Monday, 3:30-4:45, Seismology Conference Room

**Weekly Topics:**

Week 1. Normal modes: 1-D, 2-D, 3-D. Orthogonality of basis functions.
Spherical geometry, spherical harmonics.

Computer exercises: Calculate and plot patterns of spherical harmonics.
Investigate the normalization. Demonstrate orthogonality between different
Ylm.
Description of exercises

Week 2. Earth's normal modes. FFTs and spectral analysis.

Computer exercise: Calculate a low-frequency spectrum from data and identify
some normal-mode peaks (using SAC or Matlab or Qw).
Link to exercise and materials

A classic 1971
paper by Gilbert on the subject of Earth's normal modes and earthquakes.

Week 3. Excitation of Earth's normal modes. 1-D string example.
Single-force example for the Earth. Force couples and the moment tensor.

Computer exercise: Manipulate a moment tensor (fault parameters, seismic moment,
principal axes). Rotate a second-rank tensor -- rotate a lower-hemisphere
focal mechanism into a back-hemisphere projection from an arbitrary viewpoint.
Link to exercise and materials

Week 4. Mode summation for a spherical Earth with an arbitrary moment-tensor
source. Q. Source duration. Truncation issues.

Computer exercise: Calculate seismograms for a deep and a shallow earthquake.

Week 5. Higher-order moment tensors --- finite sources. Static terms.
Tsunami excitation and the tsunami branch of normal modes.

Computer exercise: Sum several sources to simulate a propagating
rupture to observe Doppler effect in radiation.

Week 6. Normal modes in different Earth structures. Effect of Q.

Computer exercise: Calculate fundamental modes in different Earth models,
observe different dispersion. [mineos, eosani, obani]

Week 7. Corrections of normal modes for ellipticity and lateral heterogeneity
in the Earth. Approximations (path-average vs. higher-order formalisms).

Computer exercise: Calculate approximate normal-mode seismograms
for an elliptical 3-D Earth model.

Week 8. Instrument response. Poles and zeros. Digital filters.
Calibration. Convolution and deconvolution.

Computer exercise: Calculate an instrument response spectrum and an
instrument impulse response from a -.RESP file.

Week 9. Seismic noise. Power-spectral density of a seismic signal.

Computer exercise: Calculate a noise spectrum.

Week 10. Determination of the moment tensor. Inversion. CMT analysis.

Computer exercise: Calculate moment-tensor kernels and invert for
a moment tensor.

Week 11-12. Other topics.

Computer exercises: Individual projects.