• Vectors and Tensors: Isotropy and Anisotropy

• Stress, Strain, Hooke’s law and Elastic coefficient tensor

• Symmetry of elastic coefficient tensor

• Elastic coefficient tensor in isotropic media and some symmetries

• Co-ordinate transformation – Bond Stress and Strain transformation matrices

• Symmetry classes: Cubic, Hexagonal, Orthorhombic, Monocilinic and triclinic systems

• Elastic Coefficient matrices for different symmetry classes

• Phase and Group Velocities

• Plane waves in anisotropic systems

• Christoffel Equation: Eigen Values and Eigen Vectors

• Phase velocities in anisotropic media

• Polarization and particle motion

• Ray tracing systems and Group velocities

• Effective Medium:

• Anisotropy due to layering

• Anisotropy due to fracture

• Stress induced anisotropy

• Seismogram synthesis in layered anisotropic media

• System of ODE

• Propagator matrices

• R/T matrices

• Invariant Embedding : Iteration Equations

• Inverse Transforms

• Some observations, interpretations and applications

Students will be graded based on some homework problems. In addition, each student will be asked to write a term paper on some aspect of anisotropic wave propagation which may include new theoretical development, data analysis (modeling, imaging etc), computer code development or simply a detailed review of some concepts.

 LECTURE NOTES

Lecture 1     Lecture2   Lecture3    Lecture4    Lecture5    Lecture5A    Lecture6

Lecture7     Lecture7A   Lecture8   Lecture9

Lecture10   Lecture11    Lecture12  BoundaryConditions

Reflectivity1   Reflectivity2  Reflectivity3  Reflectivity4  Reflectivity5