Describe and analyze the stress and deformation tensors, and the coordinate transformation of the tensors. Analyses the elastic body equilibrium. Application of the analyses to the Earth's crust. Apply the stress-strain relations to real bodies, especially in cases when it is characterized by moduli of elasticity.
Synthesis of equations of motion and Hooke's law in Lame's equations. Generalization of Lame's equations in the Navier-Stokes equation. Proof and discussion of Lame's theorem. Kirchhoff's solution to the wave equation demonstrates retarded potentials and action at a distance. A generalized solution is analyzed in four cases, in one of which a Huygens' principle is recognized. Application of Kirchhoff's solution to a single force, single dipole, and double dipole point source models.
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 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 the generalization of 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 Kirchhoff's solution of the wave equation to find the far field solution and Huygens' principle,
- apply Kirchhoff solution to find the characteristics of a radiation pattern of displacement point sources model for one force, single and double dipole,
- describe the interpretation of the spatial distribution of compression and dilatation of the first arrival of the longitudinal waves of earthquakes in terms of determining the focus mechanism.
- Attending lectures, study notes, and study literature,
- Derivation of the equations
- Analysis of application examples that follow from the derived equations,
- Synthesis of resulting equations in geophysical phenomena.
- Lectures, discussions,
- Derivation of the equations,
- Analysis of the equations and their analytical solutions,
- Independent solving problems in connection with equations.
METHODS OF MONITORING AND VERIFICATION:
Homework, preliminary exam, written and oral exam.
TERMS FOR RECEIVING THE SIGNATURE:
Solved homework, Seminar papers.
Written and oral exam