Preface ........................................................ ix
1 Earthquakes and fault motion ................................. 1
1.1 The origin of earthquakes ............................... 1
1.2 Faults in the Earth's crust ............................. 2
1.3 Geometry of a fault ..................................... 5
1.4 Elastic rebound and the earthquake cycle ................ 7
1.5 Energy, stress drop and seismic moment .................. 9
1.6 Stick-slip motion on a fault ........................... 14
1.7 Seismicity and statistical properties of earthquakes ... 19
2 Processing and analysis of recorded seismic signals ......... 22
2.1 Recorded ground motion in time and frequency domains ... 22
2.2 Analogical and digital data ............................ 25
2.3 Removing the instrumental response ..................... 27
2.4 Processing a seismic signa ............................. 30
2.5 Displacement, velocity and acceleration ................ 36
2.6 Continuous GPS observations ............................ 39
3 Mathematical representation of the source ................... 41
3.1 Fundamental equations of motion for an elastic medium .. 41
3.2 Green's and Somigliana's tensors ....................... 44
3.3 Representation theorem ................................. 45
3.4 Somigliana's tensor for an infinite homogeneous
isotropic medium ....................................... 48
3.5 Green's tensor for an infinite homogeneous isotropic
medium ................................................. 52
3.6 Green's functions for layered media .................... 57
3.7 Focal region ........................................... 59
3.8 Kinematic and dynamic models ........................... 61
4 Point source models ......................................... 63
4.1 Point source approximation ............................. 63
4.2 Equivalent forces. Double couple ....................... 63
4.3 Shear fracture or dislocation .......................... 66
4.4 Point shear fracture in an infinite medium ............. 68
4.5 The geometry of a shear fracture ....................... 77
4.6 Far-field displacements referred to geographical axes .. 78
4.7 Source representation using the focal sphere ........... 80
4.8 The source time function ............................... 82
4.9 Spectral properties of the source time function ........ 86
4.10 Seismic energy radiation ............................... 88
5 The seismic moment tensor ................................... 90
5.1 Definition of the moment tensor ........................ 90
5.2 Eigenvalues and eigenvectors ........................... 93
5.3 Components of the moment tensor ........................ 94
5.4 Moment tensor and elastic dislocations ................. 95
5.5 Moment tensor components referred to geographical
axes ................................................... 98
5.6 The point source moment tensor ......................... 99
5.7 The separation of the moment tensor ................... 102
5.8 Higher-order moment tensors ........................... 105
5.9 Moments of the moment-rate distribution ............... 106
6 Determination of point source mechanisms ................... 108
6.1 Parameters and observations ........................... 108
6.2 The focal sphere ...................................... 109
6.3 Fault-plane solutions from P wave polarities .......... 110
6.4 Inversion of body wave forms .......................... 117
6.5 Empirical Green's functions ........................... 123
6.6 Moment tensor inversion ............................... 124
6.7 Centroid moment tensor inversion ...................... 133
7 Kinematics of extended sources ............................. 135
7.1 Source dimensions ..................................... 135
7.2 Rectangular fault. Haskell's model .................... 138
7.3 Bilateral rupture propagation ......................... 141
7.4 Oblique rupture propagation ........................... 142
7.5 Corner frequency ...................................... 145
7.6 Directivity effects ................................... 148
7.7 Rupture nucleation, propagation and arrest ............ 151
7.8 Kinematic models with variable slip on the fault
plane ................................................. 155
7.9 The circular kinematic model of Sato and Hirasawa ..... 157
8 Determination of source dimensions ......................... 163
8.1 Parameters of kinematic extended source models ........ 163
8.2 Analysis of seismic wave spectra ...................... 163
8.3 Directivity effects on Rayleigh waves ................. 167
8.4 Effects of directivity on body wave form modeling ..... 170
8.5 Apparent source time function ......................... 172
8.6 Far-field inversion of the slip distribution on
fault plane ........................................... 173
8.7 Kinematic inversion of the near-field waves ........... 181
9 Simple dynamic models ...................................... 189
9.1 Kinematic and dynamic models .......................... 189
9.2 Static problem ........................................ 190
9.3 Modes of propagating fractures ........................ 191
9.4 Circular fault. Static model .......................... 192
9.5 Circular fault. Brune's model ......................... 195
9.6 Scaling laws .......................................... 200
10 Dynamics of fracture. Homogeneous models ................... 205
10.1 Griffith's fracture model ............................. 205
10.2 Energy flow towards the fracture front for a growing
crack ................................................. 209
10.3 Stress singularities around a rapture front moving
at constant speed ..................................... 212
10.4 Spontaneous shear-fracture propagation ................ 216
10.5 Friction models of fracture ........................... 220
10.6 Rupture of an expanding circular fault ................ 223
10.7 Far-field displacements of a dynamic circular fault ... 227
11 Fracture dynamics. Heterogeneous models .................... 232
11.1 The cohesive zone ..................................... 232
11.2 The slip-weakening friction model ..................... 233
11.3 Friction laws ......................................... 237
11.4 Determination of Gc from seismic data ................. 243
11.5 Nucleation and arrest of rapture ...................... 246
11.6 Barriers and asperities ............................... 250
11.7 Healing and rupture pulse propagation ................. 253
11.8 Super-shear rapture velocity .......................... 254
12 Modeling earthquakes using fracture dynamics ............... 259
12.1 Dynamic models ........................................ 259
12.2 Modeling earthquakes in three dimensions .............. 260
12.3 Rupture propagation on a planar uniform fault ......... 263
12.4 A finite circular fault in a homogeneous medium ....... 265
12.5 Shallow strike-slip rectangular fault ................. 269
12.6 Spontaneous rapture on a realistic fault: the
Landers 1992 earthquake ............................... 270
12.7 Rupture of a geometrically complex earthquake: the
Izmit event of August 1999 ............................ 273
12.8 Dynamic inversion of the 2008 Iwate intermediate-
depth earthquake ...................................... 276
12.9 Conclusion and perspectives ........................... 281
References ................................................. 284
Index ......................................................... 300
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