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Index




bending, 186, 190
ab initio calculations, 104, 172, 175, 252
biharmonic equation, 119, 305
absolute plate motion, 299
body force, 51, 57, 76, 83, 110, 119, 217
acceleration, 44, 76, 96, 110, 118, 127, 132
body waves, 231, 247
gravitational, 97, 121, 216
bottom heating, 125, 126, 341, 345, 363, 364,
acceleration ¬eld, 37, 51, 58
366
acoustic waves, 110, 142
boudinage, 193
activation energy, 164, 210
boundary conditions, 107, 123, 131, 146, 217,
activation enthalpy, 158
220, 222, 223, 225, 259, 280, 287, 290,
adiabat, 330, 352
312, 313, 333, 354, 371, 388, 395
adiabatic, 12, 59, 97, 98, 144, 168, 328, 342,
boundary layer, 303, 359, 396
343, 345, 380, 400
boundary layer theory, 330
adiabatic compression, 287
boundary layers, 117
adiabatic gradient, 344
Boussinesq approximation, 122, 286, 287, 303,
adiabatic moduli, 99, 328
391
adjoint equations, 367, 371
Brillouin zone, 159, 161
adjoint problem, 335, 368, 372
brittle, 16, 193, 261, 284“286, 318, 376
advection, 287, 292, 345
brittle failure, 377
advective, 105, 117, 148
brittle“ductile transition, 16, 193, 261, 267, 268
advective boundary layer, 315
buckling, 186, 190, 193
aftershocks, 200, 203, 204
bulk modulus, 73, 97, 99, 103, 104, 108, 116,
AK135 model, 10, 11, 229, 232, 244, 251
132, 214, 249, 252, 328
Alfv´ n waves, 145
e
±-effect, 390 bulk viscosity, 66, 110, 132
bulk-modulus, 13
Anderson fracture, 198, 200
bulk-sound speed, 98, 116, 249“253, 310, 328
anelastic approximation, 286, 332, 385
buoyancy, 121, 303, 307, 329, 330, 342
angular momentum, 2
buoyancy ¬‚ux, 350, 351
angular velocity, 354
Burgers vector, 154, 165
anisotropic, 95
anisotropy, 15, 17, 186, 200, 207, 270, 294, 299,
Cauchy strain, 100, 101, 162
301, 302, 380
Cauchy strain tensor, 32, 33, 67, 72
azimuthal, 299
Cauchy stress, 106
Arrhenius form, 158, 286, 291
centrifugal force, 127, 323, 386
asperities, 255
centrifugal forces, 127
asthenosphere, 17, 154, 257, 259, 284, 288, 294,
centroid moment tensor, 253, 274
295, 297, 303, 335, 341, 372
chemical components, 378
asthenospheric ¬‚ow, 302
chemical heterogeneity, 18, 252, 253, 328
atomic level, 153, 162
chemical potential, 157, 163, 286, 399
attenuation, 17, 154, 209
Clapeyron slope, 321, 322, 329
scattering, 209
Clausius“Clapeyron equation, 135
barriers, 255 coef¬cient of thermal expansion, 122
bathymetric swells, 349 collisional resistance, 273


423
424 Index

252, 301, 325, 328, 329, 333, 345, 350,
complex refractive index, 140
352, 364, 366, 381, 382, 384, 388, 398,
composition, 286, 327, 391
400, 401
compositional boundary layer, 400
Coriolis force, 127, 128, 130, 391
compositional convection, 381
correspondence principle, 91, 93, 280
compositional effects, 388
compressibility, 110, 115, 341 Couette ¬‚ow, 118
compressible, 364 Coulomb failure, 195, 198, 200, 202, 267
compression, 71, 99, 164, 168, 185, 190, 269, craton, 266, 284, 296, 302
283, 288 creep, 162, 163
conservation laws, 2 diffusion, 164, 189, 298
conservation of angular momentum, 42, 44, 359 dislocation, 164, 189, 298, 376, 377
conservation of electric charge, 136 power law, 163, 166, 193, 298, 374
conservation of energy, 21, 51, 58, 59, 97, 133, creep function, 88, 90“92
134, 139, 143, 146, 338 critical stress, 267
conservation of heat ¬‚ux, 316 crust, 16, 262, 271, 277, 282, 286, 288, 360
conservation of linear momentum, 21, 42 continental, 344
