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E-raamat: Finite-Difference Modelling of Earthquake Motions: Waves and Ruptures

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(King Abdullah University of Science and Technology, Saudi Arabia), (Univerzita Komenského v Bratislave, Slovakia), (Univerzita Komenského v Bratislave, Slovakia)
  • Formaat: EPUB+DRM
  • Ilmumisaeg: 24-Apr-2014
  • Kirjastus: Cambridge University Press
  • Keel: eng
  • ISBN-13: 9781139861953
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Finite-Difference Modelling of Earthquake Motions: Waves and RupturesSuurem pilt
  • Formaat: EPUB+DRM
  • Ilmumisaeg: 24-Apr-2014
  • Kirjastus: Cambridge University Press
  • Keel: eng
  • ISBN-13: 9781139861953
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Among all the numerical methods in seismology, the finite-difference (FD) technique provides the best balance of accuracy and computational efficiency. This book offers a comprehensive introduction to FD and its applications to earthquake motion. Using a systematic tutorial approach, the book requires only undergraduate degree-level mathematics and provides a user-friendly explanation of the relevant theory. It explains FD schemes for solving wave equations and elastodynamic equations of motion in heterogeneous media, and provides an introduction to the rheology of viscoelastic and elastoplastic media. It also presents an advanced FD time-domain method for efficient numerical simulations of earthquake ground motion in realistic complex models of local surface sedimentary structures. Accompanied by a suite of online resources to help put the theory into practice, this is a vital resource for professionals and academic researchers using numerical seismological techniques, and graduate students in earthquake seismology, computational and numerical modelling, and applied mathematics.

Arvustused

'This is an excellent book for those who wish to learn about the current state of the art of FD modeling of earthquake ground motion, bring themselves 'up to speed' in it, and apply it to their own research problems. Aside from the introductory chapters containing preliminary material, all chapters include detailed and comprehensive discussions of the various topics Given that this book covers both past work and recent advances in the subject of the FD modeling of earthquake ground motion, it should make a significant contribution to the discipline.' Edward S. Krebes, The Leading Edge

Muu info

A systematic tutorial introduction to the finite-difference (FD) numerical modelling technique for professionals, academic researchers, and graduate students in seismology.
Acknowledgements xv
List of selected symbols xvii
1 Introduction
1(6)
Part I Mathematical-Physical Model
2 Basic mathematical-physical model
7(11)
2.1 Medium
7(1)
2.2 Governing equation: equation of motion
8(3)
2.2.1 Strong form
9(1)
2.2.2 Weak form
10(1)
2.2.3 Integral strong form
11(1)
2.2.4 Concluding remark
11(1)
2.3 Constitutive law: stress-strain relation
11(2)
2.3.1 Elastic continuum
12(1)
2.3.2 Viscoelastic continuum
13(1)
2.4 Strong-form formulations of equations
13(3)
2.4.1 Displacement-stress formulation
14(1)
2.4.2 Displacement formulation
14(1)
2.4.3 Displacement-velocity-stress formulation
14(1)
2.4.4 Velocity-stress formulation
14(2)
2.5 Boundary conditions
16(1)
2.5.1 Free surface
16(1)
2.5.2 Welded material interface
16(1)
2.6 Initial conditions
17(1)
2.7 Wavefield source (wavefield excitation)
17(1)
3 Rheological models of a continuum
18(40)
3.1 Basic rheological models
20(3)
