Some studies on the computation and interpretation of seismic interface waves and modes in Earth’s mantle

Abstract

I discuss ways in which seismic data can be used to constrain the elastic parameters, density, mineralogy, and rheology of planetary interiors, focusing on interface waves and modes in Earth’s mantle. The thesis consists of two parts.

In the first part, I characterise the lithospheric mantle in southwestern Tibet, based on Rayleigh wave dispersion, receiver functions, and virtual deep seismic sounding profiles. These observations indicate a crust thickness of 70 ± 4 km, and high shear wave speeds of 4.6 ± 0.1 km s−1 down to around 300 km, which is interpreted as the base of the lithosphere. I combine these constraints and gravity data in an isostatic balance, which indicates that the lithospheric mantle is negatively buoyant, ruling out a depleted composition.

In the second part, I build upon a recently-developed finite-element technique for the calculation of planetary normal modes. Starting with the spherically-symmetric case, I compare the new technique against the conventional numerical integration approach. Then, for a rotating Earth model with a lower-mantle anomaly, I calculate the modes without recourse to perturbation theory. Motivated by the goal of testing the accuracy of perturbation theory, I develop tools for the spherical harmonic analysis of modes calculated using the new method.

I apply all of these new methods to investigate the ‘mixed Rayleigh-Stoneley modes’, which arise when Rayleigh modes and core-mantle-boundary (CMB) Stoneley modes have very similar frequencies. I identify this as an example of seismic waveguide coupling, show numerically that the coupling is stronger at lower frequencies, relate this to previous observations, and demonstrate that the coupling persists in nonspherically-symmetric planets.

Finally, I generalise the finite-element technique to anelastic Earth models, in which the shear modulus is frequency-dependent. This results in a non-linear eigenvalue problem, which I solve with the Infinite Arnoldi method. I explore the oscillation modes of simple mechanical systems, and show how more complicated rheologies, such as the Extended Burgers model, can be handled, with comparisons to previous work. I conclude by discussing applications on Earth, where a physically-consistent rheological model is within reach, and on other worlds, where exact methods will prove even more valuable.