Page 12 - Physical Principles of Sedimentary Basin Analysis

x Contents

9.5 The deflection of a plate under compression 298
9.6 Damped flexure of a plate above a viscous mantle 301
9.7 The equation for viscoelastic flexure of a plate 302
9.8 Elastic and viscous deformations 304
9.9 Flexure of a viscoelastic plate 307
9.10 Buckling of a viscous plate 310
9.11 Further reading 315
10 Gravity and gravity anomalies 316
10.1 Newton’s law of gravity 316
10.2 Potential energy and the potential 321
10.3 Conservative fields 323
10.4 Gauss’s law 323
10.5 Bouguer’s formula for gravity due to a horizontal
layer 325
10.6 Laplace’s and Poisson’s equations for the potential 327
10.7 Gravity from a buried sphere 329
10.8 Gravity from a horizontal cylinder 330
10.9 Gravity from a prism with rectangular cross-section 332
10.10 Gravity from a 2D polygonal body 334
10.11 Excess mass causing gravity anomalies 340
10.12 Vertical continuation of gravity 341
10.13 Reduction of gravity data 344
10.14 Gravity and isostasy over continents 347
10.15 Gravity and sea bed topography 356
10.16 Further reading 360
11 Quartz cementation of sandstones 361
11.1 Introduction 361
11.2 Quartz kinetics and precipitation rates 362
11.3 Surface area 364
11.4 Isothermal quartz cementation 365
11.5 Calibration of quartz kinetics 367
11.6 Cementation during constant burial 369
11.7 Cementation for general burial histories 374
11.8 Strain rate 375
11.9 A reaction–diffusion equation for silica 377
11.10 The silica concentration between stylolites 379
11.11 Further reading 384
12 Overpressure and compaction: exact solutions 385
12.1 The pressure equation in 1D 386
12.2 The Darcy flux caused by compaction 388
12.3 Void ratio as a function of depth 389
12.4 A simple model for overpressure build-up 392