Introduction to Petroleum Seismology

706 Pages·2005·159.528 MB·English

by  Luc T. Ikelle, Lasse Amundsen

INTRODUCTION TO
PETROLEUM SEISMOLOGY
Luc T. Ikelle
Lasse Amundsen
Investigations in Geophysics Series No. 12
Michael R. Cooper, series editor
Anthony F. Gangi, volume editor
Society of Exploration Geophysicists
Tulsa, Oklahoma, USA
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ISBN0-931830-46-X(Series)
ISBN1-56080-129-8(Volume)
©2005bySocietyofExplorationGeophysicists
Allrightsreserved.Thisbookorpartshereofmaynotbereproducedinanyformwithout
permissioninwritingfromthepublisher.
Published2005
PrintedintheUnitedStatesofAmerica
LibraryofCongressCataloging-in-PublicationData
Introductiontopetroleumseismology/LucT.Ikelle,LasseAmundsen.
p.cm.—(Investigationsingeophysics;no.12)
Includesbibliographicalreferencesandindex.
ISBN1-56080-129-8(alk.paper)
1.Petroleum—Prospecting.2.Petroleumengineering.3.Seismicwaves.4.Seismic
prospecting.5.Petroleum—Geology. I.Ikelle,L.(Luc)II.Amundsen,Lasse,1957-III.
Series.
TN271.P4I652005
622'.1828–dc22
2005051614
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This book is dedicated to
Caroline Ikelle, my loving and caring wife
—Luc T. Ikelle
Eli Reisaeter, Christine, and Birgitte, my loving family
—Lasse Amundsen
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SEG
wishes to thank the following for their generous contributions to
Introduction to Petroleum Seismology
Statoil ASA
Texas A&M University
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OVERVIEW
Chapter1 Introduction .................................................................... 1
Chapter2 TheRelationshipbetweenPropagationofSeismicWavesandParticleMotions
inIsotropicMedia ............................................................... 17
Chapter3 PartitionofEnergyatanInterface .................................................. 63
Chapter4 TheFourierRepresentationofSeismicSignals ....................................... 127
Chapter5 CharacterizationofSeismicSignalsbyStatisticalAverages............................. 181
Chapter6 TheConceptsofReciprocityandGreen’sFunctions................................... 233
Chapter7 AcquisitionGeometriesandSeismicData ........................................... 255
Chapter8 WavefieldSampling.............................................................. 315
Chapter9 WavefieldDecompositionintoP-andS-wavesandUpgoing
andDowngoingWaves ........................................................... 361
Chapter10 MultipleAttenuation ............................................................. 395
Chapter11 AnExampleofanInverseProblem:LinearizedSeismicInversion ....................... 445
Chapter12 AnisotropyandBeyond........................................................... 517
AppendixA SomeTerminologyofPetroleumGeology ........................................... 615
AppendixB VelocitiesandDensitiesofReservoirFluids.......................................... 619
AppendixC AReviewofFinite-differenceModeling:ExplicitImplementation....................... 623
AppendixD DefinitionsofSomeoftheIntegralTransformsUsedinPetroleumSeismology ............ 641
AppendixE 3D-to-2DTransformationand2D-to-3DTransformation ............................... 649
AppendixF ADerivationoftheLinearizedForwardProblem ..................................... 653
References .................................................................................. 659
Index....................................................................................... 669
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TABLE OF CONTENTS
Preface ..................................................................................... xix
Acknowledgments............................................................................ xxi
AbouttheAuthors............................................................................ xxiii
Chapter1 Introduction .................................................................... 1
The“BottomLine”ofPetroleumSeismology................................................. 1
PetroleumTraps ....................................................................... 1
HowDoesPetroleumSeismologyWork? .................................................. 1
ChallengesofPetroleumSeismology........................................................ 3
ExploringforStratigraphicTraps ......................................................... 3
ExploringtheSubsaltStratigraphicColumn ................................................ 3
ExploringtheSubbasaltStratigraphicColumn .............................................. 6
EnvironmentalChallengesofExploringtheArctic .......................................... 7
ExploringforGasHydrates.............................................................. 8
PetroleumSeismologistsinProductionofOilandGas ....................................... 10
TechnologicalAdvancesoutsidetheE&PIndustry ............................................ 11
TechnologicalAdvancesinsidetheE&PIndustry.............................................. 11
InstrumentedOilFields ................................................................. 11
MeasurementwhileDrilling ............................................................. 12
ReservoirModel ....................................................................... 12
Box1.1 MarineElectromagneticSurveyingforHydrocarbonDetection......................... 13
TheScopeofthisBook ................................................................... 15
