Introduction

Active basaltic volcanism, which is the dominant mode of volcanism on Earth, is characterized by low-viscosity lavas and frequent to persistent eruptions1. It includes some of the most famous and well-instrumented volcanoes and regions on Earth, e.g., Iceland, Kīlauea (Hawaii), Etna, or Stromboli (Italy). Recording seismicity is widely recognized as essential for tracking magma movements at depth2,3 but must be complemented with other observations for monitoring eruptions, which are by essence atmospheric processes. Short-range and high frame rate visible/infrared camera recordings can provide essential insights into the eruptive processes and their timing4,5,6,7. In the absence of such visual monitoring tools or if the view is hampered by clouds (including volcanic ashes from the eruption itself), infrasound (acoustic waves <20 Hz) may be the only way to capture timely information on new or changing eruptive stages. At local distance, generally defined within 15 km from the active vent(s)8,9, numerous studies over the past two decades have investigated the acoustic signature of volcanic eruptions over long periods of time (months to years), with strong implications for monitoring aspects, e.g., at Kīlauea (Hawaii)10,11, Etna (Italy)12,13, Stromboli (Italy)14,15, Villarica (Chile)16 or Nyiragongo (D.R. Congo)17,18. Moreover, infrasound may propagate over long distance in the atmosphere, thus offering the opportunity of monitoring eruptive activity from regional (15–250 km) to global distance8,19. Violent explosive eruptions (i.e., Vulcanian–Plinian), which are not characteristic of the aforementioned basaltic volcanoes, are the more prone to generate long-range signals19. This includes remote volcanoes such as Hunga Tonga-Hunga Ha’apai (Tonga)20, Eyjafjallajökull (Iceland)21, or Yasur (Vanuatu)22. Nevertheless, powerful Strombolian explosions were also successfully monitored over hundreds of km from typical basaltic volcanoes, e.g., at Stromboli23 or Etna24. On another hand, Hawaiian-like eruptions (e.g., lava lake, lava fountaining) require local observations, such as encountered at Kīlauea10,11,25 or Nyiragongo17,18,26 for characterizing low-level infrasonic tremors due to persistent intra-crater effusive eruptive activity.

We focus in this study on the last-mentioned volcano located in the Kivu rift (East Africa), which is a remarkable extensional continental setting characterized by active tectonic and magmatic processes. Nyiragongo is one of the most active volcanoes on Earth27. Effusive activity within its ~1.2 km wide crater takes most of the time the form of a long-lived lava lake, of which the dimensions reached 200 m in diameter and 300 m deep in early 2021, making this lava lake the largest on Earth at that time28. In the past two decades, days-long experiments within its crater (degassing29,30, thermal26,31, infrasound26, seismic32) and long-term monitoring deployments around the edifice (seismic18,28,33, infrasound17,18, degassing34) have led to an increasing understanding of the lava-lake convective processes maintaining large volume of molten lava within its pit crater. Such ground-based observations were also sometimes coupled with space-based measurements (Synthetic-Aperture-Radar17,18,28,35, thermal imagery17,31, SO2 degassing17,32,33,35), which allow extending the observational window both in time and space, though their temporal sampling rate (daily at best) is much lower than the ones from ground measurements (milliseconds to minutes). Also, seismic28,32,36,37 and petrological38,39 investigations all converge to a plumbing architecture formed by a deep reservoir (9–15 km depth) well connected to the lava-lake system, as evidenced by the piezometer-like behavior of the lava-lake level reacting synchronously with pressure variations induced by deep (>10 km b.s.l.) magmatic intrusions28,32,40.

On 22 May 2021, the drainage of Nyiragongo’s lava lake was accompanied by lava flows from eruptive fissures toward a one-million urban area composed of the cities of Goma (D.R. Congo) and Gisenyi (Rwanda)35 (Fig. 1 and Supplementary Fig. S1). After 1977 and 2002, this was the third known flank eruption and the first one adequately monitored with seismic and geodetic instruments to understand magma movements at depth. A probable scenario supported by these geophysical observations is the rupture of the edifice, starting around 15:57 UTC (all times are given as UTC time from here), draining the lava lake and initiating a week-long magmatic intrusion (dyke) in the Earth’s crust35 (Fig. 1a). Visual accounts of lava outburst on the flank were reported tens of minutes later, which shocked the nearby population41 due to the absence of clear precursory seismicity or ground deformation hours, days or weeks before35,42. The subsequent migration of magma at shallow depth, accompanied by moderate-size earthquakes directly beneath the city of Goma strongly contributed to a dramatic humanitarian crisis with hundreds of casualties and chaotic population movements35,41 (Fig. 1). In this study, we use infrasound sensors for inferring the main eruptive processes during the very first hours of the eruption on 22 May 2021. Three stations (NYI, KBTI, GOM) deployed at local to near-regional distances (approx. 0.6, 6, and 18 km from Nyiragongo’s main crater/lava-lake) are co-located with broadband seismometers (Fig. 1). Moreover, we investigate long-range records more than 800 km away at the infrasound array I32KE in Nairobi (Kenya), which is part of the International Monitoring System (IMS)8,43 (see “Methods”).

Fig. 1: The May 2021 Nyiragongo flank eruption.
Fig. 1: The May 2021 Nyiragongo flank eruption.The alternative text for this image may have been generated using AI.
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a Map of Africa situating Mount Nyiragongo and zoom into the study area. Local stations (KivuSNet network90) with co-located seismic and infrasound sensors are depicted as green triangles. Data for the Nyiragongo 2021 flank eruption35 are the seismic events over time (blue to yellow from 22 to 28 May 2021, with marker size corresponding to the magnitude between 1 and 5, minimum latitudes along the path of the dyke at 00:00 UTC on 23, 24, 25 and 26 May are indicated by horizontal black dashed lines); the lava flows (red area); the eruptive fissures (yellow lines); the ground fissures detected from Interferometric Synthetic Aperture Radar (InSAR) (black lines); the dyke top trace connected to eruptive fractures (thick transparent yellow line) obtained from InSAR modeling. The main roads (green lines) are plotted from datasets available at the WFPgeonode (https://geonode.wfp.org). The boundary R. D. Congo/Rwanda (dashed gray line) is plotted according to the 2015 GADM database (https://gadm.org). The background topography (shaded gray) is derived from SRTM data with 1 arc-s resolution (NASA/USGS). RMS seismic amplitude time series between 11:00 on 22 May and 05:00 on 23 May for frequency bands (b) 0.333-15 Hz and (c) 0.0083-0.333 Hz at stations NYI, KBTI, and GOM. 1-min RMS amplitude time series are plotted in background and moving averages over centered 5-min windows are plotted as thick lines. Note that the y-scale is logarithmic.

