UID:
almafu_9960117333702883
Format:
1 online resource (xx, 365 pages) :
,
digital, PDF file(s).
ISBN:
1-139-69893-1
,
1-139-86195-6
,
1-139-86087-9
,
1-139-23691-1
,
1-139-86302-9
,
1-139-86872-1
,
1-139-87087-4
,
1-139-86514-5
Content:
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.
Note:
Title from publisher's bibliographic system (viewed on 05 Oct 2015).
,
Cover; Half title; Epigraph; Title; Copyright; Dedication; Contents; Acknowledgements; Selected symbols; Abbreviations; Mathematical notation; Greek symbols; Latin symbols; 1 Introduction; Part I Mathematical-physical model; 2 Basic mathematical-physical model; 2.1 Medium; 2.2 Governing equation: equation of motion; 2.2.1 Strong form; 2.2.2 Weak form; 2.2.3 Integral strong form; 2.2.4 Concluding remark; 2.3 Constitutive law: stress-strain relation; 2.3.1 Elastic continuum; 2.3.2 Viscoelastic continuum; 2.4 Strong-form formulations of equations; 2.4.1 Displacement-stress formulation
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2.4.2 Displacement formulation2.4.3 Displacement-velocity-stress formulation; 2.4.4 Velocity-stress formulation; 2.5 Boundary conditions; 2.5.1 Free surface; 2.5.2 Welded material interface; 2.6 Initial conditions; 2.7 Wavefield source (wavefield excitation); 3 Rheological models of a continuum; 3.1 Basic rheological models; 3.1.1 Hooke elastic solid; 3.1.2 Newton viscous liquid; 3.1.3 Saint-Venant plastic solid; 3.2 Combined rheological models; 3.3 Viscoelastic continuum and its rheological models; 3.3.1 Stress-strain and strain-stress relations in a viscoelastic continuum
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3.3.1.1 Preliminary considerations3.3.1.2 General theory in 1D; 3.3.2 Maxwell and Kelvin-Voigt bodies; 3.3.3 Zener body (standard linear solid); 3.3.4 Phase velocity in elastic and viscoelastic continua; 3.3.5 Measure of dissipation and attenuation in a viscoelastic continuum; 3.3.6 Attenuation in a Zener body; 3.3.7 Generalized Zener body (GZB); 3.3.8 Generalized Maxwell body (GMB-EK); 3.3.9 Equivalence of GZB and GMB-EK; 3.3.10 Anelastic functions (memory variables); 3.3.11 Anelastic coefficients and unrelaxed modulus; 3.3.12 Attenuation and phase velocity in GMB-EK/GZB continuum
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3.3.13 Stress-strain relation in 3D3.4 Elastoplastic continuum; 3.4.1 Simplest elastoplastic bodies; 3.4.2 Iwan elastoplastic model for hysteretic stress-strain behaviour; 3.4.2.1 Preliminary considerations; 3.4.2.2 Iwan model; 3.4.2.3 Iwan model and Masing rules; 3.4.2.4 Determination of parameters for Iwan model; 3.4.2.5 Note on damping; 3.4.2.6 Concluding remark; 4 Earthquake source; 4.1 Dynamic model of an earthquake source; 4.1.1 Boundary conditions for dynamic shear faulting; 4.1.2 Friction law; 4.1.2.1 Linear slip-weakening friction law; 4.1.2.2 Rate- and state-dependent friction law
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4.2 Kinematic model of an earthquake source4.2.1 Point source; 4.2.2 Finite-fault kinematic source; Part II The finite-difference method; 5 Time-domain numerical methods; 5.1 Introduction; 5.2 Fourier pseudo-spectral method; 5.3 Spectral element method; 5.4 Spectral discontinuous Galerkin scheme with ADER time integration; 5.5 Hybrid methods; 6 Brief introduction to the finite-difference method; 6.1 Space-time grids; 6.1.1 Cartesian grid; 6.1.2 Uniform, nonuniform and discontinuous grids; 6.1.3 Structured and unstructured grids; 6.1.4 Space-time locations of field variables
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6.2 FD approximations based on Taylor series
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English
Additional Edition:
ISBN 1-107-02881-7
Language:
English
URL:
https://doi.org/10.1017/CBO9781139236911
