Cambridge University Press 978-1-107-03506-5 — Structural Geology: a Quantitative Introduction David D

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Cambridge University Press 978-1-107-03506-5 — Structural Geology: A Quantitative Introduction David D. Pollard , Stephen J. Martel Index More Information

INDEX

acceleration buoyancy mass, 85, 88 particle, 52, 92 neutral, 389, 409 momentum, 89, 91–92 accuracy, 73 Burgers circuit, 165 constitutive law acoustic impedance, 271 Burgers vector, 165, 170 linear elastic, 134, 325 Airborne Laser Swath Mapping, 42, 310, Byerlee’s law, 368 linear viscous, 331, 410 313 continuum Airy stress function, 238, 283 calculus material, 79, 85, 89, 230, 235, 279 Anderson’s standard state, 334, 408 vector, 43 mathematical, 79 angle canonical model, 18 continuum mechanics, 230 geographic, 39, 45 bending, 323 contour, 27 propagation, 251–252 buckling, 334 contour map, 27 rotation, 289 faulting, 279 contraction, 106 Anisotropy of Magnetic Susceptibility, fracturing, 230 controversy 385 intrusion, 411 laccolith-stock, 405 anticline, 272, 303, 310, 313 shearing, 365 convention fault-cored, 339 cataclasis, 152, 163 geologic, 28, 36 antiform, 303–304, 316, 319 distributed, 152 on-in, 55, 91 arc length, 43, 332 localized, 152 RH/SF, 165, 168 differential, 318 cataclasite, 260, 295, 368 right-hand, 33–34 Archimedes’ principle, 8 Cauchy’s first law, 92, 135, 206, coordinate asthenosphere, 4–5, 7 330, 333 Cartesian, 30, 39, 41, 55, 62, 411 axis, 28 Cauchy’s formula, 60, 127, 232, 234, 282, cylindrical, 401 crystallographic, 348 334 geographic, 28, 34, 39 fold, 350 Cauchy’s laws of motion, 176, 230, 235, spherical, 411 azimuth, 34, 39 279, 282, 324, 331, 333, 365 Coulomb criterion, 121, 125, 371 Cauchy’s second law, 94, 117, 135, 206, crack barreling, 150 330, 333, 399 secondary, 247 basin, 319 chain rule, 53 wing, 230, 264, 266, 286 bending, 324 circle creep bending moment, 324–325, 327 great, 37 diffusion, 175, 196–197 body force small, 37 dislocation, 148, 154, 174–175, 197 buoyant, 8, 409 cleavage, 349 ductile, 295 gravitational, 7, 409 cleavage fan, 352 test, 147, 152, 195 bonded interface, 336 Coble creep, 196 cross section, 50, 274, 327, 403 boundary condition, 232, 235, 389, 392 coefficients strike-view, 25, 267, 272, 310 displacement, 232, 243, 327 first fundamental form, 318 crust, 5, 7, 154, 190, 409 no flow, 413 second fundamental form, 319 continental, 5 no interpenetration, 413 commutative oceanic, 5 no separation, 336 matrix multiplication, 57 crystal system, 347 no slip, 213, 336, 366, 413 compass, 34 Crystallographic Preferred Orientation, stress, 281 component 348 symmetry, 326 tensor, 54–55, 60 curvature, 301, 308, 319 traction, 232, 243, 281 vector, 29, 31, 60 Gaussian, 321 traction-free, 247, 401 compressible, 112, 114 mean normal, 321 Boundary Element Method, 340 compression, 106, 116 radius of, 308, 325 breccia, 260, 384 conduction scalar, 310, 314 brecciation, 384 heat, 405 curve brittle, 106, 145, 152 conductivity plane, 307 Brittle–Ductile Transition, 368 thermal, 95, 392 synformal, 309 buckling, 331 conservation u-parameter, 315 bud, 383 energy, 96 v-parameter, 316

© in this web service Cambridge University Press www.cambridge.org Cambridge University Press 978-1-107-03506-5 — Structural Geology: A Quantitative Introduction David D. Pollard , Stephen J. Martel Index More Information