3.1.1 Hooke elastic solid .
20(2)
3.1.2 Newton viscous liquid
22(1)
3.1.3 Saint-Venant plastic solid
22(1)
3.2 Combined rheological models
23(1)
3.3 Viscoelastic continuum and its rheological models
23(23)
3.3.1 Stress-strain and strain-stress relations in a viscoelastic continuum
24(3)
3.3.2 Maxwell and Kelvin-Voigt bodies
27(1)
3.3.3 Zener body (standard linear solid)
27(4)
3.3.4 Phase velocity in elastic and viscoelastic continua
31(2)
3.3.5 Measure of dissipation and attenuation in a viscoelastic continuum
33(2)
3.3.6 Attenuation in Zener body
35(1)
3.3.7 Generalized Zener body (GZB)
35(3)
3.3.8 Generalized Maxwell body (GMB-EK)
38(1)
3.3.9 Equivalence of GZB and GMB-EK
39(1)
3.3.10 Anelastic functions (memory variables)
40(3)
3.3.11 Anelastic coefficients and unrelaxed modulus
43(1)
3.3.12 Attenuation and phase velocity in GMB-EK/GZB continuum
44(1)
3.3.13 Stress-strain relation in 3D
45(1)
3.4 Elastoplastic continuum
46(12)
3.4.1 Simplest elastoplastic bodies
47(3)
3.4.2 Iwan elastoplastic model for hysteretic stress-strain behaviour
50(8)
4 Earthquake source
58(15)
4.1 Dynamic model of an earthquake source
59(5)
4.1.1 Boundary conditions for dynamic shear faulting
60(1)
4.1.2 Friction law
61(3)
4.2 Kinematic model of an earthquake source
64(9)
4.2.1 Point source
65(3)
4.2.2 Finite-fault kinematic source
68(5)
Part II The Finite-Difference Method
5 Time-domain numerical methods
73(10)
5.1 Introduction
73(1)
5.2 Fourier pseudo-spectral method
74(2)
5.3 Spectral element method
76(3)
5.4 Spectral discontinuous Galerkin scheme with ADER time integration
79(2)
5.5 Hybrid methods
81(2)
6 Brief introduction to the finite-difference method
83(14)
6.1 Space-time grids
83(3)
6.1.1 Cartesian grid
83(1)
6.1.2 Uniform, nonuniform and discontinuous grids
84(1)
6.1.3 Structured and unstructured grids
84(1)
6.1.4 Space-time locations of field variables
84(2)
6.2 FD approximations based on Taylor series
86(7)
6.2.1 Simple approximations
86(2)
6.2.2 Combined approximations: convolution
88(2)
6.2.3 Approximations applied to a harmonic wave
90(1)
6.2.4 General note on the FD approximations
91(2)
6.3 Explicit and implicit FD schemes
93(1)
6.4 Basic properties of FD schemes
94(2)
6.5 Approximations based on dispersion-relation-preserving criterion
96(1)
7 1D problem
97(69)
7.1 Equation of motion and the stress-strain relation
97(2)
7.2 A simple FD scheme: a tutorial introduction to FD schemes
99(24)
7.2.1 Plane harmonic wave in a physical continuum
100(1)
7.2.2 Plane harmonic wave in a grid
100(1)
7.2.3 (2,2) 1D FD scheme on a conventional grid
101(2)
7.2.4 Analysis of grid-dispersion relations
103(11)
7.2.5 Summary of the identified partial regimes
114(1)
7.2.6 Grid phase and group velocities
115(4)
7.2.7 Local error
119(2)
7.2.8 Sufficiently accurate numerical simulation
121(2)
7.3 FD schemes for an unbounded smoothly heterogeneous medium
123(28)
7.3.1 (2,2) displacement scheme on a conventional grid
123(2)
7.3.2 (2,2) displacement-stress scheme on a spatially staggered grid
125(2)
7.3.3 (2,2) velocity-stress scheme on a staggered grid
127(2)
7.3.4 Optimally accurate displacement scheme on a conventional grid
129(4)
7.3.5 (2,4) and (4,4) velocity-stress schemes on a staggered grid
133(11)
7.3.6 (4,4) velocity-stress schemes on a collocated grid
144(7)
7.4 FD schemes for a material interface
151(4)
7.4.1 Simple general consideration
152(1)
7.4.2 Hooke's law and equation of motion for a welded interface
153(1)
7.4.3 Simple rheological model of a welded interface
154(1)
7.4.4 FD schemes
154(1)
7.5 FD schemes for a free surface
155(3)
7.5.1 Stress imaging
156(1)
7.5.2 Adjusted FD approximations
157(1)
7.6 Boundaries of a spatial grid
158(3)
7.6.1 Perfectly matched layer: theory
159(1)
7.6.2 Perfectly matched layer: scheme
160(1)
7.7 Wavefield excitation
161(2)
7.7.1 Body-force term and incremental stress
162(1)
7.7.2 Wavefield injection based on wavefield decomposition
162(1)
7.8 FD scheme for the anelastic functions for a smooth medium
163(3)
8 3D finite-difference schemes
