Table Of ContentThe Seismoelectric Method
The Seismoelectric
Method
Theory and applications
André Revil
AssociateProfessor,ColoradoSchoolofMines,Golden,CO,USA
DirecteurdeRechercheattheNationalCentreforScientificResearch(CNRS),
ISTerre,Grenoble,France
Abderrahim Jardani
AssociateProfessor,MaîtredeConférence,UniversitédeRouen,Mont-Saint-Aignan,France
Paul Sava
AssociateProfessor,ColoradoSchoolofMines,Golden,CO,USA
Allan Haas
SeniorEngineeringGeophysicist,hydroGEOPHYSICS,Inc.,Tuscon,AZ,USA
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LibraryofCongressCataloging-in-PublicationData
Revil,André,1970–
Theseismoelectricmethod:theoryandapplications/AndréRevil,associateprofessor,ColoradoSchool
ofMines,GoldenCO,USA[and]DirecteurdeRechercheattheNationalCentreforScientificResearch(CNRS),
ISTerre,Grenoble,France,AbderrahimJardani,associateprofessor,MaîtredeConference,Universitéde
Rouen,Mont-Saint-Aignan,France,PaulSava,associateprofessor,ColoradoSchoolofMines,GoldenCO,
USA,AllanHaas,seniorengineeringgeophysicist,HydroGEOPHYSICS,Inc.,Tuscon,AZ,USA.
pages cm
Includesindex.
ISBN978-1-118-66026-3(cloth)
1. Seismicprospecting. 2. Prospecting–Geophysicalmethods. I. Jardani,Abderrahim. II. Sava,Paul.
III. Haas,Allan. IV. Title.
TN269.8.R482015
622.1592–dc23
2015002784
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1 2015
ThisbookisdedicatedtotwoRussianscientistswhodevelopedtheelectrokineticconcepts
attachedtotheseismoelectriceffects.
AndreyGermogenovichIvanov(1907–1972).Sonofateacherofgeography,Andrey
worked at the Institute of Earth Physics (SU Academia of Sciences) in 1930s and up to
mid-1950s. His work was mostly concerned with the seismoelectrical method, but he
worked also on low-frequency electromagnetic methods. Andrey wrote two handbooks.
Thefirstbookwasconcernedwithgeophysicalmethodsappliedtothedetectionofmineral
deposits.Itwaspublishedin1961andincollaborationwithFeofanBubleinikov.Thesecond
bookwasentitledPhysicsinInvestigationsofEarthInterior(1971).AndreyGermogenovich
Ivanov is usually credited to have been the first scientist to record seismoelectric effects
infieldconditions.
YakovIl’ichFrenkel(1894–1952).FrenkelwasbornonFebruary10,1894,inthesouth-
ernRussiancityofRostov-on-Don.HewasaveryinfluentialRussianscientistduringthe
first halfofthe20thcentury.Geophysics wasafieldofFrenkel’s earlyinterest.In1944,
FrenkelvisitedtheInstituteofTheoreticalGeophysicsinMoscow.There,hebecameinter-
estedintheworkofAndreyGermogenovichIvanov.Asmentionedabove,Ivanovwasthe
firsttodiscover,in1939,thatthepropagationofseismicwavesinsoilswasaccompaniedby
the appearance of an electrical field. Ivanov recognized that this new phenomenon was
causedbythepressuredifferencebetweentwopointsinwetsoilresultingfromtheprop-
agationoflongitudinal(P-)waves.Frenkelmodeledthewetsoilasatwo-phasematerial,
andheformulatedthefirstcontinuumhydromechanicaltheoryforwavepropagationin
porousmedia.FrenkeldiscoveredtheexistenceofthesecondcompressionalP-wave(usu-
allynamedlatertheBiotslowP-wave),buthedismissedtheelectricaleffectsassociatedwith
thistypeofwaveasunimportantbecauseofthestrongdampingofthisslowP-wave.Frenkel
wasthefirsttounderstandthattheseismoelectriceffectrecordedbyIvanovcouldbeelec-
trokineticinnature.Indeed,thepresenceofwaterinaporousmaterialisresponsibleforthe
formationofanelectricdoublelayeronthemineralsurface.Therelativemovementofthe
excesschargeoftheelectricaldiffuselayer(theexternalpartoftheelectricaldoublelayer)
duetothepassageofaseismicwaveisresponsibleforthegenerationofasourcecurrent
density.Thesecurrentsareresponsibleinturnforthegenerationofelectromagneticdistur-
bances. Frenkel’s 1944 paper “On the theory of seismic and seismoelectric phenomena
in moist soil” is the first to theoretically describe wave propagation in porous media.
Acompletetheorywashoweverproducedin1956byMauriceBiot.Thelinearporoelasticity
theoryshouldgenerallybereferredtoastheBiot–FrenkeltheoryrathertheBiottheoryas
doneclassicallyintheliterature.HislifeandcontributionsaredescribedinthebookYakov
IlichFrenkel:HisWork,LifeandLettersbyFrenkel,V.Ya.,andBirkhäuserVerlag(1996).
