Non-symmetric seismic moment tensors and seismic torques: Theory and application to caldera collapse earthquakes at Kīlauea Volcano in 2018

Taiyi A. Wang, & Eric M. Dunham

Published September 8, 2024, SCEC Contribution #13685, 2024 SCEC Annual Meeting Poster #018 (PDF)

Unsteady subsurface magma movement radiates seismic waves that encode source dynamics. Kinematic source inversions are widely used to determine equivalent seismic force and moment tensors that represent source dynamics, but the relationship between seismic representations and source dynamics is often ambiguous. Building on Brodsky et al. (1999), Coppess et al. (2022) showed that magma movement in a narrow conduit can be represented with axial forces and moment tensors easily calculable from unsteady conduit flow modeling. Here we extend that work, using a generalization of the procedure of Burridge et al. (1993), to arbitrarily shaped volumetric source regions containing a viscous, compressible fluid or solid.

We show that when the wavelength is longer than the source dimension, the source is completely described by a seismic force, a symmetric moment tensor, and an anti-symmetric moment tensor, globally conserving both linear and angular momentum. The curl of the anti-symmetric moment tensor is a seismic torque, which can result from gravitational imbalance in the source volume, Cosserat type rheology, or rotational motion in the source volume. Our representation theorem is complementary to that of Takei & Kumazawa (1994), but it offers the advantage of sources being directly calculable from the output of computational fluid dynamics and/or solid mechanics simulations without the need to determine inertial gluts and stress gluts.

We develop a workflow to convert the displacement and stress fields from numerical simulations into equivalent point sources. We apply the workflow to dynamic rupture simulations of caldera collapse earthquakes during the 2018 eruption of Kīlauea Volcano, characterized by rupture propagation on a ring fault and the dynamic coupling between the subsiding caldera block and the underlying fluid magma reservoir. Our point source representation produces a seismic wavefield that, at low frequencies, is in good agreement with that produced by the dynamic rupture simulations. In particular, the seismic torque, arising from the rotational motion of the caldera block and magma in the underlying reservoir, contributes significantly to the seismic wavefield. This indicates that seismic source inversions for magma reservoir dynamics should account for the anti-symmetric moment tensor.

Key Words
seismic torque, moment tensor, dynamic rupture

Citation
Wang, T. A., & Dunham, E. M. (2024, 09). Non-symmetric seismic moment tensors and seismic torques: Theory and application to caldera collapse earthquakes at Kīlauea Volcano in 2018. Poster Presentation at 2024 SCEC Annual Meeting.

Related Projects & Working Groups
Seismology