Chapter2 TheRelationshipbetweenPropagationofSeismicWavesandParticleMotions
inIsotropicMedia ............................................................... 17
AnExampleofWavePropagation .......................................................... 17
TheAssumptionofaContinuousMedium ................................................... 19
ContinuousandIsotropicMedia.......................................................... 19
ParticlePositionsandCoordinateSystems ................................................. 20
HomogeneousMediaandHeterogeneousMedia ............................................ 20
InternalForces(Stresses).................................................................. 20
TheStressTensor ...................................................................... 20
Box2.1 ScalarProductandVectorProduct................................................. 21
ExamplesofStresses ................................................................... 24
Example1 .......................................................................... 24
Example2 .......................................................................... 24
Example3 .......................................................................... 25
Box2.2 ConventionsofSummation....................................................... 25
AbbreviatedNotationoftheStressTensor.................................................. 26
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TableofContents vii
Box2.3 ChangeofOrthonormalBasis:Vectors ............................................. 26
Box2.4 EulerAngles................................................................... 28
TheStressField ....................................................................... 28
Box2.5 ChangesofOrthonormalBasis(StressTensor) ...................................... 29
PrincipalStresses ...................................................................... 29
ParticleDisplacementandStrain ........................................................... 30
ParticleDisplacement................................................................... 30
StrainTensor.......................................................................... 31
AbbreviatedNotationoftheStrainTensor.................................................. 32
ExamplesofStrainTensors.............................................................. 33
Example4 .......................................................................... 33
Example5 .......................................................................... 33
Example6 .......................................................................... 34
ElasticModuli........................................................................... 34
LinearElasticity(Hooke’sLaw):GeneralCase ............................................. 34
Hooke’sLawwithAbbreviatedTensorNotation ............................................ 35
Box2.6 ChangeofOrthonormalBasis(StiffnessTensor)..................................... 36
LinearElasticity(Hooke’sLaw):IsotropicCase............................................. 36
PhysicalInterpretationofElasticModuliforanIsotropicMedium ............................. 38
EquationsofElastodynamicWaveMotion ................................................... 39
Newton’sEquationofMotion ............................................................ 39
ElasticWaves:P-wavesandS-waves ...................................................... 41
Box2.7 HelmholtzDecompositionofVectorFields ......................................... 43
Box2.8 PlaneWaves ................................................................... 44
ParametersofIsotropic,ElasticRockFormations ........................................... 45
RelatingElasticParameterstoPetrophysicalParameters...................................... 46
SourcesofSeismicWaves ................................................................. 49
DefinitionofSourcesintheContextofPetroleumSeismology ................................ 49
EquationsofWaveMotionandtheGeneralizedHooke’sLaw ................................. 49
ExamplesofSeismic-waveRadiation ..................................................... 50
GeometricSpreading ..................................................................... 53
Box2.9 AnotherFormoftheEquationsofWaveMotion ..................................... 54
Box2.10 AcousticEquationsofWaveMotion.............................................. 54
Box2.11 TheEquivalenceFluidModelforP-wavesinaSolid ................................ 55
Isotropy,Anisotropy,Homogeneity,andHeterogeneity......................................... 56
ExercisesinProblemSolving .............................................................. 60
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viii TableofContents
Chapter3 PartitionofEnergyatanInterface................................................. 63
Introduction............................................................................. 63
Huygens’Principle ....................................................................... 63
Fermat’sPrinciple........................................................................ 64
Snell’sLaw ............................................................................. 64
ReflectionandTransmission ............................................................. 64
Snell’sLaw:Fluid-fluidInterface ......................................................... 65
Snell’sLaw:Solid-solidandFluid-solidInterfaces .......................................... 67
Snell’sLaw:Air-waterandAir-solidInterfaces ............................................. 70
