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ABSTRACT Seismic waves can couple with the atmosphere and generate sound waves. The influence of faulting mechanisms on earthquake sound patterns provides opportunities for earthquake source characterization. Sound radiated from earthquakes can be perceived as disturbing, even at low ground-shaking levels, which can negatively impact the social acceptance of geoengineering applications. Motivated by consistent reports of felt and heard disturbances associated with the weeks-long stimulation of a 6-km-deep geothermal system in 2018 below the Otaniemi district of Espoo, Helsinki, we conduct fully coupled 3D numerical simulations of wave propagation in the solid Earth and the atmosphere. We assess the sensitivity of the ground shaking and audible noise distributions to the source geometry of the induced earthquakes based on the properties of the largest local magnitude ML 1.8 event. Utilizing recent computational advances and the open-source software SeisSol, we model seismoacoustic frequencies up to 25 Hz, thereby reaching the lower limit of the human audible sound frequency range. We present synthetic distributions of shaking and audible sounds at the 50–100 m scale across a 12 km × 12 km area and discuss implications for better understanding seismic nuisances in metropolitan regions. In five 3D coupled elastic–acoustic scenario simulations that include data on topography and subsurface structure, we analyze the ground velocity and pressure levels of earthquake-generated seismic and acoustic waves. We show that S waves generate the strongest sound disturbance with sound pressure levels ≤0.04 Pa. We use statistical analysis to compare our noise distributions with commonly used empirical relationships. We find that our 3D synthetic amplitudes are generally smaller than the empirical predictions and that the interaction of the source mechanism-specific radiation pattern and topography can lead to significant nonlinear effects. Our study highlights the complexity and information content of spatially variable audible effects associated with small induced earthquakes on local scales. 

SUMMARY Tsunami generation by offshore earthquakes is a problem of scientific interest and practical relevance, and one that requires numerical modelling for data interpretation and hazard assessment. Most numerical models utilize two-step methods with one-way coupling between separate earthquake and tsunami models, based on approximations that might limit the applicability and accuracy of the resulting solution. In particular, standard methods focus exclusively on tsunami wave modelling, neglecting larger amplitude ocean acoustic and seismic waves that are superimposed on tsunami waves in the source region. In this study, we compare four earthquake-tsunami modelling methods. We identify dimensionless parameters to quantitatively approximate dominant wave modes in the earthquake-tsunami source region, highlighting how the method assumptions affect the results and discuss which methods are appropriate for various applications such as interpretation of data from offshore instruments in the source region. Most methods couple a 3-D solid earth model, which provides the seismic wavefield or at least the static elastic displacements, with a 2-D depth-averaged shallow water tsunami model. Assuming the ocean is incompressible and tsunami propagation is negligible over the earthquake duration leads to the instantaneous source method, which equates the static earthquake seafloor uplift with the initial tsunami sea surface height. For longer duration earthquakes, it is appropriate to follow the time-dependent source method, which uses time-dependent earthquake seafloor velocity as a forcing term in the tsunami mass balance. Neither method captures ocean acoustic or seismic waves, motivating more advanced methods that capture the full wavefield. The superposition method of Saito et al. solves the 3-D elastic and acoustic equations to model the seismic wavefield and response of a compressible ocean without gravity. Then, changes in sea surface height from the zero-gravity solution are used as a forcing term in a separate tsunami simulation, typically run with a shallow water solver. A superposition of the earthquake and tsunami solutions provides an approximation to the complete wavefield. This method is algorithmically a two-step method. The complete wavefield is captured in the fully coupled method, which utilizes a coupled solid Earth and compressible ocean model with gravity. The fully coupled method, recently incorporated into the 3-D open-source code SeisSol, simultaneously solves earthquake rupture, seismic waves and ocean response (including gravity). We show that the superposition method emerges as an approximation to the fully coupled method subject to often well-justified assumptions. Furthermore, using the fully coupled method, we examine how the source spectrum and ocean depth influence the expression of oceanic Rayleigh waves. Understanding the range of validity of each method, as well as its computational expense, facilitates the selection of modelling methods for the accurate assessment of earthquake and tsunami hazards and the interpretation of data from offshore instruments. 

Abstract All instrumented basaltic caldera collapses have generated M_w > 5 very long period earthquakes. However, previous studies of source dynamics have been limited to lumped models treating the caldera block as rigid, leaving open questions related to how ruptures initiate and propagate around the ring fault, and the seismic expressions of those dynamics. We present the first 3D numerical model capturing the nucleation and propagation of ring fault rupture, the mechanical coupling to the underlying viscoelastic magma, and the associated seismic wavefield. We demonstrate that seismic radiation, neglected in previous models, acts as a damping mechanism reducing coseismic slip by up to half, with effects most pronounced for large magma chamber volume/ring fault radius or highly compliant crust/compressible magma. Viscosity of basaltic magma has negligible effect on collapse dynamics. In contrast, viscosity of silicic magma significantly reduces ring fault slip. We use the model to simulate the 2018 Kı̄lauea caldera collapse. Three stages of collapse, characterized by ring fault rupture initiation and propagation, deceleration of the downward‐moving caldera block and magma column, and post‐collapse resonant oscillations, in addition to chamber pressurization, are identified in simulated and observed (unfiltered) near‐field seismograms. A detailed comparison of simulated and observed displacement waveforms corresponding to collapse earthquakes with hypocenters at various azimuths of the ring fault reveals a complex nucleation phase for earthquakes initiated on the northwest. Our numerical simulation framework will enhance future efforts to reconcile seismic and geodetic observations of caldera collapse with conceptual models of ring fault and magma chamber dynamics.