conservation of mass, 2, 21, 38, 106, 132, 142, crust“mantle boundary, 285, 286, 288
217, 332, 338, 385, 399 crystal lattices, 153
conservation of momentum, 132, 143
constitutive relation, 3, 4, 54, 64, 107, 111, 112,
D layer, 12“15, 18, 104, 109, 294, 301, 328,
131, 136, 153, 162, 166, 180, 267, 283, 312
329, 364, 389
elastic, 72
data assimilation, 363, 367
constitutive relations, 212
sequential, 366, 367
continental crust, 9, 16, 269
variational, 366, 368
continental lithosphere, 16, 269
Debye lattice spectrum, 161
continents, 299, 302
Debye temperature, 161, 177
continua, 71
decay time, 121
continuity
decollement, 189, 204
displacement, 88, 107
defect energy, 179
heat ¬‚ux, 135
defects, 153, 154, 157, 163, 164, 178, 179, 181
pressure, 134
de¬‚ection, 265
traction, 88, 107, 134
deformation, 3, 6, 16, 17, 21, 22, 110, 132, 135,
velocity, 134
180, 182, 186, 258, 261, 276, 280, 285,
continuity condition, 382
291, 318
continuity conditions, 46, 137, 218, 227, 318
co-seismic, 277
continuity equation, 38, 115, 117, 132
creep, 164
continuity of traction, 46
element of area, 25
continuum, 1, 2, 6, 7, 22, 41, 131, 132, 153,
element of volume, 24, 25
155, 285
¬nite strain, 100
continuum electrodynamics, 21, 131, 135
geometry, 21, 54
continuum mechanics, 1, 21
history, 54, 56, 132
continuum thermodynamics, 57
homogeneous, 23, 25
convection, 21, 293, 391, 400
incremental, 64
convective forces, 359
linearisation, 71, 74
convective instability, 341
plane, 34
convective motions, 14, 15, 18
plastic, 165, 189
convective planform, 330, 339
post-seismic, 277
convergence, 288, 293
shear, 73
conversions, 10
successive, 187, 188
cooling, 149
successive deformation, 24
core, 1, 8“10, 13, 21, 110, 129, 133, 137, 139,
vector element, 23
166, 220, 222, 231, 237, 241, 330, 333,
deformation gradient, 23, 24, 26, 30, 31, 34, 39,
352, 380“382, 384, 385, 389, 398, 400
60
density, 380
deformation mechanisms, 153, 373
core convection, 385
deformation tomography, 280
core“mantle boundary, 11, 13, 14, 18, 97, 220,
227, 231, 233, 235, 236, 238, 241, 249, deformed state, 3, 21, 22, 41, 53
Index 425

density, 2, 6, 11, 13, 14, 16, 18, 25, 38, 64, 97, interrelations, 74
102, 113, 116, 121, 122, 132, 134, 142, elastic wave, 97
144, 166, 167, 216, 249, 260, 262, elastic waves, 83, 158, 160
286“288, 297, 303, 327, 328, 350, 364, interfaces, 86
367, 386, 388, 391 elasticity, 1, 4, 16, 21, 60, 107, 132, 258
density contrast, 325“327 crystal, 162
density functional method, 173 Kirchhoff™s theorem, 77
density jump, 380, 402 linearised, 71, 95, 105, 132, 207
density of states, 160 reciprocal theorem, 80
deviatoric strain-rate tensor, 387 representation theorem, 81
diamond anvil cell, 170 uniqueness theorem, 76
dielectric constant, 136 electric charge density, 136
diffusion, 145, 157, 158, 164, 186, 387, 399 electric current, 135, 136, 141
atomic, 157, 182, 184 electric displacement, 136, 138
diffusive, 117 electric ¬eld, 135, 141
diffusivity, 157, 158 electric vector, 136, 138
dilatation, 26, 93 electrical conductivity, 135, 136, 141, 295, 384,
dimensionless variables, 113 387, 389
discontinuity, 9, 10, 97 electrical conductor, 141
210 km, 14 electrical conductors, 137
410 km, 12, 14, 274, 301, 319, 321, 327 electrical current density, 142
520 km, 12, 14 electromagnetic coupling, 389
660 km, 12, 14, 104, 109, 154, 274, 294, 317, electromagnetic effects, 131, 141
