Fundamentals of geophysics

Cover......Page 1
Half-title......Page 3
Title......Page 5
Copyright......Page 6
Contents......Page 7
Preface to the second edition......Page 9
Acknowledgements......Page 11
1.1.1 The discovery and description of the planets......Page 13
1.1.3 Characteristics of the planets......Page 14
1.1.3.1 Bode’s law......Page 17
1.1.3.2 The terrestrial planets and the Moon......Page 19
1.1.3.3 The great planets......Page 21
1.1.3.4 Pluto and the outer solar system......Page 23
1.1.4 The origin of the solar system......Page 24
1.2.1 Historical introduction......Page 27
1.2.2.1 Pangaea......Page 28
1.2.2.2 Computer-assisted reconstructions......Page 29
1.2.2.3 Paleomagnetism and continental drift......Page 30
1.2.3.1 Lithospheric plates......Page 32
1.2.4 Types of plate margin......Page 33
1.2.5 Sea-floor spreading......Page 34
1.2.5.1 The Vine–Matthews–Morley hypothesis......Page 35
1.2.5.2 Rates of sea-floor spreading......Page 36
1.2.6 Plate margins......Page 37
1.2.6.1 Constructive margins......Page 38
1.2.6.2 Destructive margins......Page 39
1.2.6.3 Conservative margins......Page 40
1.2.7.1 Stability of triple junctions......Page 41
1.2.7.2 Evolution of triple junctions in the northeast Pacific......Page 42
1.2.8 Hotspots......Page 44
1.2.9 Plate motion on the surface of a sphere......Page 46
1.2.9.1 Euler poles of rotation......Page 47
1.2.9.2 Absolute plate motions......Page 49
1.2.10.1 Forces acting on lithospheric plates......Page 50
Advanced level......Page 52
1.5 EXERCISES......Page 53
2.1.1 Earth’s size......Page 55
2.1.2 Earth’s shape......Page 56
2.2.1.1 Potential energy and work......Page 57
2.2.2.1 Gravitational potential......Page 58
2.2.2.3 Mass and mean density of the Earth......Page 59
2.3.2 Centripetal and centrifugal acceleration......Page 60
2.3.2.2 Centrifugal acceleration and potential......Page 61
2.3.3.1 Lunar tidal periodicity......Page 62
2.3.3.2 Tidal effect of the Sun......Page 64
2.3.3.3 Spring and neap tides......Page 65
2.3.4.1 Effect of lunar tidal friction on the length of the day......Page 66
2.3.4.2 Increase of the Earth–Moon distance......Page 68
2.3.4.3 The Chandler wobble......Page 69
2.3.4.4 Precession and nutation of the rotation axis......Page 70
2.3.4.5 Milankovitch climatic cycles......Page 71
2.3.5 Coriolis and Eötvös accelerations......Page 72
2.4.1 The figure of the Earth......Page 73
2.4.2 Gravitational potential of the spheroidal Earth......Page 74
2.4.3 Gravity and its potential......Page 75
2.4.4 Normal gravity......Page 76
2.4.5 The geoid......Page 78
2.4.6 Satellite geodesy......Page 79
2.4.6.1 Satellite laser-ranging......Page 80
2.4.6.3 Satellite-based global positioning systems (GPS)......Page 81
2.4.6.4 Measurement of gravity and the geoid from orbiting satellites......Page 82
2.4.6.5 Observation of crustal deformation with satelliteborne radar......Page 83
2.5.1 Introduction......Page 85
2.5.2.1 Free-fall method......Page 86
2.5.2.2 Rise-and-fall method......Page 87
2.5.3 Relative measurement of gravity: the gravimeter......Page 88
2.5.4 Correction of gravity measurements......Page 89
2.5.4.1 Latitude correction......Page 90
2.5.4.4 Free-air correction......Page 91
2.5.5 Density determination......Page 92
2.5.5.3 Borehole gravimetry......Page 93
2.5.6 Free-air and Bouguer gravity anomalies......Page 95
2.6.2 Separation of regional and residual anomalies......Page 96
2.6.2.2 Polynomial representation......Page 97
2.6.2.4 Anomaly enhancement and filtering......Page 99
2.6.3 Modelling gravity anomalies......Page 101
2.6.3.1 Uniform sphere: model for a diapir......Page 102
2.6.3.3 Horizontal cylinder: model for anticline or syncline......Page 103
2.6.3.4 Horizontal thin sheet......Page 104
2.6.3.5 Horizontal slab: model for a vertical fault......Page 105