Index 429

damage zone, 260, 281 diffusion equation decimal degrees, 11 chemical, 196 biharmonic, 238, 283, 337 defect diffusivity compatibility, 238, 283 line, 164, 166 thermal, 392 constitutive, 203, 333, 366, 399 point, 166 Digital Elevation Model, 312–313, 384, continuity, 88, 92, 205, 365, surface, 166 396 412 definite dike, 12, 223, 226, 241, 352, 379 equilibrium, 137, 177, 236, 283, 331, negative, 62, 117, 161 swarm, 226, 385 333, 335 positive, 62, 117, 161 dip, 35, 346 kinematic, 132, 287, 290, 333, 335 deformation apparent, 35 ordinary differential, 326 brittle, 9, 357, 359 direction, 35 equilibrium chemical, 196 direction angle, 31, 39, 62 quasi-static, 136, 209, 235, 324 coaxial, 162 direction cosine, 31, 39, 62, 317 extension, 106 ductile, 9, 13, 357, 359, 368, 370 discontinuity elastic, 105, 111, 373 displacement, 80, 128, 138, fabric, 10, 346, 350 elastic–brittle, 106, 119 169, 171, 240–241, 243, homogeneous, 360 elastic–ductile, 119, 146 259, 285 linear, 13, 40, 346, 349 elastic–plastic, 173 dislocation localized, 356 elastic–viscous, 185 climb, 175, 196 mylonitic, 357 heterogeneous, 155, 361 core, 170–171 planar, 13, 346, 348–349 homogeneous, 29, 155, 362 creep, 410 regional, 356 localized, 4, 365 edge, 82, 164, 166, 171, 279 factor mechanical, 196 glide, 174, 196 amplification, 338, 340 mechanism, 361 line, 165, 174 weighting, 63 non-coaxial, 162 loop, 167 fault, 9–10, 12, 109, 122, 124, 127–128, plastic, 166, 373 screw, 165–166, 168–170 260 progressive, 362 displacement bedding-plane, 328 viscous, 10, 188, 196, 205 relative, 287, 289 blind thrust, 339 deformation band, 121, 150, 152, dome, 275, 319 boundary, 265 267, 269 sedimentary, 323, 327, 403 left-lateral, 138 zone, 268–269 ductile, 145, 152 normal, 259, 274, 286 del operator, 54 reverse, 260 density earthquake, 188, 275, 285, 292 right-lateral, 138 dislocation, 174 Borrego Mountain, 273 strike-slip, 78, 259 mass, 8, 27, 52, 80, 87–88 fingerprint, 293 thrust, 272 derivative geology, 292 wrench, 259 material time, 50–52, 88, 92, 210 Hector Mine, 147 fault core, 260 ordinary, 317 strike-slip, 147 fault rock, 260 partial, 47, 316–317, 366 echelon, 369, 382 fault throw, 274 total, 364, 366 eigenvalue, 61 fault zone, 280 description of motion, 50 eigenvector, 61 simple, 264 material, 51 elastic, 144, 188 fence diagram, 403 referential, 17, 50, 85, 129, 154, 198, elastic constants field 201–202, 205, 287, 361 anisotropic, 135 displacement, 238, 240, 283–284 spatial, 17, 50–51, 85, 129, 187, isotropic, 135 near-tip stress, 244, 250 198–199, 201–202, 205, 212, 363 elastic theory scalar, 30 deviatoric stress dynamic, 130, 237 stress, 242, 286 second invariant, 371 quasi-static, 130, 237 tensor, 30, 53 diagonal Electron Backscatter Diffraction, 348 vector, 30, 50 principal, 55 element velocity, 335 diapir, 50, 408, 410 linear, 34, 37 Finite Element Method, 367 salt, 175, 410, 414 planar, 34–35 fissure eruption, 247 differential, 48 elliptic paraboloid, 316 flaws, 245 total, 49, 155, 200 elongation, 160, 163 flexural rigidity, 326 differential geometry, 302, 307, 313 engineering geology, 126 effective, 328

