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COSTissupportedbythe
EUFrameworkProgrammeHorizon2020
COSTAc(onTU1208
“CivilEngineeringApplica(onsofGroundPenetra(ngRadar”
Introduc(ontoelectromagne(cmodellingofGPR&
overviewonavailablecommercialandfreesoHwaretools
LaraPajewski
SapienzaUniversity,Rome,Italy
EMModellingforGPR–Whatdowemodel?
§ Knowing the iniAal and boundary condiAons (properAes of theelectromagneAc source; geometrical and physical features of the
scenario), the goal is to find a soluAon to the GPR forwardsca-ering problemand calculate the electromagneAc field in any
pointofthespaceandinanyAmeinstant.
EMModellingforGPR–Why?
§ ToimproveourunderstandingofGPR
GPR radargrams oMen have no resemblance to the subsurface or
structures over which the profile was recorded. Various factors,
including the innate design of the survey equipment and the
complexityofelectromagneAcpropagaAonintheground/structure,
candisguisecomplexstructuresrecordedonGPRreflecAonprofiles.
An EM simulator canhelpus to understandhow target structures
gettranslatedintoGPRradargrams.ItcanalsoshowthelimitaAons
of GPR, highlight its capabiliAes and help us to understandwhere
andinwhatenvironmentsthistechniquecanbeeffecAvelyused.
§ TochoosethemostproperGPRequipmentforasurvey.
§ To aid the interpreta(on of complex data sets and find out
unknowndetailsabouttheinvesAgatedstructure/subsurface.
§ To test new data-processing/imaging algorithms or assess the
effecAvenessofexisAngones.
§ Todesignandop(misenewGPRantennas.
§ AforwardEMsolvercanbeusedaspartofaninverseEMsolver
(automaAcinterpretaAonofGPRdata).
EMModellingforGPR–Why?
Geometry SyntheAcRadargram
EMModellingforGPR–Why?
This is a simple scenario, the main purpose of an electromagneAc
simulatorisnottosolvesuchasimpleproblem…
FielddistribuAonasafuncAonofAme
EMModellingforGPR–Why?
…butsAll,thismovieeffecAvely
showshowtheelectromagneAc
simulatorcanhelpustovisualize
andunderstandthe
electromagneAcphenomena
takingplaceinaGPRscenario.
EMModellingforGPR–Howcanwedoit?
§ By solving theMaxwell’s equa(ons governing the propagaAon
and scaZering of electromagneAc waves, subject to iniAal and
boundarycondiAons.
WalloftheWarsawUniversityLibrary
EMModellingforGPR–Maxwell’sEqua(ons
Faraday’sLawofinduc(on
Ampere-MaxwellLaw
describeshowaAmevaryingmagneAcfieldcreatesanelectricfield
statesthatmagneAcfieldscanbegeneratedintwoways:byan
electricalcurrent(theoriginal"Ampère'slaw")andbychanging
electricfields("Maxwell'saddiAon”)
EMModellingforGPR–Maxwell’sEqua(ons
Gauss’ElectricandMagne(cLaws
Con(nuityofElectricCharge(notpartofMaxwell’sequaAons)
describestherelaAonship
betweentheelectricfieldand
theelectricchargesthatcauseit
statesthatthereareno
"magneAccharges”
anempiricallawexpressing(local)charge
conservaAon;mathemaAcallyitisanautomaAc
consequenceofMaxwell’seqs.;itstatesthatthe
divergenceofthecurrentdensityJisequaltothe
negaAverateofchangeofthechargedensityρ
EMModellingforGPR–Maxwell’sEqua(ons
Integralequa(ons
EMModellingforGPR–Maxwell’sEqua(ons
ByusingStoke’sanddivergencetheorems…
…wegetthedifferen(alequa(ons
Differen(alEqua(ons
EMModellingforGPR–Maxwell’sEqua(ons
ThesearefirstorderparAaldifferenAalequaAonswhichexpresstherelaAonsbetweenthe
fundamentalelectromagneAcfieldquanAAesandtheirdependenceontheirsources.
EMModellingforGPR–Maxwell’sEqua(ons
§ In Maxwell’s equaAons, the field vectors are assumed to be
single-valued, bounded, conAnuous funcAons of posiAon and
Ame.
§ InordertosimulatetheGPRresponsefromaparAculartargetor
set of targets, the integral or differenAal Maxwell’s equaAons
have tobe solved subject to the geometryof theproblemand
theiniAalcondiAons.