Results and discussion

How infrasound relates to seismicity during the eruption

Infrasound and seismic records, either associated to single events (e.g., explosion, earthquakes), tremor (i.e., continuous excitation or overlapping events), or both, provide highly complementary information about volcanic processes. Volcanoes hosting active lava lakes are so-called open-vent because depressurization of the magmatic system is possible through continuous degassing, which generates coupled infrasound and seismic signals from near-surface processes44,45. Over decades at Nyiragongo, persistent lava lake activity (i.e., spattering, bubble bursting, convective flow) had generated sustained broadband seismic tremor32,33,46, which is also detectable in infrasound records17,18, in the frequency band 0.333–15 Hz (i.e., wave periods below 3 s). Such non-destructive repetitive process at shallow depth is characteristic of lava-lake volcanoes such as Kīlauea (Hawaii)47,48, Erta Ale (Ethiopia)49,50, or Villarica (Chile)51,52. In the same frequency band at Nyiragongo, swarms of earthquakes are detected during several episodic deep (>10 km b.s.l.) magmatic intrusions28,32,40 and at shallowest level during the last May 2021 flank eruption35. On a general level at active volcanoes worldwide, in the band 0.333–15 Hz, signals with dominant low-frequency content are interpreted as due to fluid-driven source mechanisms in contrast with higher-frequency signals generated by brittle-failure mechanisms2,3. However, the discrimination of seismic source mechanisms at volcanoes based solely on the signal’s frequency content is not straightforward2,3,53,54, as observed at Nyiragongo where deep repetitive events of magmatic origin can share the same high-frequency signature as typical volcano-tectonic earthquakes32. Low-frequency signal could also reflect seismic path effects between the hypocenter and the station without the need of fluid involved in the source mechanisms53,54. For now, a comprehensive classification of seismic signals assigning source mechanisms at Nyiragongo is unavailable42. However, based on some of the above-mentioned studies at Nyiragongo18,28,32,33,35,46, we can assume than the continuous seismic amplitude filtered in the band 0.333–15 Hz is representative of magmatic and (volcano-)tectonic processes in the area (Fig. 1b), and local noise sources of human origin at KBTI and GOM (Supplementary Fig. S2)42.

On 21 May 2021, before 15:57, the band 0.333–15 Hz contained the well-known seismo-acoustic tremor caused by the persistent lava-lake activity at Nyiragongo (Supplementary Figs. S2–3). After 15:57, increase of 0.333-15 Hz seismicity is first detected at the edifice (Fig. 1b and Supplementary Fig. S2), then detected across the local seismic network after 16:1535. The spatial distribution of seismic events detected within the same frequency range (Fig. 1a) reveals a major dyke intrusion trough the Earth’s crust, as the magma progressed from the crater toward Lake Kivu35. At midnight on 23 May, the tip of the dyke, as inferred by seismic epicenters, already progressed ~10 km further to the south with respect to Nyiragongo’s crater (Fig. 1a). This major magmatic intrusion can also be inferred by the sustained increase in continuous amplitude measurements at stations farther from the summit42, particularly clear during the first hours of the eruption in the comparative evolution of NYI and GOM amplitude time series (Fig. 1b).

At frequency lower than 0.333 Hz (i.e., wave periods above 3 s), so-called very-long period (VLP) seismicity is frequently observed at active volcanoes36,55,56,57,58,59,60,61,62 and is generally attributed to gas/fluid movements at shallow depth beneath the volcano. At Nyiragongo, a marked increase in VLP amplitude within the 3–120 s period range (0.0083–0.333 Hz) is observed coinciding with the onset of the eruption (Fig. 1c). In contrast to the 0.333–15 Hz band, seismicity in the VLP band began to decrease around 22:30 witnessed at all stations, suggesting a potential change within Nyiragongo’s edifice rather than along the dyke’s propagation path. The generation of VLP signals can be attributed to different source mechanisms operating across a broad frequency range, e.g., as modeled for caldera collapse57,58,60 or gas slug ascent55,59,61, either associated with infrasound signals or not. At lava lake volcanoes, the resonance of waves within the magmatic plumbing system—triggered by perturbations at the lava-lake level such as rockfalls, gas bursts, or convection—has been modeled at both Kīlauea63,64 and Nyiragongo36. At Nyiragongo, several shallow VLP events were localized at Nyiragongo’s crater in 2019–2020, presumably induced by the sloshing of lava in the lake due to degassing bursts or rockfalls36. In particular, a 76 s VLP mode was modeled as the coupling between the lava-lake bottom and a deep reservoir (8–16 km depth) through a magma-filled conduit36.

In Fig. 2, we investigate in more detail how infrasound correlates with seismicity at the summit station NYI. According to the spectrogram analysis of the 2021 eruption and the 2019-2020 seismic observations of VLPs36 (Supplementary Figs. S2 and S4), the VLP band can be further divided into two sub-bands 0.0083-0.025 Hz (i.e., periods of 40–120 s) and 0.025–0.33 Hz (i.e., 3–40 s). Also based on the corresponding spectrograms (Supplementary Fig. S3), infrasound signals are analyzed within two frequency bands, 0.1–1 Hz and 1–10 Hz. The first increase of seismic amplitude at 15:57 in the 0.333–15 Hz band is accompanied by a noticeable increase in 40–120 s VLP band without associated infrasound. 16:15 marks the first notable seismic amplitude peak impacting the whole frequency band. After 16:30, all bandpass-filtered seismo-acoustic signals clearly exhibit higher amplitude than the previous 1-year 10–90th percentile range. Right before 22:30, a double peak is noticeable in every record. After 22:30, both the VLP and infrasound amplitudes drop but remain above the pre-eruptive background levels. Between 16:30 and 22:30, the synchronicity between the increases and peaks of 3–40 s VLP and 0.1–1 Hz infrasound amplitudes is particularly striking. Looking in detail at the largest seismo-acoustic peak around 16:50 (Supplementary Fig. S5), an infrasound signal was detected at the onset of the VLP at station NYI. The detection time at KBTI ~6 km away on the flank is in accordance with a source at the main crater propagating at the speed of sound in the atmosphere (~340 m/s). The 76 s mode observed for the 2019–2020 VLPs36 is also detected. Using infrasound data available in 2019–2020, our analysis confirms that 2019–2020 VLPs were also associated with acoustic onsets (Supplementary Fig. S4) as observed during the eruption (Supplementary Fig. S5), hence supporting the hypothesis of a shallow trigger at the lava-lake level generating VLP signals at Nyiragongo.

Fig. 2: Infrasound vs. seismicity in the first hours of the eruption.
Fig. 2: Infrasound vs. seismicity in the first hours of the eruption.The alternative text for this image may have been generated using AI.
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a RMS amplitude time series at NYI filtered in frequency bands 0.1–1 and 1–10 Hz for infrasound, 0.0083–0.025 Hz (40–120 s), 0.025–0.333 Hz (3–40 s) and 0.333–15 Hz for seismic records. 1-min RMS amplitude time series are plotted in background and moving averages over centered 5-min windows are plotted as thick lines. Note that the y-scale is logarithmic. The vertical solid line marks the start of abnormal seismicity detected at the summit (15:57), the two vertical dashed lines mark the plateau of infrasound amplitude between 16:30 and 22:30. The constant interval plotted in transparency for each time series between 11:00 and 15:57 corresponds to the 1-year 10–90th percentile range of 1-min RMS amplitude at NYI between 22 May 2020 and 22 May 2021. b Two SAR amplitude images (COSMO-SkyMed) in radar geometry are displayed at acquisition time 15:37 on 22 May (descending orbit) and 04:03 on 23 May (ascending orbit). The sketch in between is a very simplified cross-section view of Nyiragongo’s edifice depicting the intra-crater changes between both satellite images. SAR images are processed with the AMSTer software104.