Whatisafreesurface?................................................................ 70
Snell’slawatthefreesurface .......................................................... 71
TraveltimeEquationsforaHorizontalInterface ............................................... 72
DirectWaves.......................................................................... 72
RefractedWaves ....................................................................... 73
ReflectedP-PandS-SWaves ............................................................ 74
P-SConvertedWaves................................................................... 75
ConversionPointOffset................................................................. 76
Box3.1 Traveltimein1DMedia ......................................................... 78
TurningRays.......................................................................... 79
VariationofLinearVelocitywithDepth ................................................... 79
Box3.2 TheNotionofrmsVelocityfor1DMedia .......................................... 81
Box3.3 Dix’sFormula ................................................................. 84
BoundaryConditionsfortheElastodynamicField ............................................. 85
Solid-solidInterface.................................................................... 85
Fluid-solidInterface.................................................................... 85
Vacuum-solidInterface ................................................................. 86
Fluid-fluidInterface .................................................................... 86
Fromelastodynamictoacousticfields:Abriefbackground ................................. 86
Boundaryconditionsattheinterfacebetweentwofluids.................................... 86
InterfacebetweenVacuumandFluid ...................................................... 86
Zoeppritz’sEquationsforaHorizontalInterface............................................... 87
Zoeppritz’sEquations:Solid-solidInterface ................................................ 88
Reflectionandtransmissioncoefficientsforadownward-travelingincidentP-wave ............. 89
Specialcase:µconstant .............................................................. 91
Specialcase:V andρ constant ........................................................ 91
S
Specialcase:Normalincidence ........................................................ 91
Reflectionandtransmissioncoefficientsforadownward-travelingincidentSV-wave............ 91
Reflectionandtransmissioncoefficientsforincidentwavesfrombelow ....................... 92
Zoeppritz’sEquations:Fluid-solidInterface ................................................ 92
Box3.4 R/TCoefficientsinTermsofSlowness:Solid-solidInterface .......................... 93
Zoeppritz’sEquations:Vacuum-solidInterface.............................................. 94
Zoeppritz’sEquations:Fluid-fluidInterface ................................................ 94
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TableofContents ix
Box3.5 R/TCoefficientsinTermsofSlowness:Fluid-solidInterface .......................... 95
ReflectionandTransmissionCoefficientsfortheEnergyofSeismicWaves ...................... 95
Normalincidence .................................................................... 95
Obliqueincidence.................................................................... 96
Examples............................................................................. 96
Example1 .......................................................................... 96
Example2 .......................................................................... 97
Example3 .......................................................................... 98
Example4 .......................................................................... 98
Example5 .......................................................................... 98
SurfaceWaves........................................................................... 98
MotivationsforStudyingSurfaceWaves................................................... 100
EvanescentPlaneWaves ................................................................ 101
PhaseVelocityofScholteandRayleighWaves.............................................. 102
Rayleighwaves...................................................................... 104
Scholtewaves:Afluidhalf-spaceonasolidhalf-space..................................... 105
Scholtewaves:Afluidlayeraboveasolidhalf-space ...................................... 105
Surface-waveParticleMotion ............................................................ 106
LinearizedZoeppritz’sEquations ........................................................... 107
MatrixFormofZoeppritz’sEquations..................................................... 107
LinearizedVersionsofReflectionCoefficients .............................................. 107
ApplicationtoAVAAnalysis:P-PReflections .............................................. 111
Box3.6 SomeProbableValuesofReflectionCoefficientsatNormalIncidence................... 113
ApplicationtoAVAAnalysis:P-PandP-SReflections ....................................... 113
DippingInterface ........................................................................ 114
TraveltimeEquationforRefractedWaves .................................................. 114
TraveltimeEquationforReflectedWaves .................................................. 116
