Physical Principles of Sedimentary Basin Analysis

Half-title......Page 3
Title......Page 5
Copyright......Page 6
Dedication
......Page 7
Contents......Page 9
Preface......Page 15
Acknowledgments......Page 17
1.1 Notation......Page 19
1.2 Further reading......Page 20
2.1 Porosity......Page 21
2.2 The correlation function and specific surface......Page 24
2.3 The penetrable grain model......Page 27
2.4 Darcy's law......Page 30
2.5 Potential flow and gravity......Page 32
2.6 Permeability as a function of porosity......Page 33
2.7 Empirical permeability relationships......Page 36
2.8 The rotation matrix......Page 38
2.9 Anisotropic permeability......Page 41
2.10 Directional permeability......Page 43
2.11 Average permeability......Page 45
2.12 Fourier's law and heat conductivity......Page 49
2.13 Further reading......Page 55
3.2 Bulk modulus......Page 56
3.3 Shear modulus......Page 57
3.4 Strain......Page 58
3.5 Stress......Page 61
3.6 Rotation of stress and strain......Page 64
3.7 Principal stress......Page 65
3.8 Mohr's circles......Page 69
3.9 Stress ellipsoid......Page 71
3.10 Deviatoric stress......Page 73
3.11 Linear stress–strain relations......Page 74
3.13 Thermal stress compared with lithostatic stress......Page 78
3.14 Buoyancy and effective stress......Page 79
3.15 Effective stress in 3D......Page 81
3.16 Euler and Lagrange coordinates......Page 82
3.17 An important Lagrange coordinate......Page 85
3.18 Conservation laws in 1D......Page 86
3.19 Mass conservation......Page 87
3.20 Momentum balance (Newton's second law)......Page 88
3.21 Particle paths and streamlines......Page 92
3.22 Streamlines in 2D......Page 93
3.23 Further reading......Page 97
4.1 Rock compressibility......Page 98
4.2 More compressibilities......Page 102
4.3 Compressibility of porosity and the solid volume......Page 104
4.5 Compaction of sediments......Page 106
4.6 Gravitational compaction of a hydrostatic clay layer......Page 108
4.7 Further reading......Page 111
5 Burial histories......Page 112
5.1 Porosity as a function of net sediment thickness......Page 113
5.2 Pre-calibration of burial history calculations......Page 115
5.3 Porosity as a function of z......Page 117
5.4 Erosion......Page 118
5.5 Numerical compaction computation......Page 120
5.6 Further reading......Page 122
6 Heat flow......Page 123
6.1 The temperature equation......Page 124
6.2 Stationary 1D temperature solutions......Page 127
6.3 Heat generation......Page 130
6.4 Stationary 1D temperature solutions with heat generation......Page 133
6.5 Heat flow and geotherms in stable continental areas......Page 140
6.6 Stationary geotherms in the lithospheric mantle......Page 142
6.7 Sediment maturity and vitrinite reflectance......Page 145
6.8 Stationary heat flow in a sphere…......Page 150
6.9 Transient cooling of a sphere…......Page 152
6.10 Heat flow and salt domes......Page 156
6.11 Forced convective heat transfer......Page 158
6.12 Transient convective heat flow......Page 165
6.13 Heat flow in fractures......Page 169
6.14 Instantaneous heating or cooling of semi-infinite half-space......Page 172
6.15 Cooling sills and dikes......Page 177
6.16 Solidification and latent heat of fusion......Page 185
6.17 Solidification of sills and dikes......Page 188
6.18 Periodic heating of the surface......Page 191
6.19 Variable surface temperature......Page 195
6.20 Temperature transients from sediment deposition orerosion......Page 199
6.21 Conservation of energy once more......Page 204
6.22 Mantle adiabat......Page 209
6.23 Further reading......Page 211
7.1 Isostatic subsidence......Page 212
7.2 Thickness of crustal roots......Page 216
7.4 Basin subsidence by crustal thinning......Page 218
7.5 The McKenzie model of basin subsidence......Page 220
7.6 The thermal transient of the McKenzie model......Page 225
7.7 The surface heat flow of the McKenzie model......Page 229
7.8 The thermal subsidence of the McKenzie model......Page 231
7.9 Lithospheric stretching of finite duration......Page 233
7.10 Finite duration stretching and temperature......Page 239
7.11 Lithospheric extension, phase changes and subsidence/uplift......Page 242
7.12 Lithospheric extension and decompression melting......Page 248
7.13 Thermal subsidence of the oceanic lithosphere......Page 256
7.14 Backstripping and tectonic subsidence......Page 260
7.15 Subsidence of the Vøring margin, NE Atlantic......Page 264
7.16 Stretching and thinning of the sediments......Page 270