From spaceborne synthetic-aperture radar (SAR) images acquired on 22 May at 15:37, we know that the pit crater was still filled with lava 20 min before the start of the seismic unrest65. Another SAR observation acquired on 23 May at 04:03 shows an empty crater enlarged by about 1.5 times its previous size (Fig. 2 and Supplementary Fig. S6). During this eruptive period marked by important changes at the summit crater and within the plumbing system, the triggering and source mechanisms of VLP and infrasound signals are likely multifaceted (e.g., rockfalls or bubble explosion at the lava lake surface, gas slug bursting in the shallow conduit, pit-crater floor and walls collapse). Contrary to the complex time-varying spectral content of seismic records (Supplementary Fig. S2), infrasound signals during the 2021 Nyiragongo flank eruption exhibit a clear, yet atypical, dominant frequency content gliding between 1 and 0.1 Hz between 16:30 and 22:30 (Supplementary Fig. S3). Understanding this infrasound signature is the key to unravel the surface eruptive processes between these two epochs.

Modeling the infrasonic harmonic tremor originating from the crater

The frequency gliding pattern was equally observed both in local records and over 840 km away at station I32KE in Kenya (Supplementary Figs. S8 and S9). We retrieve coherent signals between station pairs using cross-correlation, which are characterized by time lags indicating a source at Nyiragongo’s crater and two distinct frequency peaks gliding simultaneously (Fig. 3 and “Methods”). These observations suggest the generation of infrasonic harmonic tremor at the summit, as observed at other open-vent volcanoes worldwide, e.g., Kīlauea (Hawaii)10,25 or Villarica (Chile)16. Under persistent excitation of its lava lake generating infrasound, Nyiragongo can act as a gigantic acoustic resonator, as already established during decameter lava-lake drops in 2016–201818. For instance, deepening the lava-lake would lower the tone of the pit crater as its resonant frequency decreases16,18. Only one resonant mode with sufficient amplitude, assimilated to the fundamental one, can generally be observed at local distance at open-vent volcanoes16,66,67,68,69, making this long-range observation of two resonant frequencies remarkable and further referred to as the fundamental frequency (f0) and the first overtone (f1).

Fig. 3: Infrasound peak frequencies from cross-correlated records.
Fig. 3: Infrasound peak frequencies from cross-correlated records.The alternative text for this image may have been generated using AI.
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a Left, location map of Lake Victoria (blue area in the middle), the Nyiragongo volcano (pinned by its summit station NYI), and the infrasound station I32KE on the EAR’s eastern branch. Right, color scale representing the time lag at KBTI, GOM, and I32KE with regards to an infrasound source at Nyiragongo (i.e., NYI) assuming direct propagation path and different apparent velocities (340 m/s for local stations, 290–310 m/s for I32KE). b Infrasound records filtered between 0.1 and 2 Hz at all stations between 11:00 on 22 May and 05:00 on 23 May. Red lines (16:30–22:30) indicate the time interval associated with high amplitude in time domain and gliding dominant frequency and high correlation coefficients between NYI and I23KE (c) GOM (d) and KBTI (e). Note that NYI is used as reference providing a similar time stamp for correlation coefficients and peak frequencies between NYI and other stations.

Following the musical analogy, an interesting outcome is to describe volcanic craters with resonator models such as a closed organ pipe16,68 or a Bessel horn51 for estimating the time-varying depth of the crater (defined as the bottom crater or the lava-lake level if filled). Outperforming such simple (analytical) models, Watson and co-authors66,67,69 developed an efficient numerical scheme, called CRes70, for simulating quasi-1D wave propagation along depth inside an axisymmetric volcanic crater. Nyiragongo’s crater as defined in our simulation is the pit crater containing the lava lake. The pit crater, which is about 300-m deep and 200-m wide, can be reasonably considered as axisymmetric despite being slightly elliptical28. The dimensions of the pit crater are of the same order of magnitude as the dimensions of the main crater at other open-vent volcanoes (e.g., Etna66, Villarica16, Erebus71). At Nyiragongo, the main crater (hosting the pit crater) is much larger (about 1.2 km wide) and is only 200–250 m deep (difference of altitude between the rim of the pit crater and the rim of the main crater). The contrast of impedance (i.e., the ratio of acoustic pressure to acoustic flow) at the crater outlet describes the resistance to flow. It determines if acoustic waves are preferentially reflected inside the crater or are radiated outside. For acoustic resonance to occur, the impedance contrast must be high, which occurs when the crater radius is small compared to the infrasound wavelength and the crater depth is comparable to the wavelength67. For realistic sources with energy at frequencies below 1 Hz16,66, the conditions to excite resonant modes in Nyiragongo are met for its pit crater, but not for its main crater (Supplementary Fig. S11). Hence, the acoustic radiation from the crater outlet to any receiver starts in our simulation at the top of the pit crater and reflection inside the main wide crater is not considered (see “Methods”).

We set up an inversion strategy for both f0 and f1 using CRes to determine the pit-crater geometry (see “Methods”). The variations of f0 and f1 with time follow monotonically decreasing functions (Fig. 4). Simultaneously inverting these two interrelated resonant frequencies strongly constrains the evolving crater geometry defined by its width and depth, which either increase or stabilize with time during the drainage of the lava lake (see “Methods”). SAR observations between January 2002 and May 2021 allow to define an initial pit crater model with an estimated depth of about 300 m at the time of the eruption28 (Fig. 4 and “Methods”). According to SAR observations on 22–23 May 202165 (Fig. 2), we allow the radii of the simplified pit-crater geometry to widen uniformly by a factor ranging from 1 to 1.5 (i.e., upper radius from 110 to 165 m) and let the depth free to get any values down to 500 m. For each successive time step, we look for the best-fit model explaining both f0 and f1. The final time-dependent models depicted in Fig. 4 converge to similar solutions. The resulting, most likely scenario is a fast complete draining of lava from the crater in less than one hour between 16:30 and 17:20. There was no resonance when the lava lake was filled, so we have no clear point in time for the beginning of the drainage. However, both the sharp increase in infrasonic amplitude (Figs. 2 and 3) and the extrapolation of the lava-lake level models before 16:45 (Fig. 4), while assuming constant flush rate, point toward 16:30–16:35. Our result also suggests that the widening of the crater occurred rapidly during the same timeframe, though the uncertainty for this parameter is greater. The deepening of the lava-lake level remains the main factor controlling the decreasing frequency content of the infrasound harmonic tremor. According to our models, the crater floor collapsed after the full drainage of lava after 17:20 (~300 m), which corresponds to the moment where the deepening slowed down. After 19:00, the pit crater depth estimated around 380–390 m did not evolve much. This depth is close to the SAR-based estimate on 23 May at 04:03 (365 m)65. Several large transient infrasound signals characterize the end of the eruption signal right before 22:30 (Supplementary Fig. S3). The sporadic tremor signature after 22:30 then exhibits a slight, but noticeable higher peak frequency nearly constant around 0.21 Hz and the loss of the first overtone with an overall decreasing signal amplitude (Fig. 3). The filling of the bottom crater due to collapsing walls can explain this frequency change but the observed rise is minor and partly contained within the uncertainty of the models (Supplementary Fig. S11). These final infrasound transients, together with synchronous broadband seismic signals (Figs. 1, 2 and Supplementary Fig. S3), are thus likely coinciding with explosions or collapses that marginally changed the pit-crater geometry at that time, which remained stable up to the next satellite transit on 23 May at 04:03.

