Syllabus
* Green's tensor
Definition of Green's tensor for elastodynamic problem, units. Green's tensor for a homogeneous space, the near and far field. Space derivative of Green's tensor in the far-field approximation, relation to time derivative. Complete space derivative of Green's tensor; the near, intermediate and far-field terms.
* Seismic moment tensor
Surface moment density, complete moment tensor. Displacement discontinuity; general and pure-shear case. Eigenvalues and eigenvectors, relation with the P-T-N axes. The moment-tensor norm; scalar seismic moment. Volume and deviatoric part of the moment tensor. The double-couple (DC) and non-DC parts. Source model with tensile component. Equivalent body forces. Relation between individual focal mechanisms and the regional stress field.
* Wave field
Representation theorem and its use for the kinematically prescribed ruptures. Relations between the radiated wave field, Green's tensor and seismic moment tensor. Radiation pattern. The source time function of finite-extent sources and directivity. Haskell's source. Circular source. Principles of the moment tensor retrieval from waveforms. Estimation of the rupture propagation direction from apparent source time functions (empirical Green's function approach). Static displacement field.
* Absorption
Viscoelasticity, general Boltzman model. Complex viscoelastic modulus, complex wave speed, attenuation coefficient and phase velocity. Quality factor (Q) and logarithmic decrement; Qp and Qs. Attenuation-dispersion relations. Maxwell's, Futterman's and Kjartansson's model. Dissipation operators. Intrinsic and scattering attenuation effects. Near-surface attenuation (kappa effect).
* Seismic energy and stress drop
Ray approximation and single-station estimate of radiated energy. Relations between seismic energy and moment. Stress drop. Moment magnitude. Empirical relations between moment and fault size.
* Calculation of moment tensors from complete waveforms
Discrete wavenumber method and program AXITRA. Elementary seismograms. Various parametrizations of the inverse problem (e.g. with fixed or free source position, fixed or free time function). Uncertainty estimate. Multiple point sources. Computer code ISOLA.
* Calculation of slip from complete waveforms
Determination of fault surface. Parametrization of finite-extent sources. Linear and non-linear formulation of the inverse problem. Regularization. Uncertainty estimation. Combining seismic and geodetic data. Coulomb stress. Slip inversion from apparent source time functions.
* Basics of dynamic source models
Strength of rocks, fracture, friction. Modes of fractures. Stresses acting on faults, Mohr’s diagrame. Anderson's theory of faulting. Dynamic models of ruptures with imposed rupture velocity, stress drop of a crack model. Evolution of stress on faults during rupturing, dynamic and station stress drop. Friction laws (Slip weakening, Rate-and-state). Dynamic modeling of spontaneous rupture and seismic cycles. Co-seismic and post-seismic slip, creep, slow earthquakes. Models of subduction earthquakes.
* Forward modeling of strong ground motions
Principles of kinematic and composite models, their directivity. Combined deterministic and stochastic models. Use of empirical Green's functions. Rupture-process scenarios for seismic hazard assessment. Modeling local site effects.
Annotation
Green's tensor (far- and near-field terms, statics). Seismic moment tensor. Wave field. Absorption. Source time function (directivity). Calculating moment tensors from waveforms. Estimating size of fault plane and stress drop.
Energy of seismic waves. Moment magnitude. Principles of slip inversion from seismic and geodetic data.
Inversion of stress filed from focal mechanisms. Coulomb stress. Basic dynamic models of seismic sources.
Forward modeling of seismic strong-ground motions (deterministic and stochastic component).