319, 321“323, 327, 329 electromagnetic energy ¬‚ux, 143
dislocation, 155, 203, 212, 213 electromagnetic ¬elds, 136
climb, 165 electromagnetic force, 142
edge, 154“156, 164, 181 electromagnetic waves, 140, 142
glide, 165 electronic structure calculations, 171
glide plane, 154, 165 en-echelon segments, 198, 202
screw, 154“156, 164 endothermic, 321, 322
dislocations, 1, 153, 154, 164“166, 181, 182, energy, 2
193 energy ¬‚ux, 139
displacement, 2, 33, 34, 71, 79, 83, 105“107, energy ¬‚ux density, 134, 143
119, 120, 132, 158, 217, 218, 221, 226, 281 enthalpy, 167
integral representations, 79 entropy, 97, 98, 116, 135
displacement current, 142 epicentral distance, 10
displacement gradient, 71 equation of motion, 83, 106, 110, 111, 127, 142,
dissipation, 139, 143, 210, 212 158, 217, 218, 224, 318, 386, 391
double couple, 202, 214 equation of state, 95, 102, 103
ductile, 193, 201, 261, 268, 284“286, 376 Birch“Murnaghan, 95, 103, 252
dynamic topography, 359, 360 shock wave, 380
dynamo, 1, 13, 18 erosion, 290, 318
±ω, 390 error function, 149
±2 , 390 Eulerian, 3, 36, 41, 100“105, 107, 162, 163,
dynamos 252, 285
numerical, 393 Eulerian ellipsoid, 29, 187
Eulerian triad, 29, 31, 33, 62
Earth structure, 8“18, 231 exhumation, 318
three-dimensional, 243, 247, 248 exothermic, 321, 322, 329
earthquakes, 9, 16, 72, 76, 79, 137, 200, 204, explosions, 9, 76, 212
212, 214, 253, 254, 256, 267, 269“272, extension, 26, 283, 287, 293
274, 276, 277, 288, 297, 308, 322
Ekman boundary layers, 393 failure, 193
Ekman layer, 130 brittle, 274
Ekman number, 113, 128, 392“394, 397, 398 Coulomb, 195, 198, 200, 202, 267
elastic, 2, 6, 57, 91, 100, 261 tensile, 195
elastic moduli, 17, 64, 68, 73, 75, 95, 101, 108, fault, 107, 186, 193, 195, 200, 253“255
153, 176, 213, 253, 276, 299 detachment, 284
426 Index

dip-slip, 197 generalised gradient approximation, 173
displacement, 201, 204 generalised Hooke™s Law, 73
listric, 290 generalised Hooke™s law, 217
normal, 197, 199, 202, 275, 288, 293 geochemical constraints, 13, 17
oblique, 197 geodesic grid, 335
reverse, 198, 200 geodesy, 7
splay, 201, 204, 205 geodetic information, 277, 278
strike-slip, 197, 198, 201, 204, 275, 289, 290 geodetic methods, 253
thrust, 197, 199, 200, 202, 204, 205, 255, geodetic techniques, 276
275, 288, 293, 309 geodynamo, 16, 131, 135, 380, 381, 385, 389,
fault gouge, 196, 202 393, 398, 400
fault mechanism, 202, 355 geoid, 282, 323“325, 358
fault plane, 195, 253, 255 anomaly, 326, 327
faulting processes, 277 dynamic compensation, 325
faults, 284 response kernel, 327
¬bre, 25, 27, 188 geomagnetic ¬eld, 1, 13, 18, 21
¬gure of the Earth, 8, 323 geostrophic ¬‚ow, 128, 129
¬nite difference, 338 geostrophy, 384, 393
¬nite element, 335, 336, 338, 376 geotherm, 342, 345, 346, 352
¬nite rotation, 354, 355 Gibbs free energy, 135, 320
¬nite strain, 100, 102, 104, 252 glacial loading, 7
¬nite volume, 335, 338 glacial rebound, 119, 258, 280, 282, 307, 327
¬‚exural parameter, 264 GNSS, 276
¬‚exural rigidity, 262 GPS, 276, 277
¬‚ood basalts, 349, 351 Gr¨ neisen parameter, 98, 162, 168, 177, 328
u
¬‚ow, 17, 110, 186, 190, 294, 311, 325, 384, 389, grain boundaries, 153
390 grain size, 153, 154, 163, 189, 209, 210, 212,
glacier, 69 268, 298
¬‚uid, 1, 116, 134, 323, 380, 388, 392 grain-boundary sliding, 186, 189
¬‚uid dynamics, 141 gravitational admittance, 263“266
¬‚uid ¬‚ow, 1, 111, 112, 135, 391 gravitational coherence, 265