430 Index

flow drag, 415 displacement, 187 fully-developed plastic, 175–176 gravitational, 208 of a scalar, 49, 54 laminar, 209, 211, 333, 399, 411 inertial, 211 of a vector, 53–54 Newtonian, 147 resultant, 89 velocity, 186 plug, 400 shear, 324, 327 power-law, 147 surface, 5 hackle, 227 slow viscous, 208 viscous, 211 hazard solid-state, 152, 195–196 Fourier’s law, 95, 392 earthquake, 19, 110, 292 steady, 51 four-way closure, 276 volcano, 19, 212 steady viscous, 212 fracture, 9–10, 260 heat turbulent, 209, 411 2D blade-shaped, 247 conduction, 95 volume rate, 214 2D edge, 249 convection, 95 flow law, 147, 153–154, 195–196 3D penny-shaped, 248 radiation, 95 fluid axial splitting, 120 heat capacity dynamics, 185, 208, 211 breakdown, 251 specific, 97, 392 incompressible, 412 brittle, 295 heat transport linear viscous, 398–399, 410–411 conjugate shear, 120, 127 advection, 393 mechanics, 208 mixed-mode, 244 conduction, 97, 391, 393 power-law, 398–399 mode I, 244, 251 convection, 391 statics, 206, 208 mode II, 244, 284 helix fold, 10, 12, 301 mode III, 244 circular, 44 amplitude, 302 opening, 326, 380, 394, 401 homogeneity asymmetric, 304 shear, 121–122, 125 dimensional, 74 axial surface, 303 termination, 381 Hooke’s law, 134–135, 187, 230, axis, 302 tip, 226 236, 283 backlimb, 310 tipline, 226, 381 Hutton’s unconformity, 16 bending, 301 wedge, 120 buckling, 301 fracture mechanics inclination, 35, 39 cylindrical, 302, 313, 321 linear elastic, 250 inclinometer, 34 fault-bend, 339 fracture toughness incompressible, 88, 112, 177, 333–334, fault-propagation, 339 mode I, 250–251, 389 337 fault-tip, 339 friction initial condition, 391 flexural flow, 303 coefficient of, 371 integrability condition, 238 flexural slip, 303, 339 coefficient of internal, 125, 127, 371 interferogram, 396 forelimb, 310 fugacity International System of Units, 70–71 hinge, 274, 302 water, 153 intrusion, 10 inflection, 302 function concordant, 379, 394, 400, 403, 408 limb, 302 error, 392 discordant, 379, 403, 408 monoclinal, 267, 274 stream, 337 sheet, 379, 394 multi-layer, 301, 304 vector-valued, 41, 43, 308, 314 isochemical, 89 parallel, 303, 313 fundamental form isothermal, 89 profile, 302, 304, 309 first, 318 similar, 303 second, 318 joint, 9, 12, 109, 124–125, 128, 136, 138, single layer, 331 223, 260, 367 style, 303 geochemistry, 5 columnar, 228 synform, 309 geodynamics, 4 sheared, 228 wavelength, 302 geographic coordinate system, 11 fold mechanism glacier Keyhole Markup Language (zipped), bending, 322 ice, 188 14 buckling, 322 salt, 408, 410 kinematics, 128, 324, 350, 361 foliation, 264, 346 Global Positioning System, 34 kink band, 307 mylonitic, 266, 356, 359, 368, 372 Google Earth, 14 force Google Maps, 11 laccolith, 13, 76, 209, 323, 400, 402–403 body, 5, 409, 415 gouge, 260 Lame’s constant, 135 buoyant, 208 gradient Laplace’s equation, 169

Index 431

lengthening metamorphism parameter bulk, 333 contact, 380 arbitrary, 43, 309 level curve, 27 metrology, 71 natural, 43 Level of Neutral Buoyancy, 390 mica-fish, 359 parameter plane, 316, 320 LIDAR, 312 microstructures petrology, 5 linear algebra, 54 deformation, 361 phenocryst, 212 lineation, 41, 346, 349–350 microtectonics, 361 photoelasticity, 83 liquid, 145, 187, 197 mode photograph incompressible, 205 fracture, 243–245 orthorectified, 384 isotropic, 204 model piercing point, 225, 243, 259 Newtonian, 185, 204 canonical, 239, 242, 286, 290 plane non-Newtonian, 187 modulus extra half, 165 viscous, 9–10, 184, 187, 197, 333 elastic, 76, 325 meridian, 411 lithosphere, 4–5, 7, 10, 85 shear, 135, 187, 238 parameter, 46 tangent, 112 slip, 165 magma, 13 moment magnitude, 293 plane strain, 325 mantle, 5, 154 momentum plastic, 188 map angular, 93 rigid, 172 geological, 25, 241, 260, 267, 274, 307, linear, 89 plasticity, 368 310, 327, 350, 382–383, 403, 405 motion intracrystalline, 152, 163, 352 structure, 230, 247, 260, 265, 272, 352 rigid body, 287 time-independent, 173 structure contour, 49, 270, 272, 276, Multiples of a Uniform Density, 349 plume 311, 313 Multi-View Stereo, 384 mantle, 387 topographic, 27 mylonite, 260, 295, 348, 368 plumose structure, 227 marker horizons, 270 S-C, 357 plunge, 36, 42, 346 marks point rib, 227 Nabarro–Herring creep, 196 elliptic, 319 materials engineering, 166 Navier’s equations of motion, 136, 168 hyperbolic, 319 materials science, 166 Navier–Stokes equations, 207, parabolic, 319 MATLAB, 56, 66, 118, 132, 392 209, 365 planar, 319 functions, 57 neck point cloud, 312 scripts, 56 volcanic, 383 Poisson’s ratio, 76, 112, 134, 238, 290 matrix, 54 neutral surface, 325 Polar Decomposition Theorem, 159 column, 55 Newton’s laws, 18–19 porphyroclast, 354, 357, 368 displacement gradient, 290 Newton’s second law, 77, 93, 135–137, mantled, 359 element, 54 206–207, 235 precision, 73 identity, 59, 399 normal distribution, 73 pressure inverse, 59 normal stress, 92, 117 confining, 118, 149, 368–369 multiplication, 57 driving, 76, 398 order, 55, 57 observer effective confining, 123 orthogonal, 59, 156 moving, 414 hydrostatic, 206 rotation, 59 stationary, 414 lithostatic, 206, 334 row, 55 offset, 354 magma, 389 singular, 59 oolith, 26 magmastatic, 206 skew-symmetric, 201, 364 operator mean normal, 204, 398–399 small rotation, 288 del, 50 pore fluid, 122, 151, 381 square, 55 orientation static, 203 symmetric, 55, 117, 132, 161, 201 mean, 40 thermodynamic, 204 transpose, 58 origin, 227 thermostatic, 204 mechanics Orowan’s equation, 175 pressure solution, 163 complete, 18 overlap principal axis, 116–118, 132, 320 continuum, 5–6, 17, 19 dike segment, 382 principal curvature, 320 fracture, 244–245 principal direction, 29, 62, 118 Newtonian, 17 paraboloid principal stress, 281 solid, 236–237 elliptic, 46 greatest, 380