Fig. 4: Time-varying acoustic resonance model of Nyiragongo’s pit crater.
Fig. 4: Time-varying acoustic resonance model of Nyiragongo’s pit crater.The alternative text for this image may have been generated using AI.
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a Nyiragongo’s cross-section model on 22 May 2021 before the eruption obtained from UAV-based photogrammetry model (DEM as brown surface) and from SAR-based amplitude images28. Note that the diameter of the pit crater hosting the lava lake is poorly constrained below ~3.000 m a.s.l., that is along the last ~100 m of depth (bottom radii of 70 or 10 m are both represented). b Top, best-fit models of dominant (f0) and secondary (f1) peak frequencies. Observations are given as 1/5 octave-band intervals (blue lines) encompassing the range of observed peak frequencies. Models are colored according to misfit (L1-norm) expressed in octave band. Models in gray are the ones going over the 1/5 octave band interval (blue lines). c Inverted pit-crater depth and top radius (inset) models corresponding to f0 and f1 models plotted above. d Pit-crater cross-sections corresponding to model estimates (i.e., crater’s part not filled by lava) at 16:50, 17:20, 18:20, and 22:20 (vertical black dashed lines in (b, c)) plotted on the lava-lake extent (i.e., fully filled) estimated before the eruption (dotted lines). The inverted pit-crater models are colored according to the color code used in (b, c).

The complete scenario of the flank eruption

To understand the link between surface manifestations within the crater and along the flank of the volcano, infrasound can be used to track fissures opening and lava flows11. At KBTI, an array of three operational infrasound sensors allows to compute the Direction of Arrival (DOA in °N) of infrasound signals during the eruption (Methods). Potential sources (main crater Cr, eruptive fissures F1–F4) are in line-of-sight with the station, with low incident angles (<15°). Arrivals from the main crater (Cr) may span an angular aperture of up to 16°, overlapping with potential sources from the highest fissure F1. In contrast with the low frequency content of the intra-crater harmonic tremor mostly below 1 Hz, we analyse here signals within the range 1–8 Hz. This choice is driven by the array aperture for resolving accurate DOA17 but also corresponds to the high-frequency signals emitted during the eruption that differ from the harmonic tremor (Supplementary Fig. S3). Amplitude time-series at NYI, KBTI, and GOM filtered in this frequency band clearly show higher amplitude at KBTI between 17:00 and 19:00, thus suggesting nearby sources of infrasound (Supplementary Fig. S13). After processing (Methods and Supplementary Figs. S15–19), the relevant parts of the recording are matched to the individual lava flows based on the estimated DOA (Fig. 5). The detected sources are most likely constrained to the vicinity of the eruptive fissures (F1 to F4) where the most powerful signals are generated during fissure opening and lava fountaining, as observed at Kīlauea11 or in Iceland72. However, infrasound from high-speed lava flow, such as produced by Nyiragongo (>10 m/s)73, could also be recorded, as evidenced at Kīlauea74.

Fig. 5: Tracking of lava eruptions on the flank compared with the drainage of the lava lake.
Fig. 5: Tracking of lava eruptions on the flank compared with the drainage of the lava lake.The alternative text for this image may have been generated using AI.
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a Map of Nyiragongo’s flank from the northern limit of the urban area (in gray) including the airport to the south, up to Nyiragongo’s summit crater to the north. The background topography (contour lines) is derived from SRTM data with 1 arc-second resolution (NASA/USGS). The abbreviation Cr denotes Nyiragongo’s crater and the main eruptive fissures are numbered F1, F2a,b, F3, and F4 from highest to lowest elevations, respectively. A picture taken from a helicopter on 4 June 2021 shows the Shaheru adventive crater and the fissure F2a (inset). The lava flows are colored (from blue to red) according to the DOA (°N) with respect to KBTI station (green triangle). Intra-crater activity (CR) and F1 corresponds to DOA colored in black. Considering the location of eruptive fissures, DOA that do not correspond to potential eruptive sources are colored in light blue/magenta and light brown. The corresponding color scale is plotted in (b). b Infrasound record at KBTI colored according to DOA. Vertical dashed lines indicate 16:30, 16:50, and 17:20. c Observed DOA converted into elevation along the fissures axe from Nyiragongo’s crater to F4 plotted as error bars. The drainage of the lava lake contained within the summit pit-crater is reproduced from Fig. 4 as the transparent red-to-gray area limited by the pit-crater rim on top and the maximum depth of the pit crater after the eruption on bottom.

The DOA, being calculated by assuming source points coincide with the topography (see “Methods”), can be converted to elevation points of a topographic profile passing through the main eruptive fissures (Fig. 5 and Supplementary Fig. S20). This allows a direct comparison with the time-varying depth of the pit crater. The synchronicity of the lava-lake drainage with the successive opening of fissures from north (i.e., near the summit) to west (i.e., lower part of the flank) is obvious. The chronology of the flank eruption is deduced as follows (Fig. 5 and Supplementary Fig. S19):

  1. (1)

    Hours to minutes before the first signs of the seismic unrest at 15:57, the persistent lava lake acoustic signature from the crater (CR) is detected at the station, as for any other days in the years preceding the eruption17.

  2. (2)

    Between 15:57 and 16:50, signals with DOA spreading over ~20° toward the crater (Cr) associated with the beginning of the seismic crisis still have low amplitudes between 10−2 and 10−1 Pa commonly recorded during “quiescent” period17. Some clear impulsive signals with peak amplitude exceeding 10−1 Pa are detected, which may reflect a vigorous spattering activity of the lava lake.

  3. (3)

    A sharp amplitude increase around 16:50 may convey the first lava fountaining episodes from F1 but also intense intra-crater activity (e.g., lava lake drainage, explosions/degassing).

  4. (4)

    A clear drift of the DOAs starting after 16:55 is associated with the paroxysmal phase of the lava fountaining along the fissure F2a lasting about 15 min up to 17:10 characterized by maximum signal amplitude of a few Pa. By around 17:20, the paroxysm of the lava fountaining, associated to the signal amplitude burst at KBTI starting at 16:50, was ending.

  5. (5)

    The following 10 min mark another drift of DOAs to the south that could be associated with fissures F2b at the downstream level. Note that, at that time, many time-segments are not associated with DOAs because solutions can only be found for high apparent velocity (>400 m/s) in contradiction with straight-line propagation at local distance. Atmospheric effects and limited resolution in time and space from the three-element small aperture array are the most likely explanations (see “Methods” and Supplementary Figs. S18, S19).

  6. (6)

    Lava fountain activity persists along F2 and potentially overlaps with F3 for approximately the next two hours, up to 19:00. High amplitude impulsive signals coming from the crater are also detected around 18:20, which corresponds to the moment when the pit crater stabilized near its final depth. Amplitude at the tail of the eruptive signal continuously decreases, ending with signals from fissures F3 and F4 after 19:00. At that time, amplitudes at KBTI reach comparable lower levels recorded at NYI (Supplementary Fig. S13), which both support the overall energy decrease of the infrasound sources and their increasing distance to KBTI. Spurious arrivals from the overall fractured area persist during the following hours. Background signal amplitudes get closer to pre-eruptive level after 22:30 (see insets in Fig. 5b).

The exact start time at which lava appeared on the flank remains elusive due to DOA uncertainties. Based on our acoustic model, the lava lake level started to decrease around 16:30, which also marked a change in DOA from the main crater. However, the clearest drift with increase of infrasound amplitude appears 20–25 min later, which coincides roughly with the first visual accounts of lava on the flank35. Another 30 min later, the lava contained within the lake was completely flushed.