¬‚uid“solid boundary, 107, 134 gravitational force, 121
¬‚uids, 2, 6, 7, 21, 55, 57, 64, 69, 110 gravitational instability, 292
folding gravitational potential, 216, 217, 224, 226, 280,
fault-bend, 204, 205 311, 323, 324, 386
force, 3 gravity, 96, 281
Fourier synthesis, 119 gravity anomaly, 262, 264“266
Fourier transform, 219 Bouguer, 266
fracture, 193 free air, 266
tensile, 194 Green strain, 100
fracture envelope, 194 Green strain tensor, 32, 33, 60, 71, 72
fracture strength, 195 Green™s function, 148
free convection, 388 Green™s tensor, 79, 81, 82, 85, 86, 88, 212
free oscillations, 8, 11, 18, 207, 220, 247, 380 group velocity, 241
free surface, 10, 86, 96, 117, 123, 134, 217, 220,
half-space, 149
333
half-space cooling model, 259, 261, 269, 360
free-air gravity anomalies, 323
heat capacity, 287, 364
frequency, 6, 11, 140, 141, 149, 158, 207, 210,
heat conduction, 58
212, 223, 231, 239, 242, 247, 280
heat diffusion, 113, 330
frequency dependence, 209
heat ¬‚ow, 111, 145, 146, 259, 318, 399
frequency dependent, 212
heat ¬‚ux, 121, 131, 133, 259, 330, 333, 344,
frequency domain, 218, 219
347, 351, 352, 363, 364, 388, 400, 401
frequency modes, 160
heat ¬‚ux vector, 58
friction, 267, 284
heat loss, 346, 352
frictional heating, 287
heat production, 111, 133
frozen ¬‚ux, 143, 144, 384
heat transport, 59, 342, 346
garnet, 319, 321, 323 heaviness, 273, 274
Index 427

Helmholtz free energy, 97, 101“103, 107, 163, latent heat, 135, 321, 381, 389, 400
176, 177 lattice dynamics, 176
heterogeneity, 14, 18 lattice preferred orientation, 299
lattice vibrations, 158
heterogeneity patterns, 250, 252
linear momentum, 2
horizontal wavenumber, 124
lithosphere, 1, 16, 17, 109, 186, 257, 260, 262,
hot spots, 342, 348, 349, 351, 355, 360
265, 266, 280, 283, 288, 290, 293“297,
hotspots, 330
308, 310, 312, 318, 342, 349, 360, 362,
Hugoniot, 167, 168
364, 365, 372, 374, 376, 378
hydration potential, 322
continental, 269, 344
hydrostatic, 388, 400
cooling, 260
hydrostatic pressure, 78
elastic thickness, 265, 266, 270
ice history, 283 mechanical, 257
ice loading, 280 oceanic, 258, 259, 268, 271, 354, 358
incompressibility, 108, 118, 123, 129, 132, 142, strength, 267
286, 303, 311, 332, 385, 394 thermal, 257
incompressible, 26, 115, 117, 338, 347 viscoelastic thickness, 283
incompressible medium, 74 lithosphere-asthenosphere boundary, 285, 288,
incremental, 105 295“298
inertia forces, 128 local density approximation, 173
initial condition, 368 local equations, 44
initial conditions, 354, 362, 367 Lorentz force, 384, 369“391, 400
inner core, 9, 10, 13, 14, 18, 97, 226, 234, loss factor, 93
237“239, 241, 380, 387, 388, 394, 397 Love numbers, 281“283
inner core boundary, 11, 15, 97, 239, 380, 388, Love waves, 224, 239, 241, 245, 247, 299
389, 398, 400, 402 low velocity zone, 295
inner core growth, 398, 400 lower mantle, 12, 17, 95, 303, 323
InSAR, 254, 277
Mach number, 116
interatomic potentials, 171, 174
magma, 118, 284
interface conditions, 134, 137
magnetic continuum, 142
internal energy, 58, 59, 111, 146, 167, 168, 399
magnetic diffusivity, 142, 387
internal heating, 122, 125, 126, 287, 341,
magnetic energy, 389, 399
345“347, 352, 363, 365, 366, 373, 392
magnetic ¬eld, 131, 135, 141, 144, 381, 382,
internal load, 263, 264
384, 385, 387“390, 397, 398
interstitials, 154
core“mantle boundary, 383, 384
intrinsic anelasticity, 209
reversal, 381, 390
