Index

Activation Body torque, 68 — energy, 263 Bookshelf faulting, 48 — enthalphy, 263 Borehole breakout, 115 — volume, 263 Boudin, 215, 217 Almansi’s finite strain tensor, 17, 32 — line, 215 α-line, 250 Boundary condition, 113, 114 Amazon submarine fan, 172 Boussinesq approximation, 227 Anderson’s theory of faulting, 137 Breakup unconformity, 98 Angle of internal friction, 135 Brittle Angle of shear, 135 — deformation, 126, 156, 178, 303 Angular stress distance, 328 — ductile transition, 305 Anisotropic, 64, 127, 339, 341, 359 — failure, 126, 305 — tensor, 341 — faulting, 303 Antisymmetric — material, 126 — matrix, 334 — strength, 132, 135, 276, 304, 305 — part, 33, 38, 45 Brittle-ductile transition, 305 — tensor, 35, 337, 348 Buckling, 185 Archimedes’ principle, 75 — load, 188 Argand number, 86, 235 — mode, 188 Asymmetric moment tensor, 53 Euler’s critical — load, 188 Auxiliary plane, 275 Buoyancy, 171, 172, 180, 181 Average stress difference, 287 Axial Caldera, 255 — compression, 109 Cayley-Hamilton theorem, 129, 341, 349 — stress, 125 Central peak crater, 251 — tension, 109 Characteristic equation, 45, 334, 340, 341 — vector, 35, 43–46, 56, 348, 354 Clastic dike, 148–150, 190 Coaxial deformation, 11, 13, 14, 17, 41, 42, 44, Backstripping technique, 80 353 Balanced cross-section, 25, 27 Coefficient of Basic flow, 216 — friction, 104, 138 Basin and Range Province, 120, 308 — internal friction, 135 Basin inversion, 141 — linear expansion, 160 β factor, 42, 56, 353 — volume expansion, 161 β-line, 250 Coherence, 199 Biaxial stress, 109 Cohesion, 135 Biharmonic equation, 209, 210 Columnar joint, 161 Bingham fluid, 237, 239 Compaction, 80 Body force, 64, 67, 209, 235 Complementary error function, 90

379 380 INDEX

Complex crater, 251 — deformation, 178, 303, 304 Compressive strength, 134 — strength, 87 Confining pressure, 125, 126 Dummy index, 331, 348, 352 Conjugate Dynamic pressure, 206 — faults, 49, 135 Dynamic topography, 225 — sets, 302 — shear planes, 135 Earth pressure at rest, 158 Constitutive equation, 128, 129, 153, 154, 156, 174, Effective elastic thickness, 178 177, 205, 206, 237–239 — of oceanic lithosphere, 181 Contraction, 339 Effective stress, 139 Cooling joint, 161 Effective viscosity, 260, 261 Coulomb-Navier criterion, 131, 135, 279, 302 Eigenvalue, 334 Couple stress, 68 Eigenvector, 334 Crater Ejecta, 70 central peak —, 251 Elastic, 125 Euler —, 13 — limit, 125, 303 impact —, 12, 212 Elastic core, 247 multi-ring —, 251 Elasticity peak-ring —, 251 linear —, 125, 153, 156, 174, 177 Cross-section balancing, 25 Elementary orthogonal projector, 338 Curvature, 175–177, 180, 360 Elongation, 3 radius of —, 175, 177, 360 quadratic —, 3, 15 Enceradus, 315, 321 Deformation, 3 Energy equation, 70 — gradient tensor, 7, 9, 10, 12, 14, 31, 32, 40 Engineering shear strain, 4, 5, 18, 20, 28, 34 coaxial —, 11, 13, 14, 17, 41, 42, 44, 353 Epeirogenic movement, 233 ductile —, 304 Epeirogeny, 83, 232 homogeneous —, 10 Equation infinitesimal —, 10, 31–34, 37, 39, 40, 44, 45 — of motion, 65 zero —, 10 biharmonic—, 209, 210 Degree of compensation, 197 characteristic —, 45, 334, 340, 341 Depth of compensation, 76 constitutive —, 128, 129, 153, 154, 156, 174, Deviatoric 177, 205, 206, 237–239 — plane, 240 energy —, 70 — stress, 103, 239, 240, 304 Navier-Stokes —, 206, 207 — stress space, 327 Rodrigues’ —, 349, 354 — tensor, 237, 341, 342 Stokes —, 206 Differential stress, 101 Equivalent Diffusion lenfth, 89 — plastic strain increment, 249 Dike, 116–118 — strain rate, 249 — swarm, 12, 48, 118, 119 — stress, 249 clastic —, 148–150 Equivalent elastic thickness, 178 ring —, 119 Error function, 89 Dilatant fluids, 238 Euler Dilatation, 15, 34 — angle, 347 Dipole moment of vertical density profile, 85 — angles, 346 Dorn’s equation, 263 — coordinates, 6 Drucker-Prager yield criterion, 246 — description, 6 Ductile Extended Tresca yield criterion, 246 INDEX 381

