AxiSEM3D: broad-band seismic wavefields in 3-D global earth models with undulating discontinuities

Abstract

We present a novel numerical method to simulate global seismic wave propagation in realistic aspherical 3-D earth models across the observable frequency band of global seismic data. Our method, named AxiSEM3D, is a hybrid of spectral element method (SEM) and pseudospectral method. It describes the azimuthal dimension of global wavefields with a substantially reduced number of degrees of freedom via a global Fourier series parametrization, of which the number of terms can be locally adapted to the inherent azimuthal complexity of the wavefields. 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, surface topography, variable crustal thickness, undulating transition zone and core–mantle boundary topography. Undulating discontinuities are honoured by means of the ‘particle relabelling transformation’, so that the spectral element mesh can be kept spherical. The implementation of the particle relabelling transformation is verified by benchmark solutions against a discretized 3-D SEM, considering ellipticity, topography and bathymetry (with the ocean approximated as a hydrodynamic load) and a tomographic mantle model with an undulating transition zone. For the state-of-the-art global tomographic models with aspherical geometry but without a 3-D crust, efficiency comparisons suggest that AxiSEM3D can be two to three orders of magnitude faster than a discretized 3-D method for a seismic period at 5 s or below, with the speed-up increasing with frequency and decreasing with model complexity. We also verify AxiSEM3D for localized small-scale heterogeneities with strong perturbation strength. With reasonable computing resources, we have achieved a corner frequency of up to 1 Hz for 3-D mantle models.