isentropic, 59, 99, 101, 168
reversals, 398
isostasy, 259, 260, 288, 297, 323, 376, 377
surface, 383
isothermal, 59, 97“99, 101“104, 123, 163, 168,
magnetic ¬‚uid, 143, 386, 392
328, 333
magnetic ¬‚uid dynamics, 141, 385
isothermal moduli, 328
magnetic force, 386, 389
magnetic induction, 136, 138
Joule heating, 139, 143, 387, 389, 399
magnetic isochron, 354, 355
jump
magnetic permeability, 136, 142
displacement, 213, 214
magnetic potential, 381
traction, 213, 214
magnetic Rossby number, 392, 393, 397
magnetic vector, 136, 138
kinematic viscosity, 112, 121, 127, 386
magnetohydrodynamic approximation, 386, 399
kinetic energy, 133, 158, 230, 389
magnetohydrodynamic waves, 144
Lagrangian, 3, 36, 100, 102, 103, 105“108, 132, mantle, 1, 9, 10, 12, 14“17, 21, 110, 114, 117,
252, 285 121, 133, 139, 153, 157, 166, 169, 222,
Lagrangian ellipsoid, 28 226, 231, 249, 252, 266, 277, 283, 286,
Lagrangian strain-energy, 53 294, 314, 317, 320, 323, 327, 330, 331,
Lagrangian triad, 28, 29, 31, 32, 61 333, 336, 341, 364, 380, 382, 389, 400, 401
Lam´ moduli, 73
e mantle circulation, 353, 354, 362, 363, 372, 376
Laplace transform, 280, 281 mantle convection, 1, 14, 17, 113, 294, 308,
latent, 402 330, 335, 341, 346, 351, 371, 401
428 Index

mantle drag, 273 outer core, 9, 11, 13“15, 18, 226, 234, 237, 239,
mantle viscosity, 331 241, 380, 387, 388, 391, 392
mantle wedge, 312, 313, 315
P waves, 9, 83, 84, 87, 88, 93, 109, 169, 202,
mass of the Earth, 8, 11
209, 214, 231“235, 237, 247, 249, 253,
material derivative, 39
297, 310
material description, 22
P wavespeed, 13, 98, 104, 208, 231, 234, 249,
material properties, 54
253, 310
material symmetry, 55, 56, 61, 73, 137
P-SV waves, 209
material time derivative, 36, 38
parallel computation, 335, 338
material triad, 28
partial melting, 294, 297, 298
Maxwell stress tensor, 143
particle, 25
Maxwell™s equations, 135“137, 139, 142, 381,
P´ clet number, 113, 117, 315, 345
e
386
penetration depth, 141
melt, 17, 284
peridotite, 319
metastable states, 322
permittivity, 136
microfabric, 180
perovskite, 14, 17, 154, 319, 321, 328, 329
microstructure, 181, 182, 184, 298
perturbation, 105
mid-ocean ridges, 271, 354, 360
perturbations, 106, 107, 207
mineral physics, 104, 252
phase transition, 12, 135, 294, 320, 322, 328,
mobile derivative, 37, 60
341, 342, 402
mobile-lid regime, 347, 374
phase transitions, 6, 17, 18, 97, 154, 168, 169,
modi¬ed Rayleigh number, 392
319, 321, 322, 340
molecular dynamics, 177
phase velocity, 221
moment magnitude, 215
piezoelectricity, 137
moment of inertia, 8, 11
Piola“Kirchhoff stress tensor, 53, 61, 106, 107
moment rate tensor, 220
piston cylinder, 168
moment tensor, 214, 215, 219, 246, 253
plane wave, 83, 88, 109
moment tensor density, 212
plastic, 261, 286
momentum, 2
plastic failure, 290
momentum balance, 330
plastic ¬‚ow, 4, 193, 201
momentum ¬‚ux density tensor, 133, 143
plastic yielding, 76
momentum transport, 113
plasticity, 4, 16, 69
monent magnitude, 216
plate boundaries, 271, 272, 376
motion, 36
convergent, 271, 272, 288, 290
multi-anvil press, 168, 171
divergent, 271, 272
mylonite, 197, 205
plate boundary forces, 272, 273, 362
plate cooling model, 261, 269
Navier“Stokes equation, 111, 113, 114, 118,
plate motion, 353, 358, 359, 361“365
122, 142, 144, 303, 304, 330, 335, 362, 386
plate motion history, 330
negative buoyancy, 273, 274
plate reconstructions, 355
Newtonian viscous ¬‚uid, 6, 57, 66