EMModellingforGPR–Cons(tu(veRela(ons
§ ForsimplecaseswheretheelectricalproperAescanbeassumed
to be frequency independent, the convoluAons reduce to
mulAplicaAons. For isotropic media, the tensors reduce to
scalars.Inthesecases,computaAonsaresimplified.
EMModellingforGPR–
HowcanwesolveMaxwell’sequa(ons?
§ Analy(callywithgreatbraineffortandonlyforsimplescenarios!
Lotsofbrainpower Li-lecompu9ngpower
§ Numerically with less brain effort
andformorecomplexandrealisAc
scenarios!
Lotsofcompu9ngpower Li-lebrainpower
Integral /Differential Formulations Frequency /Time Domain
EMModellingforGPR–
HowcanwesolveMaxwell’sequa(ons?
§ HigheraccuracyàlongerAme&highermemoryrequirements.
§ AnalyAcal-numerical techniques contemplaAng a relaAvely
simplemathemaAcalformulaAonandamostlynumericalnature
areeasytoimplementandversaAle.
§ To develop and implement full-wave formulaAons with higher
analyAcal complexity, a deeper physical insight into the
considered problem is needed. Usually, these approaches are
lessversaAleand,whenapplicable,theyarefastandefficient.
Computa(onalissues
Accuracy Execu(on(meMemory
requirements
EMModellingforGPR–
Whatisthebestcomputa(onalmethod?
§ MethodofMoments(MoM)
§ BoundaryElementMethod(BEM)
§ FiniteElementMethod(FEM)
§ FiniteDifferenceFrequencyDomain(FDFD)
§ ParAalElementEquivalentCircuit
(PEEC)
§ FiniteIntegraAonTechnique(FIT)§ AsymptoAcMethods(GTD/UTD/
PO)
§ FiniteDifferenceTimeDomain
(FDTD)
§ TransmissionLineMatrixMethod
(TLM)
§ FiniteElementTimeDomain
(FETD)
§ FiniteVolumeTimeDomain
(FVTD)
§ GeneralizedMulApoleTechnique
(GMT)
§ Time-DomainMethodof
Moments(TDMoM)
§ CylindricalandSphericalWave
Approach(CWAandSWA)
§ OtherMethods
EMModellingforGPR–CommercialsoHware
§ AnsoMHFSS§ CSTMicrowaveStudio
§ COMSOLMulAphysics
§ XFDTD§ …
Agoodlistisat
www.cvel.clemson.edu/modeling/EMAG/csoM.html
Agoodlistisat
hZp://www.cvel.clemson.edu/modeling/EMAG/free-codes.html
• NEC2 - theNumericalElectromagneAcsModeling (NEC)codeis a widely used 3D simulator based on the method ofmoments. Itwas developed at Lawrence LivermoreNaAonalLaboratory more than 10 years ago and has been compiledand run onmany different computer systems. It uses a textinterface. There a several free or inexpensive graphicalinterfacesthatdopre-andpost-processingofNEC2models.Agoodfreeinterfaceis4nec2.
• Thereisa2DFDTDsolverincludedinmatGPR(freewaretoolforGPRdataprocessing)
EMModellingforGPR–Freewaretools
• MEEP–aFDTDsimulaAonsoMwarepackagedevelopedatMIT.Itsupports 1D/2D/3D/cylindrical problems, distributed-memoryparallelism,anddispersiveandnonlinearmedia.PMLboundariesareimplemented.ThesoMwareiscompletelyscriptableviabothC++andScheme(GNUGuile)interfaces.
• GprMax – a FDTD solver, for 2D (TMz)/3D numericalmodelling.The first version was developed by Prof. Antonis Giannopoulos(The University of Edinburgh, UK) in 1996. In the past 3 years,gprMaxhasbeensignificantly improvedby theresearch teamofTheUniversity of Edinburgh and as a contribuAon to the AcAonTU1208. E2GPR is a free graphical interface developed by aresearchteamofSapienza/RomaTreUniversity,IT,todopre-andpost-processingofgprMaxmodels.
EMModellingforGPR–Freewaretools
www.gprmax.com
www.GPRadar.eu
COSTissupportedbythe
EUFrameworkProgrammeHorizon2020
Thank you!
Join COST Action TU1208!
www.GPRadar.eu [email protected]
