Global wave propagation in three-dimensional aspherical Earth models

Earth structure and dynamics are largely inferred by seismology as the main tool for data-informed probing of Earth’s interior. Seismic wave propagation in physically realistic Earth models is one of the most funda- mental topics in seismology, not only essential to the analysis and interpre- tation of observed ground motions in terms of their source characteristics and structure-induced propagation effects, but also indispensable for seis- mic inverse techniques that deliver Earth models by minimising misfits between observations and theoretical predictions. Nevertheless, seismic wave propagation at a global scale still remains as one of the most chal- lenging problems in scientific computing, because of Earth’s multiscale constituents and the observable frequency band of global seismic data for their resolution. In this thesis, I present a new, computationally efficient numerical ap- proach to simulate global seismic wave propagation in realistic three- dimensional (3-D) Earth models. It is a hybrid method of spectral el- ement method (SEM) and pseudo-spectral method, that is, the azimuth dimension of a 3-D wavefield is characterised in terms of a global Fourier series parameterisation, such that the 3-D wave equation reduces to an al- gebraic system of coupled 2-D meridian equations, which is then solved by a 2-D SEM named AxiSEM3D. Computational efficiency of such a hybrid method stems from the inherent azimuthal smoothness of 3-D global wave- fields, resulted from the predominance of long-wavelength heterogeneity in Earth’s mantle and the axial singularity of a point seismic source. AxiSEM3D allows for material heterogeneities such as velocity, density, anisotropy and attenuation, as well as for finite undulations on radial discontinuities, both solid-solid and solid-fluid, and thereby a variety of aspherical Earth features such as ellipticity, topography and bathymetry, variable crustal thickness, and core-mantle boundary topography. Such interface undulations are equivalently interpreted as material perturba- tions of the contiguous media, based on the “particle relabelling transfor- mation”. Ocean is currently modelled as a hydrodynamic load. Benchmarked in reference to a discretised 3-D SEM for a variety of Earth models, including 3-D mantle and crustal structures, topography and bathymetry, and ellipticity, AxiSEM3D proves to be a convergent and ac- curate numerical method. Efficiency comparisons suggest that AxiSEM3D can be 1 to 3 orders of magnitude faster than a conventional 3-D SEM across a period range from 10 s down to 1 s, with its speedup increasing with simulated frequency and decreasing with model complexity. It is sufficiently comprehensive to cover all considered applications at global scale, but is maximally efficient for deep Earth studies with body wave data. The observable frequency range of global seismic data (up to 1 Hz) has been achieved for wavefield modelling upon a 3-D mantle model with moderate computing resources. The MPI-based high-performance C++ code scales up to more than 10,000 cores, available open-source at https://github.com/kuangdai/AxiSEM3D. Three applications are carried out, with different foci from Earth’s surface to the core-mantle boundary. First, surface waves are simulated within a state-of-the-art crustal model; the synthetics are compared to real seismic data to assess two different implementations of a 3-D crust. Second, wave scattering effects and cost impact of a localised small-scale structure with sharp and strong material contrast are investigated, considering a wide range of structure-wavelength combinations. And last, diffracted waves through an ultra-low velocity zone atop the core-mantle boundary are modelled at a 1 Hz frequency.