plate tectonics, 295, 346, 358, 372
non-dimensional quantities, 113, 334
plate thickness, 331, 332
non-hydrostatic stress, 95, 109
plate velocities, 277
normal mode expansion, 219
plume, 304, 306, 307, 349“352, 366
normal mode summation, 218
plume head, 349, 351
normal modes, 218, 220, 239, 242, 243, 245
plumes, 14, 333, 348
normal stress, 193, 195
point source, 202, 214, 246, 253
normal traction, 325
Poisson™s ratio, 73, 75, 156, 262
Nusselt number, 113, 121, 307
polar decomposition, 29, 30, 56
oceanic crust, 9, 16, 268 polarisation, 83
oceanic lithosphere, 11, 14, 16, 258, 259, 268, pole of rotation, 271
271, 289, 314, 317, 330 poloidal, 381, 382, 387, 394
oceans, 299 post-perovskite, 14, 18, 328, 329
ohmic dissipation, 400, 402 potential energy, 158, 230
olivine, 17, 268, 299, 301, 319, 321 Poynting vector, 139, 140, 143
ω-effect, 390 Prandtl number, 113, 304, 330, 392
orogeny, 266, 316, 319 pre-stress, 72, 107
Index 429

pressure, 6, 12, 21, 95, 97, 98, 100, 102“104, rapid, 127, 385, 386, 392
107, 111, 116, 117, 127, 128, 134, 144, rotation pole, 354, 355
158, 163, 166“168, 170, 172, 189, 294, rotation rate, 278
304, 311, 320“322, 338, 386, 390 rupture, 202, 253, 255
hydrostatic, 66, 95, 96, 100, 110, 118, 120,
S waves, 9, 85, 109, 169, 186, 231“234, 238,
189, 303
247, 249, 253, 294, 310
lithostatic, 118, 286, 291
S wavespeed, 13, 98, 104, 231, 234, 249, 253,
pore ¬‚uid, 189, 193, 267
296
pressure derivatives, 252
SH waves, 85, 86, 209, 231, 236, 248, 296
pressure gradient, 118, 127
SV waves, 85, 87, 88, 93, 209, 296, 297
PREM model, 11, 243, 245, 246, 248, 364
ScS, 224
principal axes of stress, 48
sea level, 280, 282, 283, 360
principal ¬bres, 28, 29
sea-level change, 323
principal stresses, 48, 50, 62“64, 199, 274
secular cooling, 345
principal stretches, 28, 34
secular equation, 223, 226
principle of determinism, 54
secular variation, 384
principle of local action, 4, 55
sedimentary basins, 285, 288
principle of material objectivity, 55
seismic attenuation, 6, 294, 297
pseudopotentials, 174
seismic body waves, 8
pure shear, 26, 34, 35
seismic focal mechanisms, 274, 275
radial modes, 228, 230 seismic observations, 243, 253
radioactive heat sources, 381 seismic parameter, 98, 104
radioactive heating, 399 seismic phases, 10, 231, 243, 247
radioactive isotopes, 344 converted, 235
rate of deformation tensor, 64 core phases, 232, 234, 237
ray paramater, 208 depth phases, 233
ray parameter, 209 re¬‚ected, 235
Rayleigh number, 113, 121, 124, 125, 304, 340, seismic sources, 212, 213
365 seismic tomography, 11“14, 16, 18, 231, 247,
critical, 125 248, 252, 274, 295, 296, 309, 310, 317,
Rayleigh waves, 87, 241, 245, 247, 299 328, 354, 358, 364, 367
Rayleigh“Ritz method, 230 seismic travel times, 232, 237, 243, 244
Rayleigh“Taylor instability, 292, 347 seismic waves, 1, 6, 9, 99, 207, 209, 212, 231,
reciprocal triad, 26 243
reference state, 21, 22, 53, 100, 107, 390 seismic wavespeeds, 10, 11, 15, 109, 249, 252,
referential triad, 28 258, 295
re¬‚ection, 10, 237 seismogenic zone, 290
re¬‚ection coef¬cients, 209 seismograms, 10
refraction, 234, 237, 239, 301 seismology, 7
relaxation function, 89, 90, 92 self-equilibrated, 44, 45
Reynolds number, 113“115, 334, 340 self-gravitation, 220, 280, 323, 325
thermal, 261, 273 shear, 34, 71, 93, 184, 188, 204
rheology, 1, 6, 131, 162, 165, 188“190, 193, shear ¬‚ow, 117
257, 261, 283“285, 294, 295, 316, 318, shear folds, 190