166(33)
8.1 Formulations and grids
166(4)
8.1.1 Displacement conventional-grid schemes
166(1)
8.1.2 Velocity-stress staggered-grid schemes
167(1)
8.1.3 Displacement-stress schemes on the grid staggered in space
168(1)
8.1.4 Velocity-stress partly-staggered-grid schemes
168(1)
8.1.5 Optimally accurate schemes
169(1)
8.1.6 Velocity-stress schemes on the collocated grid
170(1)
8.2 Schemes on staggered, partly-staggered, collocated and conventional grids
170(6)
8.2.1 (2,4) velocity-stress scheme on the staggered grid
171(1)
8.2.2 (2,4) velocity-stress scheme on the partly-staggered grid
172(3)
8.2.3 (4,4) velocity-stress scheme on the collocated grid
175(1)
8.2.4 Disp1a"&ment scheme on the conventional grid
175(1)
8.3 Accuracy of FD schemes with respect to P-wave to S-wave speed ratio: analysis of local errors
176(17)
8.3.1 Equations and FD schemes
176(6)
8.3.2 Local errors
182(1)
8.3.3 The exact and numerical values of displacement in a grid
183(2)
8.3.4 Equivalent spatial sampling for the errors in amplitude and the vector difference
185(2)
8.3.5 Essential summary based on the numerical investigation
187(1)
8.3.6 Interpretation of the errors
187(5)
8.3.7 Summary
192(1)
8.4 Stability and grid dispersion of the VS SG (2,4) scheme
193(6)
9 Velocity-stress staggered-grid scheme for an unbounded heterogeneous viscoelastic medium
199(18)
9.1 FD modelling of a material interface
199(3)
9.2 Stress-strain relation at a material interface
202(8)
9.2.1 Planar interface parallel to a coordinate plane
203(2)
9.2.2 Planar interface in a general orientation
205(1)
9.2.3 Effective orthorhombic averaged medium
206(2)
9.2.4 Effective grid density
208(1)
9.2.5 Simplified approach with harmonic averaging of elastic moduli: isotropic averaged medium
209(1)
9.3 Incorporation of realistic attenuation
210(7)
9.3.1 Material interface in a viscoelastic medium
210(1)
9.3.2 Scheme for the anelastic functions for an isotropic averaged medium
211(1)
9.3.3 Scheme for the anelastic functions for an orthorhombic averaged medium
212(1)
9.3.4 Coarse spatial distribution of anelastic functions
213(2)
9.3.5 VS SG (2,4) scheme for a heterogeneous viscoelastic medium
215(2)
10 Schemes for a free surface
217(10)
10.1 Planar free surface
217(6)
10.1.1 Stress imaging in the (2,4) VS SG scheme
218(3)
10.1.2 Adjusted FD approximations in the (2,4) VS SG scheme
221(2)
10.2 Free-surface topography
223(4)
11 Discontinuous spatial grid
227(7)
11.1 Overview of approaches
227(2)
11.2 Two basic problems and general considerations
229(1)
11.3 Velocity-stress discontinuous staggered grid
230(4)
11.3.1 Calculation of the field variables at the boundary of the finer grid in the overlapping zone
230(1)
11.3.2 Calculation of the field variables at the boundary of the coarser grid in the overlapping zone
231(2)
11.3.3 Calculation of the field variables at the nonreflecting boundary
233(1)
12 Perfectly matched layer
234(8)
12.1 Split formulation of the PML
235(3)
12.2 Unsplit formulation of the PML
238(1)
12.3 Summary of the formulations
239(1)
12.4 Time discretization of the unsplit formulation
239(3)
13 Simulation of the kinematic sources
242(4)
13.1 Wavefield decomposition
242(1)
13.2 Body-force term
242(3)
13.3 Incremental stress
245(1)
14 Simulation of dynamic rupture propagation
246(13)
14.1 Traction-at-split-node method
247(5)
14.2 Implementation of TSN in the staggered-grid scheme
252(4)
14.3 Initiation of spontaneous rupture propagation
256(3)
15 Preparation of computations and a computational algorithm
259(4)
Part III Finite-Element Method And Hybrid Finite-Difference-finite-Element Method
16 Finite-element method
263(22)
16.1 Weak form of the equation of motion
263(2)
16.2 Discrete weak form of the equation of motion for an element
265(2)
16.3 Shape functions
267(6)
16.4 FE scheme for an element using the local restoring-force vector
273(5)
16.5 FE scheme for the whole domain using the global restoring-force vector
278(4)
16.6 Efficient computation of the restoring-force vector
282(1)
