Index

Activation— energy, 263— enthalphy, 263— volume, 263

Almansi’s finite strain tensor, 17, 32α-line, 250Amazon submarine fan, 172Anderson’s theory of faulting, 137Angle of internal friction, 135Angle of shear, 135Angular stress distance, 328Anisotropic, 64, 127, 339, 341, 359

— tensor, 341Antisymmetric

— matrix, 334— part, 33, 38, 45— tensor, 35, 337, 348

Archimedes’ principle, 75Argand number, 86, 235Asymmetric moment tensor, 53Auxiliary plane, 275Average stress difference, 287Axial

— compression, 109— stress, 125— tension, 109— vector, 35, 43–46, 56, 348, 354

Backstripping technique, 80Balanced cross-section, 25, 27Basic flow, 216Basin and Range Province, 120, 308Basin inversion, 141β factor, 42, 56, 353β-line, 250Biaxial stress, 109Biharmonic equation, 209, 210Bingham fluid, 237, 239Body force, 64, 67, 209, 235

Body torque, 68Bookshelf faulting, 48Borehole breakout, 115Boudin, 215, 217

— line, 215Boundary condition, 113, 114Boussinesq approximation, 227Breakup unconformity, 98Brittle

— deformation, 126, 156, 178, 303— ductile transition, 305— failure, 126, 305— faulting, 303— material, 126— strength, 132, 135, 276, 304, 305

Brittle-ductile transition, 305Buckling, 185

— load, 188— mode, 188Euler’s critical — load, 188

Buoyancy, 171, 172, 180, 181

Caldera, 255Cayley-Hamilton theorem, 129, 341, 349Central peak crater, 251Characteristic equation, 45, 334, 340, 341Clastic dike, 148–150, 190Coaxial deformation, 11, 13, 14, 17, 41, 42, 44,

353Coefficient of

— friction, 104, 138— internal friction, 135— linear expansion, 160— volume expansion, 161

Coherence, 199Cohesion, 135Columnar joint, 161Compaction, 80Complementary error function, 90

379

380 INDEX

Complex crater, 251Compressive strength, 134Confining pressure, 125, 126Conjugate

— faults, 49, 135— sets, 302— shear planes, 135

Constitutive equation, 128, 129, 153, 154, 156, 174,177, 205, 206, 237–239

Contraction, 339Cooling joint, 161Coulomb-Navier criterion, 131, 135, 279, 302Couple stress, 68Crater

central peak —, 251Euler —, 13impact —, 12, 212multi-ring —, 251peak-ring —, 251

Cross-section balancing, 25Curvature, 175–177, 180, 360

radius of —, 175, 177, 360

Deformation, 3— gradient tensor, 7, 9, 10, 12, 14, 31, 32, 40coaxial —, 11, 13, 14, 17, 41, 42, 44, 353ductile —, 304homogeneous —, 10infinitesimal —, 10, 31–34, 37, 39, 40, 44, 45zero —, 10

Degree of compensation, 197Depth of compensation, 76Deviatoric

— plane, 240— stress, 103, 239, 240, 304— stress space, 327— tensor, 237, 341, 342

Differential stress, 101Diffusion lenfth, 89Dike, 116–118

— swarm, 12, 48, 118, 119clastic —, 148–150ring —, 119

Dilatant fluids, 238Dilatation, 15, 34Dipole moment of vertical density profile, 85Dorn’s equation, 263Drucker-Prager yield criterion, 246Ductile

— deformation, 178, 303, 304— strength, 87

Dummy index, 331, 348, 352Dynamic pressure, 206Dynamic topography, 225

Earth pressure at rest, 158Effective elastic thickness, 178

— of oceanic lithosphere, 181Effective stress, 139Effective viscosity, 260, 261Eigenvalue, 334Eigenvector, 334Ejecta, 70Elastic, 125

— limit, 125, 303Elastic core, 247Elasticity

linear —, 125, 153, 156, 174, 177Elementary orthogonal projector, 338Elongation, 3

quadratic —, 3, 15Enceradus, 315, 321Energy equation, 70Engineering shear strain, 4, 5, 18, 20, 28, 34Epeirogenic movement, 233Epeirogeny, 83, 232Equation