374, 376 shear localisation, 373, 374
power law, 286, 290, 292 shear modulus, 73, 75, 97, 99, 104, 108, 132,
ridge crest, 273 154, 155, 210, 212, 214, 249, 253, 327, 328
ridge push, 272, 273 shear stress, 193, 195, 199
rifts, 284 shear traction, 325
rigid-lid regime, 347, 373, 374 shear viscosity, 66
rigidity, 108, 226 shear waves, 9, 13, 17
Roberts number, 392, 394 shear wave splitting, 301, 302
roll-back, 309 shear wavespeed, 17, 250“252, 257, 310, 328
Rossby number, 113, 128 shock waves, 166
rotating reference frame, 127, 388 simple materials, 55
rotation, 3, 29“31, 44, 55, 61, 64, 71, 108, 126, simple shear, 34, 35, 184
127, 278, 323, 385, 386, 388 skin depth, 141
430 Index

slab pull, 273, 308 stress gradient, 44
stress heating, 312
slab resistance, 273
stress jumps, 46, 47
slab retreat, 316
stress measurements, 274
slab roll-back, 317
in situ, 276
slip, 107, 186, 195, 198, 200
stress power, 60, 112
segmentation, 255, 256
stress tensor, 3, 4, 21, 41, 43“46, 53, 60, 62, 67,
slip distribution, 255
72, 131, 132, 134, 142, 146, 155, 163, 276,
slowness, 83, 109, 145, 209
286
Snell™s law, 88
stress“strain relation, 73, 83, 92, 93
solids, 2, 4, 7, 21, 55, 69, 380, 388
stretch, 3, 27, 28, 31, 60, 63, 71
solidus, 209
stretch tensor, 29
source radiation, 214
stretching, 288
space geodesy, 355
strike-slip, 202
spatial description, 22
subadiabatic, 345
spatial triad, 29
subducted slabs, 14, 311“313, 315, 322, 327,
speci¬c heat, 98, 160, 333, 387
329
spectral technique, 394
subduction, 11, 12, 14, 16, 17, 294, 347, 354,
spherical harmonic expansion, 280, 324, 381
358, 362, 366, 378
spherical harmonic representation, 220“222,
geometry, 309
280, 327, 382, 395
subduction zone, 16, 249, 271, 289, 290, 308,
spherical harmonics, 394
309, 311, 316, 318, 330
spheroidal modes, 220, 222, 224“227, 229, 231,
surface charge density, 137
239“242, 245
surface current, 137
spin tensor, 64
surface load, 119, 262, 264, 265, 280, 281
spinel, 154, 301, 319, 321, 329
surface loading, 282
stagnant slabs, 14, 274, 317
surface topography, 262, 264, 265, 288, 323,
standing waves, 221
325
steady ¬‚ow, 128
surface traction, 57, 134
Stokes ¬‚ow, 115, 118, 334, 337, 362
surface waves, 10, 17, 245, 247, 295
Stokes ¬‚uid, 66, 110
synchrotron X-ray methods, 169, 170
Stoneley waves, 229, 241
strain, 1“4, 6, 21, 27, 54, 60, 61, 71, 73, 105, tangent cylinder, 394
108, 137, 153, 155, 163, 176, 180, Taylor columns, 129, 393
186“188, 207, 276, 278, 284, 286 Taylor“Proudman theorem, 129
strain energy, 60, 61, 72, 101, 107, 162, 163 tectosphere, 295
strain ¬elds, 188, 299 temperature, 6, 17, 21, 58, 64, 95, 97, 98, 100,
strain measurements, 276 111, 113, 116, 121“123, 125, 136, 145,
strain rate, 64, 69, 153, 162, 164, 180, 182, 184, 147“150, 154, 157, 158, 160, 161, 164,
193, 268, 278, 286, 301, 374 166, 167, 169, 170, 172, 176, 177, 182,
deviatoric, 112 184, 189, 193, 210, 212, 252, 253, 261,
strain rate tensor, 318, 333 268, 286, 287, 294, 298, 304, 306, 314,
strain tensor, 3, 4, 108, 184, 220 315, 320“322, 327, 328, 330“333, 338,
strainmeter 342, 343, 345, 351, 352, 358, 362, 364,
borehole, 277 373, 387, 388, 390, 391, 394
laser, 277 homologous, 158
strati¬cation melting, 158, 163, 373
radial, 95 temperature ¬eld, 112
stream function, 119, 123, 286, 304, 305, 312, temperature gradients, 125, 131, 133, 135, 146
313 tensile strength, 195
