What kinds of models and structures can be modelled?

Rheology, physical systems

AxiSEM3D solves wave propagation in two primary physical systems: (Visco-)elastic and acoustic media. Elastic media can be modeled with full anisotropy of up to 21 parameters [Tesoniero et al., 2020], acoustic media can be ocean, fluid core or atmosphere [Fernando et al., 2020]. Multiscale 3D structures are honored by a mix of 1. meshing, 2. intra-element polynomial fit, 3. azimuthal pseudo-spectral expansion. The efficiency of AxiSEM3D increases with source frequency for any given 3D structure, as it exploits any smoothness in the structures and wavefields. Localised, strong heterogeneities can be efficiently captured by the hybrid, wavefield injection approach fully embedded within AxiSEM3D [Leng et al., 2020]. Instead of a discretised ocean, the ocean-load appproximation can be used for longer periods [Fernando et al., 2020]. Given the complexity-adaptive speedup, AxiSEM3D runs at the speed of the axisymmetric method AxiSEM for 1D or axisymmetric models. The speedup gradually decreases for more and more complex 3D models, but even for very complex structures (SEG/EAGE salt model, ocean bathymetry) it is still almost an order of magnitude faster than state-of-the-art 3D SEM solvers.

Interfaces

Undulating interfaces of sharp medium contrasts (surface topography, bathymetry, internal discontinuities such as Moho) are modeled by a particle-relabeling transformation [Leng et al., 2019]. Most kinds of undulations can be modelled, but two issues need to be met with care: 1. for small-scale, strong undulations, the resultant effective stiffness tensor requires dense discretisation and a small time-step, leading to possibly significantly longer simulation times. 2. As a result of the azimuthal pseudo-spectral expansion and separate sets of equations, interfaces between solid and fluid (ocean-floor, offshore seismic, core-mantle boundary, Earth’s surface) must be laterally contiguous along the azimuth. This prevents, for instance, simulations with a local 3D ocean surrounded by continents. Work is in progress to provide an alternative to this limitation. For current workarounds in various settings, consult Leng et al. [2019], Haindl et al. [2021], Fernando et al. [2020].

Dimensionality, domains

The code always solves the 3D equations of motion, resulting in a 3-component displacement vector solution, or its derived output quantities such as curl. The dimensionality of the underlying structure can however vary between 1D (e.g. spherically symmetric), axisymmetric, or 3D (including 3D volumetric model heterogeneities, undulating interfaces, sharp or gradational boundaries). AxiSEM3D’s inherent wavefield adaptivity links computational cost to model complexity, e.g. running up to 4-5 orders of magnitude faster for 1D models compared to a conventional SEM which is largely oblivious to model complexity. The domain can either encompass a global free surface (either elastic or acoustic boundary conditions) such as for Earth, Mars, asteroids, or be truncated to a fraction of a physical object, e.g. for simulations at crustal scale, sedimentary basins, Antarctica.