— of motion, 65biharmonic—, 209, 210characteristic —, 45, 334, 340, 341constitutive —, 128, 129, 153, 154, 156, 174,

177, 205, 206, 237–239energy —, 70Navier-Stokes —, 206, 207Rodrigues’ —, 349, 354Stokes —, 206

Equivalent— plastic strain increment, 249— strain rate, 249— stress, 249

Equivalent elastic thickness, 178Error function, 89Euler

— angle, 347— angles, 346— coordinates, 6— description, 6

Extended Tresca yield criterion, 246

INDEX 381

Extended von Mises yield criterion, 246

Fabric attractor, 275Failure

— envelope, 131brittle —, 126, 305

Fault— striation, 271conjugate —, 49mesoscale —, 271orthorhombic — sets, 291

Fletcher-Hallet model, 315Flexural

— backstripping, 83, 173— parameter, 184— rigidity, 178, 180

Flexural-shear folding, 188Fold, 217Foreland basin, 173Fourier transform, 210Fracture

— plane, 131— plane angle, 131— strength, 132

Free— boundary, 109— index, 331— surface, 109

Frictional— sliding, 138— strength, 138

Fry arc, 328

Ganymede, 71, 213Gauss’s divergence theorem, 345Geohistory analysis, 80Geometric seismic moment, 53Geometrical linearity, 32, 153Graben, 22Grain fabric, 28, 352Gravitational

— acceleration, 70— collupse, 85

Green’s finite strain tensor, 16, 17, 32Griffith theory of fracture, 134

Haar-von Karman hypothesis, 254Hawaiian

— Deep, 181, 182

— Ridge, 183— Swell, 225

Heat conduction equation, 88Heat flux, 69Heterogeneous fault-slip data, 281Hinge

— line, 151— zone, 246

Homogeneous fault-slip data, 281Hooke’s law, 156

generalized —, 156Hubbert-Rubey model, 104Hydraulic fracture, 115Hydrofracturing, 115Hydrostatic

— pressure, 64, 108— state of stress, 64

Hypsometry, 77

Icy satellite, 136Ilyushin’s deviatoric stress space, 327Impact crater, 212, 251In-situ stress measurement, 115Incompressible, 9, 208Inelastic deformation, 126Infinitesimal

— deformation, 10, 31–34, 37, 39, 40, 44, 45— strain, 31, 33, 34, 153, 154— strain tensor, 4, 32–34, 38

Initial subsidence, 94Invariant, 154, 340

basic —, 34, 129, 153, 205, 237–239, 327,341, 354

Inverse stress, 287Io, 255Isostasy, 75

local —, 171regional —, 172thermal —, 87

Isostatic compensation, 212Isotropic, 127, 129, 339

Jacobian, 8, 39, 65Japan Sea, 24, 25, 52, 81, 116Joint, 147

— set, 148— system, 148columnar —, 161cooling —, 161

382 INDEX

Jump condition, 113

Kinematic viscosity, 207Kirchhoff’s hypothesis, 176Kyushu, 149

Laglangian— description, 6— Coordinates, 6

Lame’s— constants, 154— stress ellipsoid, 102

Laplacian, 344Layer-parallel shortening, 187Left Cauchy-Green tensor, 14Left stretch tensor, 13Linear

— elastic body, 126, 127, 153— elastic material, 157, 158— elasticity, 153, 154, 156, 174, 177— momentum, 59, 65— rille, 22, 168, 200— stability analysis, 221, 315

LithosphereEffective elastic thickness of —, 181

Lithostatic— pressure, 66, 108— stress, 66

Load cast, 190Lobate scarp, 56Local isostasy, 76, 171Lode angle, 241, 328Logarithmic strain, 3Longitudinal splitting, 133Lunar

— highland, 77— mare, 77— mare basin, 22— maria, 22

Magma ocean, 168Mare Selenitatis, 22, 201Mascon basin, 201Material

— coordinates, 6— derivative, 36— description, 6

Mean flow, 216Mean stress, 103

Mechanics of micropolar continua, 301Mercury, 56, 168Mesoscale fault, 271Micro cracks, 134Middle surface, 174Mineral vein, 23Miranda, 321Mohr