Toward a further understanding of Nyiragongo’s lava-lake system

Like for other long-lived lava lakes75, a stable feeding conduit connected to the bottom of the lava lake is expected. The infrasound-based results (Fig. 5) strongly suggest that a gravity-driven flow from the lava lake occurred through the vertical feeding conduit, then erupted along the flank fissures less than one hour after the start of the seismic unrest detected at NYI (i.e., 15:57). The analysis of seismicity can bring further evidence of the movement of magma from the central crater to the eruptive fissures through the lateral dyke crossing the edifice. Seismic events were detected and located between the crater and the eruptive fissures during the first hour of the eruptive unrest (i.e., ~16:00 to 17:00)35 (Fig. 1a), though the dyke propagation becomes clearer outside the edifice (i.e., below KBTI’s latitude) with swarm-like episodes of minor to moderate magnitude earthquakes. The comparative analysis of continuous amplitude time-series between NYI and KBTI in the band 0.333–15 Hz (Fig. 1b) can be used to infer magma movement within the edifice without the need of detecting/locating earthquakes42. Ignoring path or site effects on the recorded amplitude for the sake of simplicity42,76,77, the qualitative analysis of seismic amplitude ratio indicates toward which station seismicity tends to migrate if sufficient seismic energy is radiated and detected at the considered stations. The amplitude ratio KBTI/NYI (Supplementary Fig. S14) clearly conveys the starting seismic unrest detected first at NYI (decrease of ratio) and the progressively higher amplitude increase at KBTI than at NYI (increase of ratio). The increasing trend of the ratio KBTI/NYI cannot be due to a shutdown of a source at the crater and a return to the pre-eruptive state because both summit (NYI) and flank (KBTI) seismic amplitude increase following the start of the unrest. Thus, this result is most likely the signature of a seismic disturbance first localized close the central crater, then followed by the migration of seismicity toward its southern flank.

Regarding the timing of this intrusive process, lava eruption from the highest eruptive fissure F1, which is located about 2000 m away from the lava lake (Supplementary Fig. S20), occurred less than 60 min after the start of seismic unrest at 15:57. From the analysis of the seismic amplitude ratio KBTI/NYI (Supplementary Fig. S13), the migration of seismicity toward the south becomes clearer after 16:15 (i.e., ~40 min before the flank eruption), which corresponds to the timing of the first seismic events detected across the local seismic network35. According to our acoustic model, the lava-lake level did not fluctuate significantly before 16:30. If we consider the magma started to migrate from the main crater synchronously with the drainage of the lava lake, it would have taken only 25 min to reach the flank. Using this range of plausible travel times (i.e., between 25 and 60 min), we obtain dyke propagation velocities ranging between 0.55 and 1.33 m/s from the lava lake toward F1. These numbers are in accordance with observations of dyke intrusions at Piton de la Fournaise (La Réunion Island)78 or in Iceland79. Over the first 8 h since 16:00 UTC, according to seismicity (see dashed line “23 May” in Fig. 1a), the dyke progressed by about 10 km corresponding to an average velocity of ~1.25 km/h (i.e., below 0.5 m/s).

The estimated erupted volume35 of lava was 10–15 Mm3 while the pre-eruptive lava lake volume28 was estimated to be ~8 Mm3. To explain this discrepancy, an additional magma supply from depth is expected. This hypothesis is supported by the presence of primitive olivine in 2021 lava flows in notable proportion35,38 and the efficient hydraulic connection between the shallow and deepest part of the plumbing system28,32,40. Regarding the shallowest contribution to the lava flows from the lava-lake system, knowing the pit-crater geometry and the time-varying lava-lake level (Fig. 4), we can estimate the downward flow rate through the dyke. We obtain a maximum volumetric flow rate of ~3000 m3/s (see “Methods”). To accommodate a flow rate of ~3000 m3/s, the width of the dyke idealized as a rectangular structure80 should vary between 0.6 and 1.2 m (see “Methods”). These values are in accordance with the geometry of the dyke below the edifice inverted from space geodesy (InSAR) observations35 and within the typical range of dyke dimensions found in continental rift settings, like in Iceland80. Increasing the dyke’s extent at depth beneath the edifice down to 2000 m, according to the plausible range obtained from the InSAR-based dyke model, implies that the opening could be even narrower (i.e., less than 0.5 m). Thus, the observed flow rate during the lava-lake drainage was likely controlled by the dimensions of the vertical feeding conduit.

As a strong but necessary simplification, cylindrical conduit’s dimensions (diameter and length) can be considered and expressed as a function of volumetric flow rate using well-established fluid flow models, such as the Hagen–Poiseuille law for laminar flow81 and the Darcy–Weisbach empirical relation for turbulent flow82. The assumption of a gravity-driven flow in a vertical conduit implies that the influence of the conduit length on the observed flow rate can be neglected82 (see “Methods”), contrary to conduit models where horizontal magma flow is also considered, e.g., from the central crater to the flank81,83. Using the Darcy-Weisbach equation, Burgi and co-authors82 established that a conduit diameter of 15 m best explained the visual testimony of a 25-m drop of Nyiragongo’s lava-lake level in 2011. Nevertheless, the measurement of the drop duration was not precise enough (less than 1 up to 5 min)30,82 to give a well constrained estimate (values of 7.5, 10, 12.5 and 15 m were tested). The flow rate derived from infrasound might bring more constraints because the timing of the drop is obtained from an acoustic numerical model reproducing well the resonant frequencies of the observed harmonic infrasound tremor. However, because they rely on indirect observations of the lava-lake level drop, such new estimates would still need to be further confirmed by other observations. Following Burgi and co-authors82 using the Darcy-Weisbach equation and conservative experimental/empirical values for Nyiragongo’s magma properties, we obtain diameters of the shallow conduit ranging between 5 and 9 m (see “Methods”). These values are realistic bounds in agreement with modeling estimates reported at other lava lake volcanoes, Kīlauea63,64, Erebus (Antarctica)84,85 or Ambrym (Vanuatu)86.

Four months after the flank eruption, lava reappeared in the summit crater, and a new lava lake has been forming since then, well detected on seismic42 and infrasound17 recordings. Further investigations of the available seismo-acoustic records, such as waveform inversion for the source mechanisms of seismic VLP events87, are necessary to deepen our understanding of Nyiragongo’s behavior and architecture. From a monitoring perspective, while recording seismicity potentially allows for the detection of abnormal signals shortly (~min to hour) before flank eruptions35,42 (Fig. 2), like at Piton de la Fournaise88 or in Iceland89, analyzing the infrasound signature can provide timely information in time and space about the eruptive processes, aiding in assessing the level of unrest. This study, being part of a long-term (2013–2022) ground-based monitoring initiative17,18,28,32,33,35,42,46,90,91, promotes the development of infrasound measurements as a primary monitoring tool for Nyiragongo, despite recurrent socio-political issues and armed conflicts in the Kivu region. It also supports, in line with the most recent research in this field92, the development of similar approaches to other volcanoes worldwide.