16.7 Comparison of formulations with the restoring force and stiffness matrix
283(1)
16.8 Essential summary of the FEM implementation
284(1)
17 Traction-at-split-node modelling of dynamic rupture propagation
285(10)
17.1 Implementation of TSN in the FEM
285(3)
17.2 Spurious high-frequency oscillations of the slip rate
288(2)
17.3 Approaches to suppress high-frequency oscillations
290(5)
17.3.1 Adaptive smoothing
290(2)
17.3.2 Kelvin-Voigt damping
292(1)
17.3.3 A-posteriori filtration
293(2)
18 Hybrid finite-difference-finite-element method
295(12)
18.1 Computational domain
295(1)
18.2 Principle of the FD-FE causal communication
296(1)
18.3 Smooth transition zone with FD-FE averaging
297(2)
18.4 Illustrative numerical simulations using hybrid FD-FE method
299(1)
18.5 Potential improvement of the hybrid FD-FE method
300(7)
Part IV Finite-Difference Modelling Of Seismic Motion At Real Sites
19 Modelling of earthquake motion: Mygdonian basin
307(20)
19.1 Modelling of earthquake motion and real earthquakes by the FDM
307(1)
19.2 Mygdonian basin near Thessaloniki, Greece
308(19)
19.2.1 Why the Mygdonian basin? - the E2VP
308(1)
19.2.2 The realistic model and implied challenges
309(3)
19.2.3 Comparative modelling for stringent canonical models
312(8)
19.2.4 Modelling for the realistic three-layered viscoelastic model
320(2)
19.2.5 Lessons learned from ESG 2006and E2VP
322(2)
Concluding remarks: search for the best scheme 324(3)
Appendix A: Time-frequency misfit and goodness-of-fit criteria for quantitative comparison of time signals 327(8)
A.1 Characterization of a signal
327(2)
A.1.1 Simplest characteristics
327(1)
A.1.2 Time-frequency decomposition
328(1)
A.2 Comparison of signals
329(1)
A.2.1 TF envelope and phase differences
329(1)
A.2.2 Locally normalized and globally normalized criteria
329(1)
A.3 Comparison of three-component signals
330(5)
A.3.1 TF misfit criteria
331(1)
A.3.2 TF goodness-of-fit criteria
331(4)
References 335(28)
Index 363
Peter Moczo is a professor of physics and Chair of the Department of Astronomy, Physics of the Earth, and Meteorology at Comenius University, Bratislava. He is the main author of several monographs and extended articles on the finite-difference method (including the highly-respected Acta Physica Slovaca article which partly forms the basis of this book). Professor Moczo is a member of the Learned Society of the Slovak Academy of Sciences, and his awards include the Prize of the Slovak Academy of Sciences for Infrastructure, the Silver Medal of the Faculty of Mathematics, Physics and Informatics of Comenius University, and the Dionyz Stur Medal of the Slovak Academy of Sciences for Achievements in Natural Sciences. Along with his two co-authors, Professor Moczo is a leading member of the (informal) NuQuake research group, studying numerical modelling of seismic wave propagation and earthquake motion, at Comenius University and the Slovak Academy of Science in Bratislava. As part of this group, all three authors were major contributors to the elaboration of the finite-difference method and hybrid finite-difference/finite-element method. Jozef Kristek is an associate professor of physics at the Department of Astronomy, Physics of the Earth, and Meteorology at Comenius University, Bratislava. His research, as part of the NuQuake group, focuses on the development of numerical-modelling methods for seismic wave propagation and earthquake motion in structurally complex media. Dr Kristek has been awarded the Prize of the Slovak Academy of Sciences for Infrastructure and the Dean's Prize for Science for his work in this area. Martin Gális is a postdoctoral researcher at the King Abdullah University of Science and Technology (KAUST), Saudi Arabia. Dr Gális' research also focuses on the development of numerical-modelling methods for seismic wave propagation and earthquake motion in structurally complex media. He has also been awarded the Prize of the Slovak Academy of Sciences for Infrastructure.
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