— diagram, 106— envelope, 131

Mohr’s circle, 107Moon, 77, 168, 200, 251M-plane, 275Multi-ring crater, 251

Nabla, 344Natural strain, 3Navier-Stokes equation, 206, 207Newtonian fluid, 206, 237Normal fault regime, 138Normal stress, 60Northeast Japan, 22, 39, 52, 116, 273, 308Null vector, 282Number

Argand —, 86, 235Peclet —, 322, 358, 367Rayleigh —, 231

Object function, 281Oceanic lithosphere

elastic thickness of —, 181Octahedral

— normal stress, 106— plane, 106— shear stress, 106

Ooid, 28Orientale basin, 251Orthogonal

— matrix, 333— tensor, 337

Orthorhombic— fault set, 291— symmetry, 8, 103, 107, 109, 276, 289

Outer trench swell, 182Overburden

— stress, 66, 114, 138, 140, 163Overpressure, 140

Peclet number, 322, 358, 367

INDEX 383

Paleobathymetry, 78, 80Paleomagnetic rotation, 48Palimpsest, 71, 214Passive continental margin, 78, 173P-axis, 279Peak-ring crater, 251Peripheral bulge, 172Permanent strain, 126Perturbation, 216π-plane, 240Plane

— strain, 10, 42, 47, 68, 157, 174, 297, 303— stress, 68, 102, 109, 157

Planetary differentiation, 70Plastic, 126

— body, 237— deformation, 126, 156pseudo— fluid, 238rigid-perfectly — body, 238rigid-perfectly— body, 127visco— body, 237

Platform, 233Poisson effect, 156, 157Poisson’s ratio, 154Polar decomposition, 19, 343

— theorem, 12, 343left —, 343right —, 343

Polygonal terrain, 163Pore

— fluid, 139— fluid pressure, 139— fluid pressure ratio, 140— pressure, 139— water, 139

Post-glacial rebound, 212Post-rift subsidence, 92, 95Potential energy of the lithosphere, 92Power-law

— exponent, 260— fluid, 237, 260

Primary structure, 12Principal

— axes of stress, 101— axis, 7— deviatoric stress, 103— planes of strain, 8— strain, 7

— stress, 101Principle of

— material frame-indefference, 128— material objectivity, 128

Projector, 338elementary orthogonal —, 338

Proportional limit, 125Pseudoplastic fluid, 238Pure shear, 11

— rift, 41— stress, 109

Quadratic elongation, 3, 15Quantitative stratigraphy, 80Quasi-plasticity, 305Quasilinear fluid, 237

Radius of curvature, 175, 177, 360Rayleigh number, 231Reciprocal strain ellipsoid, 8, 16Reduced stress tensor, 277, 278, 287, 327Reference configuration, 38, 40Regional isostasy, 172Reiner-Rivlin fluid, 205Representation theorem, 129Retrodeformable, 27Reverse fault regime, 138Ridge push, 91Rift

— shoulder, 192— stage subsidence, 92simple shear —, 41, 192

Right Cauchy-Green tensor, 14, 16Right stretch tensor, 13Rigid body rotation, 10Rigid-perfectly-plastic body, 127, 238Rodrigues’ equation, 349, 354Rotation

— tensor, 33, 364— vector, 35

Second law of thermodynamics, 237Shear

— force, 178, 179— fracture, 134— modulus, 154, 361— strain, 4, 18, 20, 28, 34, 154— stress, 60, 64, 72, 98, 356— stress vector, 357

384 INDEX

— zone, 18simple —, 11, 18–21, 28, 238, 239

Shear-rate dependent visocity, 237Shear-thickening viscosity, 238Shear-thinning viscosity, 238Simple crater, 251Simple shear rift, 41, 192Simple stretching model, 92Single layer folding, 217, 219–222, 224, 225, 268Slip line, 250

— field, 250— theory, 248

Slip tendency, 288Southwest Japan, 23, 118, 119Spatial

— coordinates, 6— description, 6

Spin tensor, 38Stokes equation, 206Stokes’ theorem, 346Stokesian fluid, 206Strain, 3