Methods

Seismic and infrasound amplitude time series of local stations

As part of the KivuSNet seismic network (2013–2022)90, seismometers deployed at NYI, KBTI, and GOM are 3-component broadband seismometers with a corner period of 120 s at NYI (Nanometric Trillium Compact posthole), KBTI (Nanometric Trillium Compact), and 60 s at GOM (Güralp CMG-3ESPC). The co-located infrasound sensors are infraBSU instruments (corner frequency of 10 s) manufactured by Boise State University42. One acoustic sensor is deployed at NYI, while three sensors are deployed at GOM and KBTI. Only one sensor for KBTI and GOM is used for computing CCFs (Fig. 3), which is chosen as the one providing the best CCFs’ SNR (signal-to-noise ratio)35.

The sampling rate for all instruments is 50 Hz. Root mean square (RMS) amplitude timeseries (Figs. 1 and 2) are computed from records corrected for the instrumental response and filtered using zero-phase 4th-order Butterworth bandpass filter. RMS estimates are calculated over 1-min windows with 50% overlap (i.e., step every 30 s). For each time increment, moving average over centered 5-min windows are then computed. Zooming into seismo-acoustic events (Supplementary Figs. 4 and 5) is done after applying gain correction only (i.e., no deconvolution) and single pass (i.e., causal) 4th-order Butterworth bandpass filter.

Cross-correlation of infrasound records

The cross-correlation procedure is summarized as follows: (1) Raw data are filtered between 0.1 and 2 Hz and downsampled to 10 Hz; (2) Cross-correlation functions (CCFs) are calculated from successive 150-s signal segments with 75% overlap (i.e., step every 37.5 s). For the cross-correlation between NYI and I32KE, the I32KE trace is shifted by −2809 s beforehand, which corresponds to the time shift observed for the first clear coherent infrasound event recorded at both stations at the start of the eruption. (3) CCFs provide values of correlation coefficients (CCFs amplitude) with respect to (negative and positive) time lag between both records. For each time segment, a coherent acoustic wave is likely to be detected across the station pair if the corresponding normalized CCF has a clear local maximum above 0.5 (for a range between 0 and 1). Maxima of each sliding CCFs are plotted in Fig. 3. This allows us to easily infer when coherent waves recorded at the summit (NYI) are also recorded at other stations. (4) The Fourier transform of CCF is the so-called cross-spectrum which allows for the identification of coherent frequencies between both records. The time-varying frequency changes of CCFs can be estimated by calculating the corresponding spectrogram (Short-Time Fourier Transform, STFT)93. Similarly, we use the Continuous Wavelet Transform (CWT) to get the time-frequency distribution of CCFs. The STFT uses a fixed size for the sliding analyzing window that cannot be equally appropriated for every frequency component, which means a compromise must be found between time and frequency resolution. The CWT allows a more flexible 2D time-frequency resolution than STFT by convolving the 1D signal (i.e., the CCF) with scaled and translated versions of a mother wavelet (here a standard Morlet wavelet is used). From 2D time-frequency representation of each CCF, we extract the “local spectrum” corresponding to the time lag for which the correlation between both signals is maximized in order to retrieve the dominant and secondary frequency peaks. This procedure is summarized in Supplementary Fig. S10 and the results are plotted in Fig. 3. We observe that the local CWT or STFT spectra can be considered as a smoothed version of the standard cross-spectrum. Both CWT and STFT allow to identify unambiguously the same dominant and secondary frequency peaks but the prominence of the secondary peak is clearer with the CWT.

Crater acoustic resonance modeling

We used the CRes numerical model67 to simulate infrasound signals during the drainage of the lava lake. Cres uses a 1D finite-difference frequency-domain method to compute the acoustic response function for an axisymmetric crater, which includes the crater acoustic response function (wave propagation inside the crater) and the atmosphere response function (acoustic radiation from the crater outlet to the receiver).

As shown in Fig. 3 and Supplementary Fig. S3, the infrasound signal is a harmonic tremor (i.e., continuous pressure perturbation), of which the fundamental frequency and the first overtone are clearly detected at local and distant stations. The simple approximation of isotropic radiation into a half space appears sufficient in our case for retrieving these frequency attributes from the simulated infrasound waveforms. The distance and/or altitude of the virtual receiver with regard to the crater outlet will not have any effect on the retrieved resonant frequencies, contrary to the pressure level94. As suggested by Johnson and co-authors16, a baffled piston model is used at the crater outlet instead of an isotropic monopole source that radiates back into the crater and only valid for compact source dimensions, i.e., where ka «1 with k the wavenumber and a the crater radius67. Models including anisotropic radiation patterns, nonlinear propagation effects, topography, winds, and atmosphere structure must be considered in order to better constrain eruption properties (e.g., volume of erupted material) derived from infrasound waveforms94. In our case, we do not need to consider complex path effects because we do not analyze waveforms and amplitude of explosion signals at various distances and azimuth from the vent.

We also acknowledge that the chosen source models (Gauss or Brune models are available in CRes) play a role on the simulated frequency spectra66. However, we can reasonably assume that the source has sufficient energy over a large frequency range for exciting the resonant modes in line with our observations. Thus, we do not need to know in detail the source mechanisms for explaining the resonant frequencies, which are mainly modulated by the crater geometry. As pointed out by Watson and co-authors66 at Etna volcano, it is impossible to model the full complexity of the infrasound sources, which cannot be considered as a single discrete process but are rather the result of the sum of discrete processes over time generating continuous pressure perturbations. Therefore, it is unavoidable to simplify the source mechanism as a constant process that can be repeated over time, thus simulating the observed continuous signals. The volume flux source time function at the base of the crater is modeled as a Gaussian pulse with standard deviation of 0.15 s (Supplementary Fig. S11) in line with parameters set up by Johnson and co-authors16 for Villarica’s lava lake.

Aside from the crater geometry, the temperature and gas composition also modify the acoustic impedance, and thus the crater resonance. Because of the difficulty to estimate such parameters, standard values must be chosen. Atmosphere temperatures of 300–360 K ( ~27–97 °C) above the lava lake were reported26. Variations of less than 100 °C will have very limited influence on the final resonant frequencies67. Similarly, variations in gas species would reduce the sound of speed by only 10% and have little impact on the resultant resonant frequencies67. Hence, for modeling simplicity, we chose reasonable values applicable to both crater and atmosphere parts: 5 °C for the temperature and 1 kg/m3 for the gas density. Assuming dry air composition67, the resultant speed of sound would be 334 m/s. Therefore, only the crater geometry will play a role in modifying the harmonic properties of the modeled infrasound records.

Resonant frequencies inversion for time-varying crater geometry

Data to invert are selected from Fig. 3. We keep the best estimates of resonant frequencies for station pair NYIxKBTI and NYIxGOM, of which maximum CCF’s coefficients exceed 0.5 for time delays corresponding to signals originating from Nyiragongo within an interval of ±1.5 s around theoretical delay times (assuming straight-line wave propagation and velocity of 340 m/s). After a resampling to one data point per minute and per station pair, the selected data for the dominant (fundamental) and secondary (first overtone) frequencies are plotted in Supplementary Fig. S12. Best-fit models for f0 and f1 are computed, on the form \(f=a+(b-a)* 10^{(-k.* t)}\) with \(f\) the frequency, \(t\) the time, \(a\), b and \(k\) real positive numbers. Centered intervals of 1/5 octave band around the best-fit models encompass 91% and 87% of peak frequencies for f0 and f1, respectively. Hence, we consider the best-fit models and the corresponding 1/5 octave intervals as final robust datasets to be inverted. The selected period for f0 observations ranges from 16:45 to 22:30 and for f1 observations from 16:55 to 22:15. Note that there is a slight increase of f0 after 22:30 up to a value of around 0.208 Hz for the next few hours.

