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| Surface Wave Variational Priciples Jeroen's notes + Maslov Theory |
This notebook, which contains multiple parts as evidenced by its
cover page, is a collection of notes from Jeroen Tromp which Dahlen collected from 1990 to 1992
Tromp, at the time, was a graduate student of Dahlen's at Princeton, working in theoretical
seismology. The collection, all bound in a light green notebook, concludes with Tromp's
thesis, "Surface wave propagation in a slowly varying anisotropic waveguide," which was written
by both Tromp and Dahlen. Tromp's paper was accepted and he became a faculty member in the
Department of Earth and Planetary Sciences at Harvard from 1992-2000. He currently presides
as Blair Professor of Geology and Professor of Applied and Computational Mathematics
at Princeton University.
As noted earlier, the majority of the contents of this notebook recount Tromp's
notes on his way to competing his graduate degree. His work mostly consisted of theoretical
wave theory to describe the paths waves as they travel through varying (and often nonsymmetric)
media, which the Earth tends to have. What's interesting to note of Tromp's work are the connections
between seismology and quantum mechanics, which reside in his use of the Berry Phase, which in quantum
mechanics, is the phase difference aquired over the course of a cycle in some sort of geometry, in this case
nearly spherical for the Earth model. In addition to Tromp's photocopied notes there are also some
add-ins from Dahlen himself, which can be easily identified by the yellow paper upon which it is written on.
This collection can be found at: Guyot Hall, Princeton, NJ, 08544. Back to Main Page
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Pages |
Sheet Numbers |
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| Coupled wave equations; the tedious approach |
1–8 |
1–8 |
| Normalization |
9–19 |
1–5,1–6 |
| Amplitudes |
20-22 |
1–3 |
| Rayleigh waves |
23–25 |
1–3 |
| Surface waves in laterally slowly varying media – Toroidal modes (Love waves) |
26–40 |
1–6,1–9 |
| Body Waves |
41–45 |
1–4,1 |
| Two representations of the displacement field in a spherical Earth |
46–48 |
1–3 |
| Love waves |
49–51 |
1–3 |
| Rayleigh waves |
52–57 |
1–6 |
| The Lagrangian Approach |
58–65 |
1–8 |
| Pressure waves |
66–85 |
1–4,1–3,1–4,1–7,1–2 |
| Scalar wave propagation in a sphere |
86–90 |
1–5 |
| Ray tracing |
91–97 |
1–7 |
| Potentials |
98–101 |
1–4 |
| The effect of gravitation on the propagation of surface waves |
102–107 |
1–6 |
| gravity |
108–115 |
1–4,1–4 |
| Spreading |
116-121 |
1–4,1–2 |
| Moment tensors |
122–125 |
1–4 |
| What is the additional phase change on a flat Earth? |
126–134 |
1–9 |
| No additional phase shift in an isotropic medium |
135–143 |
1–9 |
| Wave action in the frequency domain |
144–158 |
1–6,1–3,1–4 |
| Green's functions and caustics |
159–167 |
1–9 |
| Point source on a spherical Earth |
168–171 |
1–4 |
| Sources |
172–183 |
1–4,1–2,1–6 |
| Orthogonality |
184–187 |
1–2,1–2 |
| The Berry phase in adiabatic quantum mechanics |
188–194 |
1–7 |
| General variational principles |
195–211 |
1–17 |
| Higher order solubility |
212–218 |
1–3,1–4 |
| Conservation of Probability |
219–224 |
1–3,1–2,1 |
| [LaTeX document about Berry Phase] |
225–233 |
N/A |
| Basic principles |
234–249 |
1–16 |
| Ray theory |
250–266 |
N/A |
| Ray tracing on an anisotropic, spherical Earth |
267–273 |
1–7 |
| Introduction to the Maslov method |
274–309 |
1–3,1–5,1–12,1–5 |
| Checking the transport equations in the mixed spaces |
310–324 |
1–9,1–6 |
| Configuration-space Jacobian |
325–329 |
1–2,1–2,1 |
| The Tidal Potential |
330–338 |
1–9 |
| Surface wave propagation in a slowly varying anisotropic waveguide [Tromp and Dahlen] |
339–362 |
N/A |
| [Fax from Jeroen Tromp to F.A. Dahlen] |
363–367 |
N/A |
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