— ellipse, 8— ellipsoid, 7— incremental theory, 248— marker, 4— rate, 37— rate tensor, 38definition of —, 3engineering shear —, 4, 5, 18, 20, 28, 34infiniteismal —, 33, 34, 153, 154infiniteismal — tensor, 4, 33, 34, 38infinitesimal —, 31logarithmic —, 3natural —, 3permanent —, 126plane —, 10, 157reciprocal — ellipsoid, 16reciprocal — ellipsoid, 8shear —, 4, 18

Stratigraphy, 23quantitative —, 80

Stream function, 208Strength profile, 305Stress

— axis, 101— concentration, 134— difference, 286, 328

— inversion, 281, 327— ratio, 103— space, 239— tensor, 60— vector, 59axial —, 125biaxial —, 109boundary condition of —, 113classes of —, 108couple —, 68deviatoric —, 103, 239, 240differential —, 101effective —, 139equivalent —, 249hydrostatic —, 64hydrostatic state of —, 64inverse —, 287lithostatic —, 66mean —, 103normal —, 60, 63plane —, 68, 102, 109, 157principal —, 101principal deviatoric —, 103pure shear —, 109shear —, 60, 63tectonic —, 103thermal —, 160triaxial —, 109yield —, 125

Stretch, 3Stretching

— factor, 94— tensor, 38

Striae, 271Strike-slip regime, 138Subsidence

— curve, 83— due to mantle convection, 225— due to sediment load, 78— of foreland basin, 173initial —, 94post-rift —, 92, 95rift-stage —, 92syn-rift, 95syn-rift —, 93thermal —, 94, 98

Suface force, 64Symmetric

INDEX 385

— matrix, 334— tensor, 337

Syn-rift subsidence, 93, 95

Tangent-lineation diagram, 275T-axis, 279Tectonic

— age, 199— inversion, 141— stress, 103

Tectonics, vTensile strength, 132Tension fracture, 133Tensor, 337

— of elastic constants, 156Almansi’s finite strain —, 17, 32anisotropic —, 341antisymmetric —, 35, 337, 348asymmetric moment —, 53basic invariants of —, 340contraction of —, 339deformation gradient —, 7, 9, 10, 12, 14, 31,

32, 40deviatoric —, 237, 341, 342Green’s finite strain —, 16, 17, 32infinitesimal strain —, 4, 32–34, 38left Cauchy-Green —, 14left stretch —, 13orthogonal —, 337reduced stress —, 287right Cauchy-Green —, 14, 16right stretch —, 13rotation —, 33, 364spin —, 38strain rate —, 38stress —, 60stretching —, 38symmetric —, 337unit —, 337velocity gradient —, 38zero —, 337

Terrain softening, 215Theorem

Cayley-Hamilton —, 341Gauss’s divergence —, 345polar decomposition —, 12, 343representation —, 129Stokes’ —, 346

Thermal

— diffusivity, 88— expansion coefficient, 89, 161— isostasy, 87— stress, 160— subsidence, 94, 98

Thrust sheet, 104Tibetan Plateau, 86Time constant for thermal conduction, 88Topographic load, 172Transient crater, 252Transpression, 50Transtension, 50Tresca yield criterion, 243Triaxial stress, 109Triple

— scalar product, 331— vector product, 331

Uncoupled thermoelastic theory, 161Uniaxial

— compression, 109— tension, 109

Unit tensor, 337

Vector— product, 329axial —, 348scalar product of —, 329stress —, 59triple — product, 331

Velocity gradient tensor, 38Venus, 163Viscoplastic body, 237Viscosity, 206

dynamic —, 207effective —, 260, 261kinematic —, 207shear-rate dependent —, 237shear-thickening —, 238shear-thinning —, 238

von Mises yield criterion, 244Vorticity, 44, 48, 56, 206, 207, 209, 235, 301

Wallace-Bott hypothesis, 273Wavenumber, 189

— selection, 189Western Interior Basin, 173, 233Whole lithosphere failure, 248, 307Wrinkle ridge, 22, 168, 200

386 INDEX

Yield— condition, 242— function, 242— locus, 244— point, 125— stress, 125, 239— surface, 242Drucker-Prager — criterion, 246extended — Tresca criterion, 246extended — von Mises criterion, 246Tresca — criterion, 243von Mises — criterion, 244

Young’s modulus, 154, 156

Zero— deformation, 10— tensor, 337