Extended von Mises yield criterion, 246 — Ridge, 183 — Swell, 225 Fabric attractor, 275 Heat conduction equation, 88 Failure Heat flux, 69 — envelope, 131 Heterogeneous fault-slip data, 281 brittle —, 126, 305 Hinge Fault — line, 151 — striation, 271 — zone, 246 conjugate —, 49 Homogeneous fault-slip data, 281 mesoscale —, 271 Hooke’s law, 156 orthorhombic — sets, 291 generalized —, 156 Fletcher-Hallet model, 315 Hubbert-Rubey model, 104 Flexural Hydraulic fracture, 115 — backstripping, 83, 173 Hydrofracturing, 115 — parameter, 184 Hydrostatic — rigidity, 178, 180 — pressure, 64, 108 Flexural-shear folding, 188 — state of stress, 64 Fold, 217 Hypsometry, 77 Foreland basin, 173 Fourier transform, 210 Icy satellite, 136 Fracture Ilyushin’s deviatoric stress space, 327 — plane, 131 Impact crater, 212, 251 — plane angle, 131 In-situ stress measurement, 115 — strength, 132 Incompressible, 9, 208 Free Inelastic deformation, 126 — boundary, 109 Infinitesimal — index, 331 — deformation, 10, 31–34, 37, 39, 40, 44, 45 — surface, 109 — strain, 31, 33, 34, 153, 154 Frictional — strain tensor, 4, 32–34, 38 — sliding, 138 Initial subsidence, 94 — strength, 138 Invariant, 154, 340 Fry arc, 328 basic —, 34, 129, 153, 205, 237–239, 327, 341, 354 Ganymede, 71, 213 Inverse stress, 287 Gauss’s divergence theorem, 345 Io, 255 Geohistory analysis, 80 Isostasy, 75 Geometric seismic moment, 53 local —, 171 Geometrical linearity, 32, 153 regional —, 172 Graben, 22 thermal —, 87 Grain fabric, 28, 352 Isostatic compensation, 212 Gravitational Isotropic, 127, 129, 339 — acceleration, 70 — collupse, 85 Jacobian, 8, 39, 65 Green’s finite strain tensor, 16, 17, 32 Japan Sea, 24, 25, 52, 81, 116 Griffith theory of fracture, 134 Joint, 147 — set, 148 Haar-von Karm´ an` hypothesis, 254 — system, 148 Hawaiian columnar —, 161 — Deep, 181, 182 cooling —, 161 382 INDEX

Jump condition, 113 Mechanics of micropolar continua, 301 Mercury, 56, 168 Kinematic viscosity, 207 Mesoscale fault, 271 Kirchhoff’s hypothesis, 176 Micro cracks, 134 Kyushu, 149 Middle surface, 174 Mineral vein, 23 Laglangian Miranda, 321 — description, 6 Mohr — Coordinates, 6 — diagram, 106 Lame’s´ — envelope, 131 — constants, 154 Mohr’s circle, 107 — stress ellipsoid, 102 Moon, 77, 168, 200, 251 Laplacian, 344 M-plane, 275 Layer-parallel shortening, 187 Multi-ring crater, 251 Left Cauchy-Green tensor, 14 Left stretch tensor, 13 Nabla, 344 Linear Natural strain, 3 — elastic body, 126, 127, 153 Navier-Stokes equation, 206, 207 — elastic material, 157, 158 Newtonian fluid, 206, 237 — elasticity, 153, 154, 156, 174, 177 Normal fault regime, 138 — momentum, 59, 65 Normal stress, 60 — rille, 22, 168, 200 Northeast Japan, 22, 39, 52, 116, 273, 308 — stability analysis, 221, 315 Null vector, 282 Lithosphere Number Effective elastic thickness of —, 181 Argand —, 86, 235 Lithostatic Peclet´ —, 322, 358, 367 — pressure, 66, 108 Rayleigh —, 231 — stress, 66 Load cast, 190 Object function, 281 Lobate scarp, 56 Oceanic lithosphere Local isostasy, 76, 171 elastic thickness of —, 181 Lode angle, 241, 328 Octahedral Logarithmic strain, 3 — normal stress, 106 Longitudinal splitting, 133 — plane, 106 Lunar — shear stress, 106 — highland, 77 Ooid, 28 — mare, 77 Orientale basin, 251 — mare basin, 22 Orthogonal — maria, 22 — matrix, 333 — tensor, 337 Magma ocean, 168 Orthorhombic Mare Selenitatis, 22, 201 — fault set, 291 Mascon basin, 201 — symmetry, 8, 103, 107, 109, 276, 289 Material Outer trench swell, 182 — coordinates, 6 Overburden — derivative, 36 — stress, 66, 114, 138, 140, 163 — description, 6 Overpressure, 140 Mean flow, 216 Mean stress, 103 Peclet´ number, 322, 358, 367 INDEX 383