7.17 Further reading......Page 277
8.2 Friction......Page 278
8.3 Stick–slip faulting......Page 281
8.4 The slider-block model of stick–slip motion......Page 282
8.5 Fracture......Page 286
8.6 Hydrofracturing......Page 289
8.7 Ductile flow and yield strength envelopes......Page 291
8.8 Further reading......Page 299
9.1 Equation for flexure of a plate......Page 300
9.2 Flexure from a point load......Page 307
9.3 Flexure from a point load on a broken plate......Page 312
9.4 Flexure and lateral variations of the load......Page 313
9.5 The deflection of a plate under compression......Page 316
9.6 Damped flexure of a plate above a viscous mantle......Page 319
9.7 The equation for viscoelastic flexure of a plate......Page 320
9.8 Elastic and viscous deformations......Page 322
9.9 Flexure of a viscoelastic plate......Page 325
9.10 Buckling of a viscous plate......Page 328
9.11 Further reading......Page 333
10.1 Newton's law of gravity......Page 334
10.2 Potential energy and the potential......Page 339
10.4 Gauss's law......Page 341
10.5 Bouguer's formula for gravity due to a horizontal layer......Page 343
10.6 Laplace's and Poisson's equations for the potential......Page 345
10.7 Gravity from a buried sphere......Page 347
10.8 Gravity from a horizontal cylinder......Page 348
10.9 Gravity from a prism with rectangular cross-section......Page 350
10.10 Gravity from a 2D polygonal body......Page 352
10.11 Excess mass causing gravity anomalies......Page 358
10.12 Vertical continuation of gravity......Page 359
10.13 Reduction of gravity data......Page 362
10.14 Gravity and isostasy over continents......Page 365
10.15 Gravity and sea bed topography......Page 374
10.16 Further reading......Page 378
11.1 Introduction......Page 379
11.2 Quartz kinetics and precipitation rates......Page 380
11.3 Surface area......Page 382
11.4 Isothermal quartz cementation......Page 383
11.5 Calibration of quartz kinetics......Page 385
11.6 Cementation during constant burial......Page 387
11.7 Cementation for general burial histories......Page 392
11.8 Strain rate......Page 393
11.9 A reaction–diffusion equation for silica......Page 395
11.10 The silica concentration between stylolites......Page 397
11.11 Further reading......Page 402
12 Overpressure and compaction: exact solutions......Page 403
12.1 The pressure equation in 1D......Page 404
12.2 The Darcy flux caused by compaction......Page 406
12.3 Void ratio as a function of depth......Page 407
12.4 A simple model for overpressure build-up......Page 410
12.5 Hydrofracturing......Page 415
12.6 Gibson's solution for overpressure......Page 419
12.7 Gibson's solution for porosity reduction......Page 423
12.8 Overpressure and mechanical compaction......Page 425
12.9 The dimensionless Gibson solution......Page 430
12.10 Further reading......Page 433
13.1 Conservation of solid......Page 435
13.2 Conservation of fluid......Page 438
13.3 Poroelastic pressure equation......Page 439
13.4 Storage coefficients......Page 440
13.5 Stress, strain and poroelasticity......Page 443
13.6 Stress caused by overpressure......Page 446
13.7 The rate of change of porosity......Page 449
13.8 A general pressure equation......Page 451
13.9 Potential flow......Page 452
13.11 Simple pressure equations......Page 455
13.12 Further reading......Page 457
14.1 Unconfined flow......Page 458
14.2 Meteoric fluid flow......Page 460
14.3 Decay of overpressure and pressure seals......Page 464
14.4 Overpressure decay in clay......Page 470
14.5 Overpressure build-up in clay......Page 472
14.6 The gravity number......Page 475
14.7 Overpressure from thermal expansion......Page 477
14.8 Special cases of fluid expulsion and mineralreactions......Page 481
14.10 Overpressure from cementation of pore space......Page 483
14.11 Fluid expulsion and mineral reactions......Page 490
14.12 Overpressure from dehydration of clay......Page 491
14.13 Weak (non-Rayleigh) thermal convection......Page 495
14.14 Thermal convection......Page 500
14.15 Further reading......Page 504
15.1 Stationary pressure from a well......Page 506
15.2 Wells and streamlines......Page 509
15.3 The skin factor......Page 511
15.4 Transient pressure from a well......Page 512
15.5 Well testing......Page 517
A.1 Fourier series......Page 520
A.2 Interpolation with Fourier series......Page 521
A.3 The discrete Fourier transform......Page 522
A.4 The fast Fourier transform......Page 523
References......Page 531
Index......Page 541