Simulating Shear-wave Splitting at Volcanoes Using Finite Element Models

Abstract:

Shear-wave splitting – the separation of a propagating shear wave into fast and slow velocity components – is a consequence of structural and/or stress-induced anisotropy. In volcanic regions, structural anisotropy may result from preferential orientation of rock-forming minerals, particularly olivine, or geological structures such as fracture zones, which cause directional variation in shear wave velocities. Variations in applied stress, including due to dike propagation, magma reservoir pressurisation, or changing eruptive activity, can facilitate the preferential closure of randomly-oriented fluid-filled microcracks, also causing directional variation in shear wave velocities.

We use finite element models (Comsol Multiphysics) to compute numerical solutions for the propagation of seismic body waves through media with a range of structural and stress-induced anisotropies. A seismic source is generated, and the subsequent propagation of body waves is monitored within each medium. Shear-wave splitting is simulated, and the numerical-model results for shear-wave splitting parameters (velocities and delay times) are compared to analytical solutions by solving the Christoffel equation.

Preliminary simulations elucidate particular challenges for the finite element modelling of shear-wave splitting. To consider the entire raypath, all elements of the stiffness tensor are required in the analytical solutions. In addition, artefacts appear in the finite element waveforms, including ringing and an apparent reduction in velocity compared to the analytical solutions.

Finite element models provide a powerful medium for investigating the cause of anisotropy, particularly when it is influenced by the shape and content of microcracks. Investigations into crack fluids will be facilitated through nested models, where microscopic interaction between stress, fluid and microcracks are calculated, and their influence on the bulk rock is applied on the whole-system model. Understanding the influence of these microscopic processes is essential for interpreting temporal variations in seismic anisotropy (inferred from shear-wave splitting), including those that precede or accompany volcanic activity.