SP2DINV: A 2 D forward and inverse code for streaming potential problems
Résumé
The self-potentialmethodcorrespondstothepassivemeasurementoftheelectrical field inresponseto the occurrenceofnaturalsourcesofcurrentintheground.Oneofthesesourcescorrespondstothe streaming currentassociatedwiththe flow ofthegroundwater.Wecanthereforeapplytheself- potentialmethodtorecovernon-intrusivelysomeinformationregardingthegroundwater flow.We first solvetheforwardproblemstartingwiththesolutionofthegroundwater flowproblem,thencomputing the sourcecurrentdensity,and finally solvingaPoissonequationfortheelectricalpotential.Weusethe finite-element methodtosolvetherelevantpartialdifferentialequations.Inordertoreducethenumber of (petrophysical)modelparametersrequiredtosolvetheforwardproblem,weintroducedaneffective charge densitytensoroftheporewater,whichcanbedetermineddirectlyfromthepermeabilitytensor for neutralporewaters.Thesecondaspectofourworkconcernstheinversionoftheself-potentialdata using Tikhonovregularizationwithsmoothnessandweightingdepthconstraints.Thisapproachaccounts for thedistributionoftheelectricalresistivity,whichcanbeindependentlyandapproximately determined fromelectricalresistivitytomography.Anumericalcode,SP2DINV,hasbeenimplemented in Matlabtoperformboththeforwardandinversemodeling.Threesyntheticcasestudiesarediscussed.