Monday, 2:00-4:00, Seismology Conference Room

Class participation and short in-class presentations (not graded).

Completing and handing in the assigned computer exercises (not graded).

A paper based on a term project (graded).

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

Computer exercise 1: Calculate and plot patterns of spherical harmonics. Investigate the normalization. Demonstrate orthogonality between different Ylm. Link to exercises and materials

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 in detail. 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. Mode-sum 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 FIR 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. Noise cross correlation and noise tomography.

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.