Schematic representation of the main mechanisms that contributed to ground motions during the eruption. (A) Downward reaction forces from jetting at the vent, which are modeled as vertical point forces, and magma reservoir deflation, which is modeled as an isotropic implosive source, produce similar waveform fits. The true source must be a combination of both effects. Propagation of the atmospheric acoustic-gravity pressure wave (Lamb wave) also produced ground displacements recorded at seismic stations worldwide. (B) Atmospheric acoustic waves oscillating for ~8000 s coupled to the solid Earth, producing harmonic Rayleigh waves that radiated away from the source. HTHH: Hunga Tonga-Hunga Ha'apai. Credit: Science Advances (2023). DOI: 10.1126/sciadv.add4931

Vertical component profiles obtained from GSN, GEOSCOPE, and other broadband stations, bandpass filtered from 0.01 to 0.05 Hz, exemplifying seismic P, S, and R1 arrivals for the first two blasts. (A) Displacement records section showing the R1 arrival (dashed green lines) of the first two subevents E1 and E2. (B) Displacement records of all the stations used in this study. Solid red and blue and green dashed curves indicate the seismic wave arrivals P, S, and R1, respectively. P waves from these records quantify the time history of forcing from the first two volcanic subevents within 6 min of the M5.8 origin time. While P waves from later volcanic subevents cannot be identified because of interference from other phases, the relatively large-amplitude Rayleigh waves reveal numerous volcanic subevents recorded across all distances, allowing quantification of the time history of forcing out to ~4.5 hours after the main blast. Credit: Science Advances (2023). DOI: 10.1126/sciadv.add4931

Global P-wave ground motion and reaction force time series. (A) Global stack of 518 vertical component P-wave ground motions from stations shown in the inset map, filtered in the passband of 0.01 to 0.05 Hz and corrected to a reference distance of 78.5°, which is the median distance of all stations used for the body wave analysis. Time is from 100 s before the P-wave arrival time at 78.5° [04:26:46 UTC, red dashed line] relative to the origin time of the M5.8 event (04:14:45 UTC), located by the USGS. Note the smooth low-amplitude long-period energy within 40 s preceding the expected arrival. (B) Vertical downward (reaction) point-force time history obtained by deconvolving the global stack by an impulse response Green's function, with imposed positivity constraint. The first two main volcanic events E1 and E2 are shown in the gray boxes. Credit: Science Advances (2023). DOI: 10.1126/sciadv.add4931

Vertical reaction force time history from Rayleigh waves. The median stack vertical point-force time histories obtained by deconvolving individual displacement recordings extending for 5000 (A) and 16,300 s (B) after the source began by corresponding Green's functions for vertical motion (LHZ) and horizontal motion (LHR) of short-arc Rayleigh waves. The inset map shows locations of the 30 stations used. Consistency of the LHZ and LHR time series confirms that the motions are Rayleigh waves. Intervals of the seismograms when ground motion was contaminated by the passage of the atmospheric Lamb pulse were screened out before stacking the individual force time histories. The first three main volcanic events E1, E2, and E3 are shown in the gray boxes. Credit: Science Advances (2023). DOI: 10.1126/sciadv.add4931

Long-period Rayleigh waves generated by resonating atmospheric acoustic modes coupled with the solid Earth at the source region. (A) Ground displacements, filtered in the 0.003- to 0.005-Hz passband, recorded at stations ADK, MAJO, PASC, and YBH at varying epicentral distances (Δ) and azimuths from the source (ϕ). (B) Spectra of the vertical ground motions filtered in the 0.003- to 0.005-Hz passband. Spectral peaks at 3.4 and 4.6 mHz correspond to the frequencies of atmospheric acoustic standing wave modes that couple to the ground to excite Rayleigh waves that spread from the source region. Credit: Science Advances (2023). DOI: 10.1126/sciadv.add4931