432 Index

principal stretch, 351, 371 set initial, 130, 154, 161–162, 287, 351 greatest, 347, 351 fault, 38, 270 perturbed, 336 least, 347, 351 joint, 109, 224 steady, 186 principal value, 29, 61, 116, 118, shape stress, 118, 124 132, 320 second-order, 319 undeformed, 61 principal vector, 61 shape operator, 320 step problem shear modulus, 173, 284, 290 contractional, 368 boundary-value, 6, 8, 282 shear strain, 363 dike segment, 382 eigenvalue, 118 angle of, 363 extensional, 368 three-point, 42, 353 distributed, 356 left, 264, 272, 368 product pure, 157, 347, 351 right, 272, 356, 359, 368 scalar, 31, 57, 318–319 simple, 157, 362–363 stereonet, 37 vector, 32–33, 43, 318 shear stress, 83, 92, 94–95, 117 stiffness, 107, 111, 114, 119 projection drop, 284–286, 290 stock, 403, 405 stereographic, 37 shear zone, 352, 365 Stokes’ stream function, 412–414 Universal Transverse Mercator, ductile, 146 stoping, 384, 403 34 mylonitic, 352 strain pseudotachylyte, 260, 294–295 viscous, 185–186 axial, 153, 195 shearing, 130 contractional, 129 rate shortening, 160, 163 elastic, 144–145, 280 strain, 151, 153 bulk, 332 extensional, 129 rate of deformation, 333 significant figures, 74 finite, 162 deviatoric, 399 sill, 13, 209, 223, 394, 403 inelastic, 281 mean normal, 399 climbing, 395 infinitesimal, 133 relaxation time, 340 slickenline, 9, 34, 45, 228, 259 longitudinal, 106 representation slip maximum principal logarithmic, 372 parametric, 43, 46–47, 314 dip, 259, 273–274 maximum shear, 173 Reynolds number, 211, 213, 365 direction, 259 normal, 325 Richter magnitude, 293 left-lateral, 368 plane, 136, 170, 176, 236, 281, 283, rigidity localized, 356 370 flexural, 76 magnitude, 259 plastic shear, 173 rock mechanics, 109, 118, 120 oblique, 259 principal axis, 161 rotation right-lateral, 272–273 principal value, 161 coordinate, 62 seismic, 295 rate, 195 pure, 58, 60, 133, 156, 158–159, 162, strike, 259 shear, 129, 131, 283, 291, 355 202, 287, 365 slip surface, 269 small, 162, 287, 290 small, 288, 290–291 solid, 145 small normal, 131 brittle, 9 small shear, 132 saddles ductile, 9 stratigraphic section, 270–271, 311, 327 antiformal, 275 elastic, 145 strength, 106 synformal, 275 isotropic, 205 compressive, 119 sample mean, 73 plastic, 145 differential, 121 San Andreas Fault, 30, 274 viscoelastic, 188 frictional, 281, 371 scalar, 25, 27 spherulites, 294 inherent shear, 125, 371 scale factor, 211 spring constant, 106 shear, 109, 281 seismic energy standard deviation, 73 tensile, 109, 251 reflected, 271 state theoretical shear, 172 transmitted, 271 base, 334, 336 uniaxial compressive, 112, 114 seismic moment, 293 brittle, 112, 119, 148 uniaxial tensile, 112, 114 seismic reflection, 271 current, 187, 199 yield, 144, 370 seismic survey, 50, 275 deformed, 61 stress, 106 separation ductile, 112, 119, 148 component, 116 horizontal, 259 elastic, 119, 148 concentration, 226, 243, 245, 249–250, strike, 260 equation of, 204 286 vertical, 259 final, 130, 154, 162, 287, 351 conjugate shear, 94, 116