2.6.3.6 Iterative modelling......Page 106
2.6.4.1 Continental and oceanic gravity anomalies......Page 107
2.6.4.2 Gravity anomalies across mountain chains......Page 108
2.6.4.3 Gravity anomalies across an oceanic ridge......Page 109
2.7.1 The discovery of isostasy......Page 111
2.7.2.1 The Airy–Heiskanen model......Page 113
2.7.2.3 Vening Meinesz elastic plate model......Page 114
2.7.4 Isostatic gravity anomalies......Page 115
2.8.1 Brittle and ductile deformation......Page 117
2.8.2 Viscous flow in liquids......Page 118
2.8.3.1 Viscoelastic model......Page 119
2.8.4 Creep......Page 120
2.8.4.1 Crystal defects......Page 121
2.8.5 Rigidity of the lithosphere......Page 122
2.8.5.1 Lithospheric flexure caused by oceanic islands......Page 123
2.8.5.2 Lithospheric flexure at a subduction zone......Page 124
2.8.5.3 Thickness of the lithosphere......Page 125
2.8.6 Mantle viscosity......Page 126
2.8.6.1 Viscosity of the upper mantle......Page 127
2.8.6.2 Viscosity of the lower mantle......Page 128
Introductory level......Page 129
2.11 EXERCISES......Page 130
3.1 INTRODUCTION......Page 133
3.2.1 Elastic, anelastic and plastic behavior of materials......Page 134
3.2.3.1 Longitudinal strain......Page 135
3.2.3.3 Shear strain......Page 136
3.2.4.2 Shear modulus in terms of Young’s modulus and Poisson’s ratio......Page 138
3.2.4.4 Anisotropy......Page 139
3.2.5 Imperfect elasticity in the Earth......Page 140
3.3.2.1 Compressional waves......Page 142
3.3.2.2 Transverse waves......Page 143
3.3.2.4 D’Alembert’s principle......Page 145
3.3.2.6 The energy in a seismic disturbance......Page 146
3.3.2.7 Attenuation of seismic waves......Page 147
3.3.3.3 The dispersion of surface waves......Page 148
3.3.4 Free oscillations of the Earth......Page 149
3.3.4.3 Toroidal oscillations......Page 150
3.3.4.4 Comparison with surface waves......Page 151
3.4.1 Introduction......Page 152
3.4.2.1 Vertical-motion seismometer......Page 153
3.4.2.3 Strain seismometer......Page 154
3.4.3.1 Effect of instrumental damping......Page 155
3.4.3.2 Long-period and short-period seismometers......Page 156
3.4.3.3 Broadband seismometers......Page 157
3.4.4.2 Digital recording......Page 158
3.4.4.3 Phases on a seismogram......Page 159
3.5.1 Introduction......Page 160
3.5.2 Location of the epicenter of an earthquake......Page 161
3.5.3 Global seismicity......Page 162
3.5.4 Analysis of earthquake focal mechanisms......Page 163
3.5.4.1 Single-couple and double-couple radiation patterns......Page 164
3.5.4.2 Fault-plane solutions......Page 165
3.5.4.3 Mechanics of faulting......Page 166
3.5.4.4 Focal mechanisms at active plate margins......Page 167
3.5.4.5 Focal mechanisms in continental collisional zones......Page 169
3.5.5 Secondary effects of earthquakes: landslides, tsunami, fires and fatalities......Page 170
3.5.6.1 Earthquake intensity......Page 172
3.5.6.2 Earthquake magnitude......Page 174
3.5.6.3 Relationship between magnitude and intensity......Page 177
3.5.8 Energy released in an earthquake......Page 178
3.5.9.1 Prediction of the location of an earthquake......Page 179
3.5.9.2 Prediction of the time and size of an earthquake......Page 180
3.5.10 Earthquake control......Page 181
3.5.11 Monitoring nuclear explosions......Page 182
3.6.2.1 The law of reflection using Huygens’ principle......Page 183
3.6.2.3 Diffraction......Page 184
3.6.3.1 The law of reflection using Fermat’s principle......Page 185
3.6.4 Partitioning of seismic body waves at a boundary......Page 186
3.6.5 Reflection seismology......Page 187
3.6.5.1 Reflection at a horizontal interface......Page 188
3.6.5.2 Reflection at an inclined interface......Page 190
3.6.5.3 Reflection and transmission coefficients......Page 192
3.6.5.5 Seismic noise......Page 193
3.6.6.1 Refraction at a horizontal interface......Page 194
