Nonsymmetric Seismic Moment Tensors and Seismic Torques: Theory and Application to Caldera Collapse Earthquakes at the Kīlauea Volcano in 2018

ABSTRACT We derive a novel seismic representation theorem for nonelastic dynamics in an arbitrarily shaped 3D volume enclosed by a surface S, building on Burridge et al. (1993) and extending Coppess et al. (2022). The novel result is the generalized seismic moment tensor with nine independent components, Mji(t)=∫S[λδijuknk+μ(uinj+ujni)−xj′ΔTi]dA, the antisymmetric part of which gives rise to the seismic torque, Nl(t)=−ϵlji∫Sxj′ΔTidA. The expressions are written in terms of surface integrals of perturbation tractions ΔTi (exerted on the source region by the surrounding solid), elastic displacements ui, lever arms xi′ extending from the source centroid to S, and elastic moduli λ and μ in an isotropic solid. Here, δij is the Kronecker delta, ϵlji the Levi-Civita symbol, and nj the outward unit normal on S. The expressions are valid for arbitrary rheology inside the source region. When combined with appropriate Green’s functions, the expressions provide a rigorous connection between nonelastic dynamics inside the source region and the displacement (at wavelengths large compared with the source dimensions) outside the source region. We apply the theorem to dynamic rupture simulations of basaltic caldera collapse earthquakes, a complex source process involving ring faulting, caldera block subsidence, and the mechanical coupling between the caldera block and the subcaldera magma chamber, yielding a time-dependent force, moment, and torque representing the dynamics. The results establish the correct interpretations of seismic representations in terms of the dynamics of collapse earthquakes. We empirically validate the theorem by demonstrating that the surface wavefield generated by the seismic representation converges to that of the dynamic rupture simulation, in the long wavelength limit. The theorem enables an efficient forward modeling approach when the long-period wavefield of exotic geophysical phenomena is simulated independently of the source dynamics, significantly reducing the complexity of modeling.