to frequency, there is a tradeoff between resolution and penetration depth. For increasing resolution a full-wave electromagnetic analysis of GPR signal propagation is essential. There is evidence that sub-wavelength structures may be manifest in the radargram. We will use a 3-dimensional, full-wave model of a simplified GPR system. We adopt a near field electromag- 8.99 7.86 6.74 5.61 4.49 3.36 2.24 1.11 [dB] [-] netic approach, originally [Ohtsu & Kobayashi, 2004] employed in scanning near field optical microscopy (SNOM). We study the GPR’s response to sub-wavelength sized objects and investigate the capability of GPR to resolve those structures. Funding IUP Methods and results We have implemented a 3-dimensional finite element code to solve the electric field vector wave equation (3.5) in the time domain [Oswald & Roth, 2005a]. ∇ × 1 µ ∇ × E + σ ∂E ∂t + ɛ∂2 E ∂2 = −∂J t ∂t (3.5) Locally refined, tetrahedral grids are used to describe the geometry of the GPR configuration; this allows for detailed models of delicate geometrical features. In order to model open region problems we employ an absorbing boundary condition (ABC). The code has been validated on a Hertzian dipole radiating into free space. We study a simplified GPR configuration of two spherical objects separated by a sub-wavelength distance, 0.3 m in the shown example, buried in the subsurface. The distance between the sphericals is small with respect to the dominang wavelength λ. The dielectric structure of the buried spheres is mapped into the electric field observed on the surface. Outlook/Future work The code will be used in order to study more complicated underground structures; in particular we want to investigate synthetical radargram generation in order to compare those to measured radargrams. We will use dielectric material properties measured from real soil [Oswald et al. , 2006] to obtain a realistic model. This will be one of the first steps towards the challenge of GPR full-wave inversion. Main publication Oswald et al. [2006]
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Institut für Umweltphysik und Arbe
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Contents 1 Introduction/Overview of
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CONTENTS 7 3.2.1 Glaciological pilo
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