3.6.6.2 Refraction at an inclined interface......Page 196
3.6.6.3 Refraction with continuous change of velocity with depth......Page 197
3.7.1 Introduction......Page 198
3.7.2.1 Seismic rays in a uniformly layered Earth......Page 200
3.7.2.2 Travel-time curves for P-, PKP- and PKIKP-waves......Page 201
3.7.3.1 Inversion of travel-time versus distance curves......Page 202
3.7.4 Radial variations of density, gravity and pressure......Page 203
3.7.4.1 Density inside the Earth......Page 204
3.7.5 Models of the Earth’s internal structure......Page 205
3.7.5.1 The crust......Page 206
3.7.5.2 The upper mantle......Page 207
3.7.5.3 The lower mantle......Page 208
3.7.6 Seismic tomography......Page 209
3.7.6.1 Travel-time residuals and velocity anomalies......Page 210
3.7.6.2 Mantle tomography......Page 211
Introductory level......Page 213
3.9 REVIEW QUESTIONS......Page 214
3.10 EXERCISES......Page 215
4.1.1.2 Units of time......Page 219
4.1.2 Estimating the Earth’s age......Page 220
4.1.2.1 Cooling of the Sun......Page 221
4.1.2.4 Oceanic salinity......Page 222
4.1.3.1 Radioactive decay......Page 223
4.1.4.1 Radioactive carbon......Page 224
4.1.4.2 The mass spectrometer......Page 225
4.1.4.3 Rubidium–strontium......Page 226
4.1.4.4 Potassium–argon......Page 227
4.1.4.5 Argon–argon......Page 228
4.1.4.6 Uranium–lead: the concordia–discordia diagram......Page 229
4.1.5 Ages of the Earth and solar system......Page 231
4.2.1 introduction......Page 232
4.2.2 Thermodynamic principles......Page 233
4.2.3 Temperature inside the Earth......Page 234
4.2.3.2 The melting point gradient......Page 235
4.2.4.1 Conduction......Page 236
4.2.4.2 Convection......Page 238
4.2.5 Sources of heat in the Earth......Page 239
4.2.5.1 Radioactive heat production......Page 240
4.2.6.1 Penetration of external heat into the Earth......Page 242
4.2.6.2 Cooling of the oceanic lithosphere......Page 243
4.2.7 Continental heat flow......Page 245
4.2.7.2 Variation of continental heat flow with age......Page 247
4.2.7.3 Heat transfer through porous crustal rocks......Page 248
4.2.8 Oceanic heat flow......Page 249
4.2.8.1 Variation of oceanic heat flow and depth with lithospheric age......Page 251
4.2.8.2 Global heat flow......Page 253
4.2.8.3 Models for the cooling of oceanic lithosphere......Page 255
4.2.8.5 Heat flow at subduction zones......Page 258
4.2.9.1 Thermal convection......Page 259
4.2.9.2 Convection at high Rayleigh numbers......Page 260
4.2.9.3 Models of mantle convection......Page 262
4.2.9.4 Mantle plumes......Page 263
4.3.2 Electrical principles......Page 264
4.3.2.1 Electric field and potential......Page 265
4.3.2.3 Types of electrical conduction......Page 266
4.3.3 Electrical properties of the Earth......Page 267
4.3.3.1 Electrical surveying......Page 268
4.3.4.1 Self-potential (spontaneous potential)......Page 269
4.3.4.2 SP surveying......Page 270
4.3.4.3 Telluric currents......Page 271
4.3.5.1 Potential of a single electrode......Page 272
4.3.5.3 Special electrode configurations......Page 273
4.3.5.4 Current distribution......Page 274
4.3.5.5 Apparent resistivity......Page 275
4.3.5.6 Vertical electrical sounding......Page 276
4.3.5.7 Induced polarization......Page 277
4.3.5.8 Electrical resistivity tomography......Page 279
4.3.6 Electromagnetic surveying......Page 280
4.3.6.1 Electromagnetic induction......Page 281
4.3.6.2 EM induction surveying......Page 283
4.3.6.3 Magnetotelluric sounding......Page 284
4.3.6.4 Ground-penetrating radar......Page 285
4.3.7 Electrical conductivity in the Earth......Page 286
4.5 REVIEW QUESTIONS......Page 288
Geochronology......Page 289
The Earth’s heat......Page 290
Geoelectricity......Page 291
5.1.2 Pioneering studies in terrestrial magnetism......Page 293
5.1.3 The physical origins of magnetism......Page 294
5.2.1 Introduction......Page 295
