subsurface imaging with ground penetrating radar carey m. rappaport censsis dept. elect. and comp....

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  • Carey M. Rappaport CenSSISDept. Elect. and Comp. EngineeringNortheastern UniversitySubsurface Imaging with Ground Penetrating RadarApril 2011 Carey Rappaport 2011

  • Propagation Characteristics in Real SoilConcepts of dielectric constant, electrical conductivityVelocity, attenuation, dispersion, reflection and refraction at interfacesMoisture and density dependence Nonmetallic target scattering in lossy mediaRough surface effects

  • Wave and Helmholtz Equation:Lossy Media (Soil, Water, Tissue)The electric field for a wave traveling in linear, homogeneous, non-dispersive, and lossy medium is given by: 2E - E/ t - 2E/ t2 = 02E + k2E=0k = [00 (1 - j tan)] = - j For time harmonic wave, the Helmholtz Equation remains: = conductivity (S/m), ranging from ~ 0 to 107But the dispersion relation is modified by :tan = / ( 0)With Loss Tangent defined by:

  • Electromagnetic Waves in Lossy MediaImpedancePropagation (Wave) Number

  • Propagation in Soil is Frequency DependentFrequency f (1 MHz 10 GHz)Dielectric constant (1 25) Electrical conductivity (0.0001 1)Wave Number, k (meters-1)

  • Exact derivation of Wave Numbers in Lossy MediaStarting from scalar Helmholtz Eqn.where the complex wave number is:

  • Decibel ScaleThe decibel (dB) is a logarithmic transformation of ratios of amplitudes or powers. A power ratio R corresponds to r = 10log10R (dB). An amplitude ratio R corresponds to 20log10R (dB).

    1/10 power 10log10(1/10)= -10 dB. 1/2 power 10log10(1/2) = -3 dB.

    1/10 amplitude 20log10(1/10) = -20 dB. 1/2 amplitude 20log10(1/2) = -6 dB.

    An intensity attenuation by a factor exp(-a) is equivalent to -4.3a dB .

    The decibel changes multiplication into additionWhen a wave is transmitted through a cascade of two media resulting in intensity reduction by factors R1 and R2, the overall reduction is a factor R = R1R2.The change in dB units is r = r1+ r2.If the rate of attenuation of a medium is a dB/m, a distance z (m), corresponds to attenuation of az (dB). Courtesy of B. Saleh, BU

  • Logarithms Without CalculatorsLog 10 = 1.0Log 1 = 0Log 2 ~ 0.3 Log 5 = Log 10/2 = Log 10 Log 2 = 0.7 Log 3 ~ Log 101/2 = Log 10 = 0.5-Log 4 = Log 22 = 2 Log 2 = 0.6Log 6 = Log (2 X 3) = Log 2 + Log 3 = 0.8Log 8 = Log 23 = 3 Log 2 = 0.9Log10 e = 1/ Loge 10 = 1/2.302

  • Penetration Depth v. Frequency for Various Dielectric MaterialsPenetration Depth d10= Distance for the power to drop by a factor of 10 (10 dB) (19%) (26%)

  • Wavelengths for Various Dielectric MaterialsWavelength: l= 2/

  • Fields for Different Soil TypesDry SandYPGSaturated SandA.P. HillBosnian (Alicia); 25% moisture

  • Exercise: Microwave Penetration in SoilDetermine the loss in dB for a wave at 300 GHz penetrating 1.0 mm into uniform soil and then reflecting back out for a) Yuma and b) AP Hill Soil Hint: Extrapolate the loss curves from previous slide.

  • Extrapolated Penetration Depths at 300 GHz (Terahertz range)Return signal power (in dB) from a radar source incident on a metallic target buried a depth D in lossy soil: -20 D/d

    Soil Typed=Penetration DepthRadar Return (dB) (D = 1 mm)Yuma PG55.7 cm-0.036Dry Sand4.57 cm-0.44Wet Sand0.31 cm-6.5Bosnian soil54.3 mm-368A P Hill40.0 mm-500

  • Wire on Flat Ground:Bosnian Soil 26% MoistureE-field parallel to wire

  • Wire on Rough Ground:Bosnian Soil 26% MoistureE-field parallel to wire (Ez)

  • Modeling Soil Media for Electromagnetic Wave PropagationType of modelsSimulated wave response

  • Summary of Dielectric Mixing Models Source: Kansas Geological Survey, 2001

    CategoryMethodTypesAdvantagesDisadvantagesReferencesPhenomeno-logical Relate frequency dependent behavior to characteristic relaxation times.Cole-Cole; Debye, Lorentz- Component properties/geometry relationships unnecessary- Dependent on frequency-specific parameters.Powers, 1997; Ulaby 1986; Wang, 1980.VolumetricRelate bulk dielectric properties of a mixture to the dielectric properties of its constituents.ComplexRefractive Index (CRI); Arithmetic average; Harmonic average; Lichetenecker-Rother; - Volumetric data relatively easy to obtain.- Do not account for micro-geometry of components, -Do not account for electrochemical interaction between components.Alharthi 1987; Birchak 1974; Knoll, 1996; Lange, 1983; Lichtenecker 1931; Roth 1990; Wharton 1980.Empirical and Semi-empiricalMathematical relationship between dielectric and other measurable properties.Logarithmic; Polynomial.- Easy to develop quantitative relationships, -Able to handle complex materials in models.- No physical justification for the relationship, -Valid only for the specific data used to develop the relation may not be applicable to other data sets.Dobson 1985; Olhoeft 1975; Topp 1980; Wang 1980.Effective mediumCompute dielectric properties by successive substitutions.Bruggeman-Hanai-Sen (BHS)- Accurate for known geometries.- Cumbersome to implement, - Must choose number of inputs, initial material, and order and shape of replacement material.Sen 1981; Ulaby 1986.