Index 433

deviatoric, 371, 399 rate of spin, 199, 202–203, 364 base, 31 differential, 120, 153, 173, 195 rate of stretch and shearing, 201 curvature, 309 effective, 123, 125, 381, 384 small strain, 134 differential normal, 319 first invariant, 371 spatial gradient of deformation, differential tangent, 318 isotropic, 117, 203 201 direction, 29 least compressive, 389, 394 spatial gradient of velocity, 201–202, displacement discontinuity, 354 maximum shear, 172, 203 363 fixed, 31, 34 mean normal, 369–371 stress, 55, 60, 116–117, 203 gradient, 133 mode I driving, 239–240, 243–244 symmetric, 95 gravitational acceleration, 319 mode II driving, 284, 286 velocity gradient, 54 heat flux, 95 normal, 94, 116, 203, 326 vorticity, 202, 364 magnitude, 29, 31 principal, 117, 203 test mapping, 34 remote, 281 axisymmetric, 118 mathematical, 27 shadow, 243, 286 compression, 118 physical, 29 shear, 116, 186, 192, 331 conventional triaxial, 118 position, 34, 41, 43, 46, 308, thermal, 407 creep, 195 314, 411 stress intensity, 244 extension, 118 resultant, 40 mode I, 244, 247, 250, 389–390, 395 true triaxial, 119 sense, 165 mode II, 251, 395 uniaxial, 109 tangent, 47, 165, 316, 318 mode III, 252, 382 testing machine temperature gradient, 96 stretch, 29, 53, 160, 332, 346 universal, 109 traction, 60 ellipse, 162 thickness unit, 29–30, 34, 39, 41 principal, 162 effective, 190, 330, 402 unit normal, 33–34, 43, 47, 60, stretching, 130 thin-plate theory, 324 317–318 strike, 34, 346 tide unit tangent, 44–45, 309 direction, 34 solid Earth, 107 vein, 9, 12, 223, 326, 405 structural geology, 5, 9, 13, 17–18 time injection, 295 structural petrology, 360 dimensionless, 392 sheared, 228 structure torque, 93, 192 velocity linear, 259 traction, 5 angular, 191 planar, 259 trajectory local, 51–52, 86, 199 Structure from Motion, 384 principal stress, 124 particle, 87 symmetry condition, 412 transducer relative, 53 syncline, 303, 321 displacement, 109 rise, 415 synform, 303–304, 319 force, 109 rupture tip, 293 Synthetic Aperture Radar transition slip, 293 Interferometry, 83, 396 sill–laccolith, 401–402 velocity field translation, 287 layer, 337 tangent line, 45, 48 trend, 36, 346 medium, 337 tangent plane, 49 Tresca’s yield criterion, 173, 176 vessel tectonics triaxial pressure, 118 plate, 4 unit, 27, 29 viscometer, 190 temperature base, 70 viscosity, 184, 186, 192 liquidus, 10 common, 70 isotropic, 190 solidus, 10 derived, 70 Newtonian, 186–187, 191, tension, 106, 116 Universal Transverse Mercator, 205, 400 tensor, 25, 29, 54 11 ratio, 413, 415 deformation gradient, 29, 155, 163, silica dependence, 192 351, 361 variables temperature dependence, 193 displacement gradient, 133 state, 204 water dependence, 193 finite strain, 159, 163 variance, 73 viscous, 184 Lagrangian strain, 160 spherical, 40 linear properties, 60 vector, 25, 27, 30 wall rate of deformation, 186, 199, arbitrary tangent, 317 foot, 259 201–202, 364, 366 arrow, 28 hanging, 259

434 Index

wavelength xenolith, 212 yield point, 112, 145, 148 current, 332 yielding dominant, 338, 340 yield criterion, 370 small scale, 281 initial, 332 Drucker–Prager, 371–372 Young’s modulus, 106, 112, 115, wing cracks, 368 von Mises, 371–372 134, 145