Analysis of stress. Analysis of strain. Strain of the Earth's crust. The stress-strain relations. Constants and modules of elasticity. Lame's equations. Motion and potential. Kirchhoff's solution of the wave equation. Application of the Kirchhoff's solution to different point source models.
After the final exam for the course Theory of elasticity with applications in geophysics student will be able to:
distinguished members of the relative displacement of the translational and rotational deformity,
propose and split the potential of displacement in the translational and rotational,
determine the direction and magnitude of the principal axes of stress and strain,
calculate the amount of major deformation of the Earth's crust and decide which geographic direction they provide in relation to the measured values,
calculate surface and volume dilatation on the basis of the known displacement,
express Lame's constants and Poisson's ratio using the strain and stress of a core sample of the well, and evaluate material samples,
synthesize nucleation phases of the earthquakes (starting from stress-strain relations in real media),
understand the meaning of Hooke's law and motion in the continuum,
explain generalization Lame's equations to the Navier-Stokes equation,
prove Lame's theorem and discuss the decomposition into the scalar and vector wave equation,
explain the retarded potentials; derive Kirchhoff's solution in the absence of singularities, generalizing including sources,
analyze the Kirchhoff's solution of the wave equation to find the far field solution and Huygens' principle,
apply Kirchhoff solution to find the characteristics of radiation pattern of displacement point sources model for one force, single and double-dipole,
describe the interpretation the spatial distribution of compression and dilatation of the first arrival of the longitudinal waves of earthquakes in terms of determining the focus mechanism.
- Aki, K., P.G. Richards: Quantitative Seismology, 2nd Ed., University Science Books, Sansalito, California 2002.
- Bath, M.: Mathemathical Aspects of Seismology, Elsevier, Amsterdam, 1968.