Paleobathymetry, 78, 80 — stress, 101 Paleomagnetic rotation, 48 Principle of Palimpsest, 71, 214 — material frame-indefference, 128 Passive continental margin, 78, 173 — material objectivity, 128 P-axis, 279 Projector, 338 Peak-ring crater, 251 elementary orthogonal —, 338 Peripheral bulge, 172 Proportional limit, 125 Permanent strain, 126 Pseudoplastic fluid, 238 Perturbation, 216 Pure shear, 11 π-plane, 240 — rift, 41 Plane — stress, 109 — strain, 10, 42, 47, 68, 157, 174, 297, 303 — stress, 68, 102, 109, 157 Quadratic elongation, 3, 15 Planetary differentiation, 70 Quantitative stratigraphy, 80 Plastic, 126 Quasi-plasticity, 305 — body, 237 Quasilinear fluid, 237 — deformation, 126, 156 pseudo— fluid, 238 Radius of curvature, 175, 177, 360 Rayleigh number, 231 rigid-perfectly — body, 238 Reciprocal strain ellipsoid, 8, 16 rigid-perfectly— body, 127 Reduced stress tensor, 277, 278, 287, 327 visco— body, 237 Reference configuration, 38, 40 Platform, 233 Regional isostasy, 172 Poisson effect, 156, 157 Reiner-Rivlin fluid, 205 Poisson’s ratio, 154 Representation theorem, 129 Polar decomposition, 19, 343 Retrodeformable, 27 — theorem, 12, 343 Reverse fault regime, 138 left —, 343 Ridge push, 91 right —, 343 Rift Polygonal terrain, 163 — shoulder, 192 Pore — stage subsidence, 92 — fluid, 139 simple shear —, 41, 192 — fluid pressure, 139 Right Cauchy-Green tensor, 14, 16 — fluid pressure ratio, 140 Right stretch tensor, 13 — pressure, 139 Rigid body rotation, 10 — water, 139 Rigid-perfectly-plastic body, 127, 238 Post-glacial rebound, 212 Rodrigues’ equation, 349, 354 Post-rift subsidence, 92, 95 Rotation Potential energy of the lithosphere, 92 — tensor, 33, 364 Power-law — vector, 35 — exponent, 260 — fluid, 237, 260 Second law of thermodynamics, 237 Primary structure, 12 Shear Principal — force, 178, 179 — axes of stress, 101 — fracture, 134 — axis, 7 — modulus, 154, 361 — deviatoric stress, 103 — strain, 4, 18, 20, 28, 34, 154 — planes of strain, 8 — stress, 60, 64, 72, 98, 356 — strain, 7 — stress vector, 357 384 INDEX