  • Fourier Transformtft1/tShort pulse in time transforms into broadband frequency signalLong pulse in time transforms into narrow frequency signal

  • Temporal DispersionPulses in time are composed of many frequencies (Fourier relationship)Most real material has frequency-dependent dielectric parametersEach frequency component travels at a different velocity and with a different decay rateAmplitude of each frequency component lessens by a different amount with distance

  • Dispersion of a Pulse 3 Fourier Components of Pulse at t0Each component travels at a different velocity (dispersion)Amplitude of component lessens in time (loss)

  • Modeling Dispersion for Easy Transformation to Time DomainStandard (2nd Order) Debye Model: simple form for complex permittivity, easily transformed to time domain differential equation Lorentz Model: 2nd order when N = 1 [Cole-Cole Model is more accurate, not easily converted to time domain]

  • Conversion of Dispersion Models to Time DomainReplace e by D/E and multiply through by denominatorDebye

  • Modeling Dispersion for Easy Transformation to Time DomainZ-Transform model keeps real permittivity constant, and matches conductivity to measured values in terms of Z-1 [4 Zero Model]

  • Dielectric Constant and Conductivity for Puerto Rican Clay Loam (1.2 g/cc)Frequency (MHz)050010003456789Frequency (MHz)0500100010-410-310-210-1RappaportDebyedata2.5%5%10%2.5%5%10%

  • Real and Imaginary Wave Number for Puerto Rican Clay Loam (1.2g/cc)77.588.599.50102030405060Log Frequency (1/m)77.588.599.5-3-2.5-2-1.5-1-0.50Log Frequency- (1/m)RappaportDebyedata2.5%5%10%2.5%5%10%

  • Wave Propagation Variation as a Function of Clay Loam Moisture

  • Rough Surface Test GeometryTransverse Position (cm)Depth (cm)

  • Non-Metallic Mine Scattered Field 10 cm Deep - Smooth Surface010002000300040005000600070008000900010000-0.4-0.3-0.2-0.100.10.20.30.4Time (ps)Relative Amplitude

  • Non-Metallic Mine Scattered Field (about 10 cm burial) - Rough Surface010002000300040005000600070008000900010000-0.4-0.3-0.2-0.100.10.20.30.4Time (ps)Relative Amplitude

  • Non-Metallic Mine Scattered Field 10 cm depth a) Flat Surface, b) Rough Surface

  • Shape Determination of Buried Non-Metallic Targets, Multiple Single-Frequency Observations80 cmSquare TargetAirSoild11.28 cm20 cm60 cmCircular TargetAirSoild10 cm20 cm60 cm10 cm80 cmSandy soil: es = 2.5, ss = 0.01Target: em = 2.9, sm = 0.004

  • Different Buried Test Target Shapes

  • Scattered Field - Real Part

  • Scattered Field - Real Part

  • Surface Field - MagnitudeHorizontal Position (cm)Intensity-40-200204000.010.020.030.040.051000 MHz, depth = 5cmsquare circle diamondstar blob -40-20020400.020.0250.030.0350.04500 MHz, depth = 5cm

  • Scattered Field - Aspect Ratio DependenceHorizontal Position (cm)Circle, r = 5.64 cmSandy Soile = 2.5, s = 0.01freq = 500 MHz depth = 5 cmHeight (cm)

  • Distinguishing Shapes of 3D Buried Objects under Rough Surfaces: GeometryPoint SourceRough SurfaceMine10 cm4 cm5 cm10 cmSoil

  • Total Ex Field from an x-Directed Point Source, with a Buried Non-Metallic Square Target

  • Total Ex Field from x-Directed Point Source, with a Buried Non-Metallic Square Target (back view)

  • Comparison of Total Ex Field for Buried Non-Metallic Square and Circular Targets

  • Comparison of Scattered Ex Field for Buried Non-Metallic Square and Circular Targets

  • Soil Packing Affects Greatly Scattering: 3D FDFD with Short Cylindrical Target TNT in 26% moist Bosnian soil at 960 MHz

  • Surface Scattering Clutter Increases with Frequency. Example: 4 GPR Freq., PRCL 10% moisture, 1.4 g/ccTransverse Position (cm)Non-Metallic TargetSoilAir-20-15-10-505101520Depth (cm)-505101520253035

  • Display Format for each of Four FrequenciesMine scattered field: smooth surfaceScattered field: rough surface with mineScattered field: rough surface onlyMine scattered field: rough surface

  • 480 MHz

  • 960 MHzTransverse Position (cm)Depth (cm)Mine scattered field: smooth surface-20-10010200102030-0.2-0.100.10.2Transverse Position (cm)Depth (cm)Scattered field: rough surface with mine-20-10010200102030-0.2-0.100.10.2Transverse Position (cm)Depth (cm)Scattered field: rough surface only-20-10010200102030-0.2-0.100.10.2Transverse Position (cm)Depth (cm)Mine scattered field: rough surface-20-10010200102030-0.2-0.100.10.2Amplitude Relative to IncidentAmplitude Relative to IncidentAmplitude Relative to IncidentAmpli