streamlines, 128, 311 tension, 74, 164, 269, 283
strength, 270 thermal activation, 158
stress, 1“4, 16, 54, 61, 64, 66, 69, 92, 93, 105, thermal boundary layer, 306, 333, 338, 341,
106, 108, 110, 132, 153, 155, 156, 163, 342, 345“348, 352, 362, 366, 400
165, 176, 182, 268, 271, 286, 294, 374 thermal capacity, 112, 146
viscous, 305 thermal conduction, 259, 342
stress circle, 49, 50, 194, 195 thermal conductivity, 58, 111, 116, 131, 133,
stress ¬eld, 276 146, 287, 333, 341, 364, 387
Index 431

thermal contraction, 260 velocity gradient, 64, 66
thermal convection, 110, 121, 125, 126 virtual work rate principle, 51, 58
thermal diffusion, 121, 367 viscoelastic, 6, 55, 91
thermal diffusivity, 112, 113, 122, 148, 333, viscoelastic relaxation, 277
342, 387 viscoelasticity, 5, 21, 57, 67, 88, 258, 280
thermal effects, 298 Burgers model, 68, 69, 91, 209, 210, 212,
thermal energy, 58 258, 298
thermal equation, 303 creep, 88
thermal evolution, 288 Kelvin-Voigt model, 5, 6, 68, 69
thermal excitation, 160 linear, 67, 88, 209, 281
thermal expansion coef¬cient, 328 Maxwell model, 5, 68, 69, 283
thermal expansivity, 98, 121, 122, 341, 364, 388 relaxation, 88
thermal heterogeneity, 252 standard linear solid, 67, 91, 94, 209
thermal model viscosity, 66, 69, 110, 111, 113, 116, 125, 164,
half-space, 314 188, 191, 283, 286, 290, 294, 303, 307,
plate, 314 323, 325, 326, 329, 330, 332“336, 347,
thermal models, 259 363, 372, 387, 392
thermal properties, 54 apparent, 163
thermal vibrations, 158 mantle, 283, 341, 342, 353, 364
thermochemical convection, 378 temperature-dependent, 373, 374
thermodynamic relations, 97, 102, 111, 116, 177 viscous damping, 6
thin-plate model, 265, 285 viscous dissipation, 312, 316, 333
thin-sheet model, 262 viscous ¬‚ow, 118, 258
thrust, 267 viscous ¬‚uid, 21, 117, 119, 132, 134, 142, 311
topography, 330, 378 viscous forces, 128
toroidal, 381, 382, 387, 394 viscous heating, 387
toroidal modes, 220, 222“224, 231, 239“241, viscous resistance, 331
245 viscoplastic, 316
total energy, 97, 133 VLBI, 276
traction, 41, 42, 86, 217, 218, 221, 226 volcanism, 284, 308
surface, 51 volume, 97
transform fault resistance, 273 volume expansion coef¬cient, 98
transform faults, 271, 272 vorticity, 311, 393
transformational faulting, 322 vorticity tensor, 64
transition zone, 12, 17, 97, 104, 154, 169, 294,
water content, 154, 182, 318, 322
365
wave
transmission coef¬cients, 209
attenuation, 93, 94
transport properties, 153, 156
conversion, 87, 88
travel time, 10
re¬‚ection, 87, 88
travel time tables, 10
transmission, 88
travelling waves, 221, 245
wavefronts, 209, 233
trench suction, 273
wavelength, 119, 121, 191
triple junctions, 272
wavenumber, 149, 223
true polar wander, 359
waves
tsunami, 289
conversion, 236
ultra-high pressure minerals, 317 damping, 92
ultrasonic interferometry, 169, 170 diffraction, 238
undeformed state, 3 re¬‚ection, 208
uplift, 280 scattering, 238
upper mantle, 12, 97, 114, 153, 169, 321, 323, transmission, 236
372 wavespeed, 208
wavespeed heterogeneity, 328
vacancies, 153, 154, 158, 164 work function, 60, 63, 74
vector spherical harmonics, 222, 382
velocity, 2, 110, 119, 125, 131, 132, 336, 350 xenoliths, 153, 297, 319
velocity ¬eld, 37, 60, 110, 132, 142, 146, 384,
385, 394 yield point, 4
432 Index

yield strength envelope, 267“269, 285, 375
yield stress, 286, 374
Young™s modulus, 73, 262

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