5.2.2.2 The potential of a magnetic pole......Page 296
5.2.4 The magnetic field of an electrical current......Page 297
5.2.5 Magnetization and the magnetic field inside a material......Page 299
5.2.6 The magnetic properties of materials......Page 300
5.2.6.2 Paramagnetism......Page 301
5.2.6.3 Ferromagnetism......Page 302
5.2.7.1 Magnetocrystalline anisotropy......Page 303
5.2.7.2 Magnetostatic (shape) anisotropy......Page 304
5.3.1 The magnetic properties of rocks......Page 305
5.3.2.1 The titanomagnetite series......Page 306
5.3.3 Other ferrimagnetic minerals......Page 307
5.3.5 Grain size dependence of ferrimagnetic properties......Page 308
5.3.5.1 Superparamagnetism......Page 309
5.3.5.3 Multidomain particles......Page 310
5.3.6.1 Thermoremanent magnetization......Page 311
5.3.6.2 Sedimentary remanent magnetizations......Page 312
5.3.6.3 Chemical remanent magnetization......Page 313
5.3.6.4 Isothermal remanent magnetization......Page 314
5.3.7 Environmental magnetism......Page 315
5.4.1 Introduction......Page 317
5.4.3 The magnetic field of external origin......Page 318
5.4.3.3 Diurnal variation and magnetic storms......Page 319
5.4.4 The magnetic field of internal origin......Page 321
5.4.4.1 The dipole field......Page 323
5.4.5 Secular variation......Page 324
5.4.5.1 Secular variation of the dipole field......Page 325
5.4.6 Origin of the internal field......Page 326
5.4.6.2 The geomagnetic dynamo......Page 327
5.4.7.1 Magnetic field of the Sun......Page 328
5.4.7.2 Lunar magnetism......Page 329
5.4.7.4 The magnetic fields of the planets......Page 330
5.5.1 The magnetization of the Earth’s crust......Page 332
5.5.2 Magnetometers......Page 333
5.5.2.2 The proton-precession magnetometer......Page 334
5.5.2.3 The absorption-cell magnetometer......Page 335
5.5.3.1 Measurement methods......Page 336
5.5.3.3 The survey pattern......Page 337
5.5.4 Reduction of magnetic field measurements......Page 338
5.5.5.2 Magnetic anomaly of a vertical dike......Page 339
5.5.5.3 Magnetic anomaly of an inclined magnetization......Page 341
5.5.5.4 Magnetic anomalies of simple geometric bodies......Page 342
5.5.6 Oceanic magnetic anomalies......Page 344
5.6.2 The time-averaged geomagnetic field......Page 346
5.6.2.1 Archeomagnetic records of secular variation......Page 347
5.6.2.2 The axial geocentric dipole hypothesis......Page 348
5.6.3 Methods of paleomagnetism......Page 349
5.6.3.2 Stepwise progressive demagnetization......Page 350
5.6.3.3 Analysis of magnetization components......Page 351
5.6.3.4 Statistical analysis of paleomagnetic directions......Page 352
5.6.3.5 Field tests of magnetization stability......Page 353
5.6.4 Paleomagnetism and tectonics......Page 355
5.6.4.1 Location of the virtual geomagnetic pole......Page 356
5.6.4.2 Apparent polar wander paths......Page 357
5.6.4.3 Paleogeographic reconstructions using APW paths......Page 358
5.6.4.4 Paleomagnetism and continental drift......Page 360
5.7.1 Introduction......Page 361
5.7.1.2 Geomagnetic polarity intervals......Page 362
5.7.2 Magnetostratigraphy in lavas and sediments......Page 363
5.7.3.1 Marine magnetic anomalies......Page 364
5.7.3.2 Uniformity of sea-floor spreading......Page 365
5.7.3.3 The marine record of geomagnetic polarity history......Page 366
5.7.4.1 Magnetostratigraphic calibration of polarity sequences......Page 367
5.7.4.2 Reconstruction of plate tectonic motions......Page 368
5.7.6 Early Mesozoic and Paleozoic reversal history......Page 370
5.9 REVIEW QUESTIONS......Page 371
5.10 EXERCISES......Page 372
Derivation of general equations of motion......Page 375
Equation of transverse waves......Page 376
Appendix B Cooling of a semi-infinite half-space......Page 378
Evaluation of the integral Y0 in Eq. (B17)......Page 379
Bibliography......Page 380
Index......Page 387