Project description
The six-year oscillation in the Earth's length of day, and its multi-decadal modulation, are among the clearest geophysical observations of dynamics in the outer core. They are interpreted as torsional Alfven waves: coaxial cylinders of liquid iron in the outer core, aligned with the Earth's rotation axis, oscillating in a twisting motion against each other, with the magnetic field threading the cylinders providing the restoring force. The strength of the deep internal magnetic field that controls the wave speed is otherwise inaccessible to direct observation, and these waves are the only known route to estimating it. The first such estimation, performed in 2009, has not been revisited with the satellite era of geomagnetic data, with modern uncertainty quantification, or with a properly asymptotic treatment of the reflection of these waves at the tangent cylinder --- the surface that demarcates the part of the outer core lying outside the inner core's projection. A separate open question is whether a thin stably stratified layer at the top of the outer core modifies the upper boundary condition.
The mathematical work is asymptotic analysis of the one-dimensional torsional-wave equation, with careful treatment of how waves reflect at the tangent cylinder. The numerical work is implementation of a one-dimensional waveequation solver with extra grid resolution near the boundaries (where the coefficients of the equation vary sharply); the first part reproduces the analytic Bessel-function solution for the simplest case (uniform background magnetic field) and the published 2009 inversion on synthetic test data. The data analysis is statistical (Bayesian) inversion --- using Markov-chain Monte Carlo sampling --- of the cylindrically averaged squared magnetic field profile from a combination of length-of-day measurements (which are geodetic observations) and records of the time-varying axisymmetric component of the geomagnetic field at the equator.
The central scientific outcome is a probabilistic estimate of the deep magnetic field profile, with explicit uncertainty intervals and a clear comparison between what the data alone constrain and what is contributed by the prior assumptions: a result of "the data alone do not strongly constrain the field profile beyond a few large-scale features" would itself be a substantive contribution, replacing existing literature with a more accurate assessment of uncertainty. If time permits, the project extends to a joint inversion using length-of-day and geomagnetic data simultaneously, and to an asymptotically-derived boundary condition representing a stratified upper-core layer, with the layer's thickness and stratification strength themselves inferred from the data.
The student taking on this project needs a geophysics bachelor or equivalent. As well as an interest in mathematics, computer programming and data analysis.