Waves on a Spherical Membrane
Waves on a spherical membrane are an analogue for seismic waves propagating on the surface of the Earth. I spent 2001–2003 doing a Master's thesis in seismology at the University of Oxford, under the supervision of John Woodhouse.
The thesis (PDF format) can be downloaded here:Full thesis (10 MB) (190 p.)
Or in parts from here:front material (abstract, table of contents, etc)Chapter 1: IntroductionChapter 2: The two-dimensional wave equationChapter 3: Analytical spherical membrane wavesChapter 4: Spherical hexagonal gridsChapter 5: Numerical spherical membrane wavesChapter 6: Ray calculations on the sphereChapter 7: Numerical model vs ray theoryAppendix A: Functions on the sphereAppendix B: Spherical harmonic functionsAppendix C: Euler angles and rotationsAppendix D: Derivations for selected equationsAppendix E: Ray-tracing equationsAppendix F: Wave parameters and dispersionAppendix G: Flow chart of computer programsBibliography
Cool YouTube movie of waves on a sphere of water: here
Daniel Peter did a more expansive study on this topic; he published a paper (pdf) and also posted his code repository here:
https://github.com/danielpeter/membraneSphere