Contents
ForewordbyBerndKulessa,xi
ForewordbyNielsGrobbe,xii
Preface,xiv
Acknowledgments,xvi
1 Introductiontothebasicconcepts, 1
1.1 Theelectricaldoublelayer, 1
1.1.1 Thecaseofsilica, 2
1.1.1.1 Asimplifiedapproach, 2
1.1.1.2 Thegeneralcase, 8
1.1.2 Thecaseofclays, 10
1.1.3 Implications, 14
1.2 Thestreamingcurrentdensity, 15
1.3 Thecomplexconductivity, 17
1.3.1 Effectiveconductivity, 18
1.3.2 Saturatedclayeymedia, 19
1.4 Principlesoftheseismoelectricmethod, 22
1.4.1 Mainideas, 22
1.4.2 Simplemodelingwiththeacousticapproximation, 25
1.4.2.1 Theacousticapproximationinafluid, 25
1.4.2.2 Extensiontoporousmedia, 26
1.4.3 Numericalexampleofthecoseismicand
seismoelectricconversions, 27
1.5 Elementsofporoelasticity, 28
1.5.1 Theeffectivestresslaw, 28
1.5.2 Hooke’slawinporoelasticmedia, 31
1.5.3 Drainedversusundrainedregimes, 31
1.5.4 Wavemodesinthepureundrainedregime, 33
1.6 Shorthistory, 34
1.7 Conclusions, 36
2 Seismoelectrictheoryinsaturatedporousmedia, 42
2.1 Poroelasticmediumfilledwithaviscoelasticfluid, 42
2.1.1 Propertiesofthetwophases, 42
2.1.2 Propertiesoftheporousmaterial, 45
2.1.3 Themechanicalequations, 49
2.1.3.1 Strain–stressrelationships, 49
2.1.3.2 Thefieldequations, 52
2.1.3.3 Noteregardingthematerialproperties, 53
2.1.3.4 Forcebalanceequations, 53
2.1.4 TheMaxwellequations, 53
vii
viii Contents
2.1.5 Analysisofthewavemodes, 54
2.1.6 Syntheticcasestudies, 56
2.1.7 Conclusions, 59
2.2 PoroelasticmediumfilledwithaNewtonianfluid, 59
2.2.1 ClassicalBiottheory, 59
2.2.2 Theu–pformulation, 60
2.2.3 Descriptionoftheelectrokineticcoupling, 62
2.3 Experimentalapproachanddata, 62
2.3.1 Measuringkeyproperties, 62
2.3.1.1 Measuringthecationexchangecapacity
andthespecificsurfacearea, 62
2.3.1.2 Measuringthecomplexconductivity, 63
2.3.1.3 Measuringthestreamingpotentialcouplingcoefficient, 63
2.3.2 Streamingpotentialdependenceonsalinity, 63
2.3.3 StreamingpotentialdependenceonpH, 66
2.3.4 Influenceoftheinertialeffect, 66
2.4 Conclusions, 69
3 Seismoelectrictheoryinpartiallysaturatedconditions, 73
3.1 Extensiontotheunsaturatedcase, 73
3.1.1 Generalizedconstitutiveequations, 73
3.1.2 Descriptionofthehydromechanicalmodel, 77
3.1.3 Maxwellequationsinunsaturatedconditions, 81
3.2 Extensiontotwo-phaseflow, 81
3.2.1 GeneralizationoftheBiottheoryintwo-phaseflowconditions, 81
3.2.2 Theu–pformulationfortwo-phaseflowproblems, 83
3.2.3 Seismoelectricconversionintwo-phaseflow, 85
3.2.4 Theeffectofwatercontentonthecoseismicwaves, 86
3.2.5 Seismoelectricconversion, 90
3.3 Extensionoftheacousticapproximation, 91
3.4 Complexconductivityinpartiallysaturatedconditions, 92
3.5 Comparisonwithexperimentaldata, 93
3.5.1 Theeffectofsaturation, 93
3.5.2 Additionalscalingrelationships, 93
3.5.3 RelativecouplingcoefficientwiththeBrooksand
Coreymodel, 95
3.5.4 RelativecouplingcoefficientwiththeVanGenuchtenmodel, 96
3.6 Conclusions, 97
4 Forwardandinversemodeling, 101
4.1 Finite-elementimplementation, 101
4.1.1 Finite-elementmodeling, 101
4.1.2 Perfectlymatchedlayerboundaryconditions, 102
4.1.3 Boundaryconditionsataninterface, 104
4.1.4 Descriptionoftheseismicsource, 104
4.1.5 Lateralresolutionofcross-holeseismoelectricdata, 104
4.1.6 Benchmarktestofthecode, 105
4.2 Syntheticcasestudy, 105
4.2.1 Simulationofwaterfloodingofa
NAPL-contaminatedaquifer, 105