— zone, 18 — inversion, 281, 327 simple —, 11, 18–21, 28, 238, 239 — ratio, 103 Shear-rate dependent visocity, 237 — space, 239 Shear-thickening viscosity, 238 — tensor, 60 Shear-thinning viscosity, 238 — vector, 59 Simple crater, 251 axial —, 125 Simple shear rift, 41, 192 biaxial —, 109 Simple stretching model, 92 boundary condition of —, 113 Single layer folding, 217, 219–222, 224, 225, 268 classes of —, 108 Slip line, 250 couple —, 68 — field, 250 deviatoric —, 103, 239, 240 — theory, 248 differential —, 101 Slip tendency, 288 effective —, 139 Southwest Japan, 23, 118, 119 equivalent —, 249 Spatial hydrostatic —, 64 — coordinates, 6 hydrostatic state of —, 64 — description, 6 inverse —, 287 Spin tensor, 38 lithostatic —, 66 Stokes equation, 206 mean —, 103 Stokes’ theorem, 346 normal —, 60, 63 Stokesian fluid, 206 plane —, 68, 102, 109, 157 Strain, 3 principal —, 101 — ellipse, 8 principal deviatoric —, 103 — ellipsoid, 7 pure shear —, 109 — incremental theory, 248 shear —, 60, 63 — marker, 4 tectonic —, 103 — rate, 37 thermal —, 160 — rate tensor, 38 triaxial —, 109 definition of —, 3 yield —, 125 engineering shear —, 4, 5, 18, 20, 28, 34 Stretch, 3 infiniteismal —, 33, 34, 153, 154 Stretching infiniteismal — tensor, 4, 33, 34, 38 — factor, 94 infinitesimal —, 31 — tensor, 38 logarithmic —, 3 Striae, 271 natural —, 3 Strike-slip regime, 138 permanent —, 126 Subsidence plane —, 10, 157 — curve, 83 reciprocal — ellipsoid, 16 — due to mantle convection, 225 reciprocal — ellipsoid, 8 — due to sediment load, 78 shear —, 4, 18 — of foreland basin, 173 Stratigraphy, 23 initial —, 94 quantitative —, 80 post-rift —, 92, 95 Stream function, 208 rift-stage —, 92 Strength profile, 305 syn-rift, 95 Stress syn-rift —, 93 — axis, 101 thermal —, 94, 98 — concentration, 134 Suface force, 64 —difference, 286, 328 Symmetric INDEX 385

— matrix, 334 —diffusivity, 88 — tensor, 337 — expansion coefficient, 89, 161 Syn-rift subsidence, 93, 95 — isostasy, 87 — stress, 160 Tangent-lineation diagram, 275 — subsidence, 94, 98 T-axis, 279 Thrust sheet, 104 Tectonic Tibetan Plateau, 86 — age, 199 Time constant for thermal conduction, 88 — inversion, 141 Topographic load, 172 — stress, 103 Transient crater, 252 Tectonics, v Transpression, 50 Tensile strength, 132 Transtension, 50 Tension fracture, 133 Tresca yield criterion, 243 Tensor, 337 Triaxial stress, 109 — of elastic constants, 156 Triple Almansi’s finite strain —, 17, 32 — scalar product, 331 anisotropic —, 341 — vector product, 331 antisymmetric —, 35, 337, 348 asymmetric moment —, 53 Uncoupled thermoelastic theory, 161 basic invariants of —, 340 Uniaxial contraction of —, 339 — compression, 109 deformation gradient —, 7, 9, 10, 12, 14, 31, — tension, 109 32, 40 Unit tensor, 337 deviatoric —, 237, 341, 342 Green’s finite strain —, 16, 17, 32 Vector infinitesimal strain —, 4, 32–34, 38 — product, 329 left Cauchy-Green —, 14 axial —, 348 left stretch —, 13 scalar product of —, 329 orthogonal —, 337 stress —, 59 reduced stress —, 287 triple — product, 331 right Cauchy-Green —, 14, 16 Velocity gradient tensor, 38 right stretch —, 13 Venus, 163 rotation —, 33, 364 Viscoplastic body, 237 spin —, 38 Viscosity, 206 strain rate —, 38 dynamic —, 207 stress —, 60 effective —, 260, 261 stretching —, 38 kinematic —, 207 symmetric —, 337 shear-rate dependent —, 237 unit —, 337 shear-thickening —, 238 velocity gradient —, 38 shear-thinning —, 238 zero —, 337 von Mises yield criterion, 244 Terrain softening, 215 Vorticity, 44, 48, 56, 206, 207, 209, 235, 301 Theorem Cayley-Hamilton —, 341 Wallace-Bott hypothesis, 273 Gauss’s divergence —, 345 Wavenumber, 189 polar decomposition —, 12, 343 — selection, 189 representation —, 129 Western Interior Basin, 173, 233 Stokes’ —, 346 Whole lithosphere failure, 248, 307 Thermal Wrinkle ridge, 22, 168, 200 386 INDEX

Yield — condition, 242 — function, 242 — locus, 244 — point, 125 — stress, 125, 239 — surface, 242 Drucker-Prager — criterion, 246 extended — Tresca criterion, 246 extended — von Mises criterion, 246 Tresca — criterion, 243 von Mises — criterion, 244 Young’s modulus, 154, 156

Zero — deformation, 10 — tensor, 337