EPS166: Problem Set 1

Due on Tuesday before class, 10/1/1996

Problem 1:

Find the eigenvectors and eigenvalues ( or principal values) of the matrix:

Suggestion:

The method to find the eigenvectors and eigenvalues of the matrix can be found in a standard textbook of linear algebra, or read the handout distributed by our professor.

Problem 2:

The moment tensor for a point dislocation in a transversely anisotropic medium can be described in a matrix:

Where is the dip angle. Please find the principal values. Is the moment tensor in a transversely aniostropic medium a double-couple? Discuss whether the dependence of the principal value on is observationally significant for typical upper mantle models, such as Preliminary Earth Reference Model (Dziewonski & Anderson, 1981) where . Assuming the principal value in an isotropic medium is . The last question is optional.

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