As a priori information about the crater geometry, we know the evolution of the mean crater radius over time between 2006 and 202128, allowing us to start with important constraints about the pit crater shape at the beginning of the eruption (Fig. 4). This complex shape is further simplified as a stack of 3 blocks made of, from top to bottom, one cylinder and two truncated inverted cones (i.e., decreasing radius with depth). From SAR images in Fig. 2, the mean top radius ranges from 110 m (value estimated before the eruption at 15:37 on 22 May) to 165 m (value estimated after the eruption at 04:03 on 23 May)65. The bottom radius is not well-constrained. Values between 10 and 70 m would be acceptable in accordance with the pit-crater model28 plotted in Fig. 4. We choose a mean bottom radius of 40 m.

The methodological inversion approach consists in computing resonant frequencies for a wide range of potential crater geometries. The free model parameters are the depth D (ranging from 15 to 500 m) and the width factor W of the crater (ranging between 1 and 1.5). The width factor W is applied uniformly to the three blocks, which implies that the top radius of the pit crater can increase from 110 to 165 and the bottom radius can increase from 40 to 60 m. For all potential values of D and W, we compute the difference between observed and simulated f0 and f1 in terms of octave band. Both residuals are averaged (i.e., f0 and f1 have the same weight) to get a final 3D matrix R of size [length(\(t\)), length(W), length(D)]. Before 16:55 and after 22:15, only f0 observations are used. Because the crater radius can only stabilize or increase with time, we further assume that the evolution of the width factor W can be approximated by pre-defined sigmoid time functions W(t)  \(=0.5* (1+erf [(t-\mu )/(\sigma \sqrt{2})])\)) with \({erf}\) the error function, \(x\) the number of time steps, \(\sigma\) the standard deviation and \(\mu\) the mean of the considered temporal distribution, always starting with W = 1 (top radius = 110 m) and with final values ranging between 1 and 1.5 (top radius between 110 and 165 m). This function, known as cumulative distributive function of the normal distribution in the context of probability theory, allows to define realistic models for the time evolution of the crater width W by varying \(\mu\) and \(\sigma\). For all time-varying models of W, we look for the depth values D in the matrix R that give the lowest misfit with the additional constraint that D can only stabilize or increase after each time step t, since both observed f0 and f1 stabilize or decrease with time.

To summarize, we generate n sigmoid functions Wn(t) obtained from n combinations of \(\mu\) and \(\sigma\). Thus, for each Wn(t) function, we perform an incremental search for the depth function Dn(t) that gives the lowest misfit at each time step between observed and computed resonant frequencies (with the constraint that Dn(t) ≥ Dn(t − 1)). This leads to 194,106 solutions, among which 23,913 models fall within the 1/5 octave intervals for both f0 and f1. These numbers can be reduced to 1029 and 257 solutions respectively (see gray and colored models in Fig. 4), after removing nearly identical models defined as models with less than 2% of variations for any depth values (i.e., maximum of 10 m for D = 500 m) and 3% for any width values (i.e., maximum of 4.95 m for W = 1.5, which corresponds to a top radius of 165 m).

Infrasound arrays processing

KBTI is equipped with three sensors (infraBSU like the one deployed at NYI and GOM). They are connected to the same acquisition system (Nanometrics Centaur) with a small aperture of ∼20-m between sensors35, like other local deployments at volcanoes95,96. Deploying at least three sensors at the same site allows performing array processing for retrieving the direction of arrival (DOA) and an apparent velocity (Vapp) of coherent waves passing through the array. Based on the array response17, this deployment is efficient at detecting coherent infrasound arrivals in the frequency range 1–8 Hz. Standard least squares beamforming12 can be applied to each 3-element array for successive windows of 10-s length overlapped by 50% to get DOA and Vapp (Supplementary Fig. S15–18). Potential sources (crater, eruptive fissures) are in line-of-sight with the station with low incident angles (<15°) (Fig. 5 and Supplementary Figs. S6, 7, 20). We can thus assume sub-horizontal plane wave propagation to the sensor array with apparent velocity close to the adiabatic sound speed (Vapp ~340 m/s). Arrivals from the main crater may cover an angle aperture up to 16°, which overlaps with potential sources from the most elevated fissure F1. The determination of DOA can be largely affected by seasonal and daily variations within the shallow atmospheric boundary layer affecting wave propagation path and amplitude due to changing temperature and wind conditions17,93 (Supplementary Figs. S15 and 16). Regarding the above-mentioned effects, the eruption on 22 May 2021 occurred during an unfavorable year and daily period where DOA estimates can be strongly biased (Supplementary Figs. S17 and S18).

With only three sensors, a least-squares fitting of observed time delays cannot provide statistical meaningful uncertainties95. In the specific timeframe of the eruption, we thus apply a grid-search strategy for finding the DOA of direct waves (Supplementary Fig. S19), which is more suited to estimate DOA errors from a three-element small aperture array95,96. First, we resample both signals by a factor 10 using cubic interpolation before cross-correlation95, because the precision to measurements of arrivals at each sensor is limited by the initial sampling rate (50 Hz). Then, three normalized CCFs are computed for 5-s signal windows at 1-s time step for the three station pairs. A mean of the CCFs maxima (MCCM, standing for Mean of Cross-Correlation Maxima) equal or superior to 0.6 indicates that a coherent acoustic wave is potentially passing through the array. We consider each grid point on a map as a potential local source. For each pair of stations, each grid point is associated to a set of modeled time lags after assuming straight-line wave propagation with incident angles <15° (including topography) and intrinsic sound speed ranging from 340 to 360 m/s. Using standard equations provided in CRes67,70 linking air temperature and sound speed, this range corresponds to realistic end members for the average air temperature above the lava flow paths (15–50 °C) before and during the flank eruption between potential sources along the flow paths and KBTI array (see Fig. 5). Using a similar grid-search approach, Johnson and Ronan96 considered a unique value of 343 m/s for locating volcanic rockfalls. The heat transfer to the atmosphere by the erupting and cooling lava flows is a complex time-dependent process and we do not intent to (and cannot) provide precise estimates of the ambient air temperature above the lava flows. The range 15–50 °C was defined according to mean air temperatures in the Kivu between Goma and Nyiragongo’s summit97 and reported measurements of atmosphere temperature above Nyiragongo’s and Erta Ale’s lava lakes26. This allows to consider conservative uncertainties about probable variations of the intrinsic sound speed velocity during the eruption. Grid points where time delays correspond to the maximum of the CCFs for this range of acceptable velocities are set to 1, otherwise 0. Three grids for three station pairs are then stacked. Hence, we obtain a final spatial grid with values ranging from 0 (no source) up to 3 if there is a source region satisfying all station-pair observations. Because of the geometry of the array with sensors close to each other, the source region looks like a narrow strip area extending from the station site. This means that only DOA can be resolved and not a specific point source in 2D space. Thus, for each sliding 5-s window, we retrieve the mean, minimum and maximum DOA of the identified source region (i.e., the one where grid values equal 3). In Fig. 5, the mean DOA over time is represented by the color code and the DOA range (minimum to maximum) is represented by the error bars.

