# 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