Diffractions ............................................................................. 118
AnIllustrationofDiffractions............................................................ 119
TraveltimeEquationforRefractedWaves .................................................. 119
TraveltimeEquationforReflectedWaves .................................................. 121
ExercisesinProblemSolving .............................................................. 123
Chapter4 TheFourierRepresentationofSeismicSignals ...................................... 127
SignalsandSystems ...................................................................... 127
Signals ............................................................................... 127
Systems .............................................................................. 128
Box4.1 PeriodicandTransientSignals.................................................... 128
TheCosineWave:ConceptofFrequency .................................................... 129
Frequency ............................................................................ 129
Delays ............................................................................... 129
AUsefulFormofCosineWaves.......................................................... 130
TheFourierSeries........................................................................ 130
BasisRepresentationforSignals.......................................................... 131
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x TableofContents
Box4.2 OrthonormalBasisoftheSpaceofSignals:TheVectorSpaceAnalogy.................. 132
TheFourierSeries:GeneralCase ......................................................... 132
TheFourierSeries:EvenandOddFunctions ............................................... 134
Example1:TheFourierSeriesofSawtoothWaves .......................................... 135
Example2:TheFourierSeriesofSquareWaves ............................................ 136
TheFourierTransform .................................................................... 138
TheFourierTransformofPeriodicFunctions ............................................... 139
TheFourierTransformofaNonperiodicSignal ............................................. 139
Box4.3 FourierTransformandSquareIntegrableFunctions .................................. 141
Example1:TheFourierTransformoftheExponentialFunction ............................... 141
Box4.4 NyquistFrequency.............................................................. 142
Example2:TheFourierTransformofaSymmetricalRectangularPulse ........................ 142
PropertiesoftheFourierTransform ....................................................... 143
TheMultidimensionalFourierTransform .................................................. 144
SamplingTheoremandDiscreteFourierTransform............................................ 144
DiscreteSignal ........................................................................ 145
Aliasing .............................................................................. 146
ReconstructionoftheContinuousSignalfromitsDiscreteSamples ............................ 148
TheDiscreteFourierTransform .......................................................... 149
SomePropertiesoftheDiscreteFourierTransform .......................................... 150
Convolution............................................................................. 150
DefinitionoftheImpulseResponseofaLinearSystem....................................... 151
ExamplesoftheImpulseResponseofaLinearSystem....................................... 151
Example1 .......................................................................... 151
Example2 .......................................................................... 152
Example3 .......................................................................... 152
ConvolutionTheorem................................................................... 153
Example1 .......................................................................... 154
Example2 .......................................................................... 154
ConvolutionSum ...................................................................... 155
Smoothness ........................................................................... 155
SeismicResolution..................................................................... 156
Filtering ................................................................................ 157
BasicTerminologyofFiltering ........................................................... 158
InverseFiltering ....................................................................... 159
AnExampleofInverseFilters:MultipleAttenuation......................................... 159
Classification............................................................................ 161
ALimitationoftheEffectivenessoftheFourierTransformAnalysis.............................. 162
ExamplesofNonstationarySignals ....................................................... 162
Example:Asignalwithimpulses ....................................................... 162
Example:Aquadraticchirpsignal ...................................................... 164
Example:Asignalwithashutdownperiod ............................................... 164
TheWindowedFourierTransform ........................................................ 165
Example:Asignalwithimpulses ....................................................... 166
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