Infrasound array I32KE in Nairobi, Kenya is part of the International Monitoring System (IMS) that is currently being installed for the verification of the Comprehensive Nuclear-Test-Ban Treaty (CTBT). I32KE consists of seven absolute MB3a microbarometers that form a 2 km aperture array. The array layout consists of a triangular outer structure enclosing a trapezoidal inner array. All microbarometers measure atmospheric pressure fluctuations through an 18-m aperture wind noise reduction system, each of which has 96 inlet ports. The array was originally installed in 2003 and was revalidated in 2019.

During the time of the eruption, element I32H1 was not operational; instead, six elements were used in this study. The processing of the array is carried out using a standard time-domain delay-and-sum beamformer. As an event detector, we evaluate the Fisher ratio for which a probability of detection can be evaluated under assumption of a given SNR93,98.

The raw signals are detrended and filtered in a 0.4–3 Hz passband. The filtered signals are upsampled to 200 Hz and processed in 30 s windows with 95% overlap. For each window, the slowness that best aligns the signals is determined following a grid search method. The slowness grid is parameterized by the back azimuth and apparent phase speed values of interest. In this case, the back azimuth values vary between 253 and 281° in steps of 0.1°. Apparent phase speeds vary between 300-400 m/s in steps of 1 m/s.

Processing results are shown in Supplementary Fig. S8. I32KE’s trace corresponds to the best beam with a back-azimuth of 267.4° (i.e., pointing toward Nyiragongo) and an apparent phase speed of 342 m/s. The best beam is computed in the frequency domain using the unfiltered, detrended signals; a wider frequency band is used to compute the spectrogram. Ray tracing modeling99,100 results for propagation from Nyiragongo to Kenya given in Supplementary Fig. S9 and Supplementary Table S1 are in good agreement with observations (Fig. 3 and Supplementary Fig. S8).

Conduit diameter and dyke width

Regarding the vertical conduit, the Hagen-Poiseuille equation for laminar flow in a cylindrical tube gives:

$$Q=\frac{\pi \, \varDelta P \, {R}^{4}}{8 \, \eta \, L},$$
(1)

with \(Q\) the volumetric flow rate (m3/s), \(\varDelta P\) the pressure gradient (Pa), \(R\) the conduit radius (m), \(\eta\) the fluid viscosity (Pa.s), and \(L\) the conduit length (m). \(\varDelta P\) can be expressed as \(\varDelta P=\rho g\varDelta H\), with \(\rho\) the fluid density (kg/m3), g the acceleration due to gravity (m/s2) and the differential height \(\varDelta H=L+h\), with \(h\) the height of the lava lake. \(h\) is obtained by subtracting the inverted depth value (distance from the rim to the lava lake surface, Fig. 4) to the total height of the pit-crater before collapse (300 m). The conduit diameter D is thus expressed by:

$$D=2\root{{4}}\of{\frac{8 \, \eta \, {Q \, L}}{\pi \, \rho g \, (L+h)}}$$
(2)

The time period used for estimating the mean flow rate \(Q\) is chosen according to 2 criteria: both f0 and f1 observations are available (i.e., after 16:55) and the geometry of the pit crater is well constrained (height of the lava lake above 90 m, i.e., before 17:03). We obtain \(Q\)~3000 m3/s, \(h\) =[94–155] m and \(L\) = [130–630] m if the differential height between the bottom of the lava lake and the eruptive fissures is assumed to be representative of the conduit length \(L\). As a reasonable simplification, the conduit length \(L\) and the height of the lava lake \(h\) can be neglected in Eq. (2) since “\(L\)” in numerator and “\((L+h)\)” in denominator are of the same order of magnitude. We thus obtain:

$$D\approx 2\root{{4}}\of{\frac{8 \, \eta \, Q}{\pi \, \rho g}}$$
(3)

Using experimental values73,101 of \(\eta\)= 30–60 Pa.s and \(\rho\)= 2800 kg/m3, Eq. (3) suggests that D would be around 3.4–4 m (close values around 2.8–3.9 are obtained using Eq. 2, \(L\)= 130–630 and \(h\)= 94–155). Taking into account other flow regimes that deviate from the laminar flow, the Darcy-Weisbach empirical equation can be considered82:

$$Q=\pi \, {D}^{5/2}\sqrt{\frac{\Delta P}{8 \, f\rho \, L}}$$
(4)

From Eq. (4) and again neglecting the conduit length \(L\) and the height of the lava lake \(h\), we get:

$$D\approx \root{{5}}\of{\frac{{8 \, {f \, Q}}^{2}}{{\pi }^{2} \, g}}$$
(5)

It introduces the dimensionless friction factor \(f\) that characterizes the resistance to flow due to friction. \(f\) is partly dependent on the conduit diameter and can be expressed through a variety of models depending on the flow regimes. For turbulent flow regime that corresponds to our situation (low viscosity magma above the fragmentation level characterized by high Reynolds number)82,102, \(f\) becomes weakly dependent on the channel geometry and is more related to the roughness of the conduit walls103, with experimental values ranging between 0.004 and 0.08 (Note that a factor 4 is applied between the definition of \(f\) by Mastin and Ghiorso102 and Wilson and Head103). At Nyiragongo, values between 0.02 and 0.06 were considered82. Thus, for a conservative range of \(f\) between 0.004 and 0.08, D would only vary between 4.9 and 9 m. As for the laminar flow, similar values (4.2–8.7) are obtained if we add the conduit length \(L\) and the height of the lava lake \(h\) to Eq. (5) in the expression of D.

To link the estimated flow rate derived from the drainage of the lava lake with the geometry of the vertical conduit, we have implicitly considered that the shallow dyke structure connecting the vertical conduit and the eruptive fissures can accommodate this flow rate. For a magma channel described as a rectangular dyke geometry, the flow rate is expressed as80:

$$Q=\frac{\varDelta {P \, d} \, {w}^{3}}{12 \, \eta \, l}$$
(6)

where \(d\) is the long-side length (extent at depth), \(w\) is the short-side length (opening of the dyke), and \(l\) is the length of the channel (lateral extent). In order to verify that realistic values of \(w\) are obtained for the inferred flow rate \(Q\) (3000 m3/s), we get:

$$w=\root{{3}}\of{\frac{12 \, Q \, \eta \, l}{d \, \varDelta P}}$$
(7)

We set \(d\) to 500 m in accordance with the extent of fissures F1/F2a (2250–2750 m a.s.l.) during the initial phase of lava flows between 16:55 and 17:03 (Fig. 5 and Supplementary Fig. S13). While the dyke was propagating toward the Lake Kivu at shallow depth (less than 500 m),\(d\) became much larger with a maximum extent of about 10–12 km beneath Goma35. \(l\) is the lateral distance between the lava lake and the eruptive fissures on the flank that reached the Shaheru crater (i.e., Fissures F1/F2a), ranging approximately between 2000 and 3000 m. \(\varDelta P\) is the driving pressure depending on conditions at the two ends of the channel. Right beneath the lava lake, at depth corresponding to the extension of fissures F1/F2a observed on the flank, the magma-static pressure would vary between ~8 and 20 MPa. We thus obtain values of \(w\) varying between 0.6 and 1.2 m in order to accommodate a flow rate of 3000 m3/s during the drainage of the lava lake. Increasing the extent of \(d\) beneath the edifice at depth down to 2000 m, according to the plausible range obtained from the InSAR-based dyke model, leads to an opening of less than 0.5 m.