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Eruption at basaltic calderas forecast by magma flow rate


Forecasting eruption is the ultimate challenge for volcanology. While there has been some success in forecasting eruptions hours to days beforehand, reliable forecasting on a longer timescale remains elusive. Here we show that magma inflow rate, derived from surface deformation, is an indicator of the probability of magma transfer towards the surface, and thus eruption, for basaltic calderas. Inflow rates ≥0.1 km3 yr−1 promote magma propagation and eruption within 1 year in all assessed case studies, whereas rates <0.01 km3 yr−1 do not lead to magma propagation in 89% of cases. We explain these behaviours with a viscoelastic model where the relaxation timescale controls whether the critical overpressure for dyke propagation is reached or not. Therefore, while surface deformation alone is a weak precursor of eruption, estimating magma inflow rates at basaltic calderas provides improved forecasting, substantially enhancing our capacity of forecasting weeks to months ahead of a possible eruption.

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Fig. 1: Unrest outcome as a function of the inflow rate in mafic calderas.
Fig. 2: Inflow rate, magma overpressure and related critical time.

Data availability

All data are available in the main text or in the supplementary materials. Source data supporting this research are also available in a permanent data repository at Source data are provided with this paper.

Code availability

MATLAB scripts associated with Fig. 2 and Extended Data Figs. 2, 4 and 5 are available at


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We thank L. Caricchi, S. Jónsson and F. Sigmundsson for constructive discussions. The grant to the Department of Science, Roma Tre University (MIUR-Italy Dipartimenti di Eccellenza, ARTICOLO 1, COMMI 314 – 337 LEGGE 232/2016) is gratefully acknowledged for covering the publication fee (V.A.). F.G. was partly supported by NASA grant 80NSSC21K0842 from the Interdisciplinary Science Program of the Earth Science Division. A.H. was supported by the UK Natural Environment Research Council (NERC) through the Centre for the Observation and Modelling of Earthquakes, Volcanoes and Tectonics (COMET) and the H2020 project EUROVOLC funded by the European Commission (grant number 731070).

Author information

Authors and Affiliations



V.A. and F.G. conceptualized the work. F.G. collected the data. F.G. and A.H. developed the modelling. All authors contributed ideas and input to the research and writing of the paper.

Corresponding author

Correspondence to Federico Galetto.

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The authors declare no competing interests.

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Nature Geoscience thanks Andrew Bell and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Primary Handling Editor: Rebecca Neely, in collaboration with the Nature Geoscience team.

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Extended data

Extended Data Fig. 1 Unrest outcome as a function of the inflow rate in mafic calderas.

a) Duration of unrest and corresponding injection rates (Q). Here we include also the data from Axial Seamount. The dotted grey area and vertical dotted line have the same meaning than those in Fig. 1a and c. The purple area on the y axis marks the syn-eruptive rates of Kilauea in the last 40 years. b) Histogram of frequency of the rates associated with the unrest episodes.

Source data

Extended Data Fig. 2 Maximum overpressure (ΔPmax) and inflow rate (Q).

Maximum overpressures (ΔPmax) depending on inflow rate and volume of the reservoir, assuming a viscoelastic rheology with viscosity 4×1018 Pa s. Grey area indicates ΔPcrit =10 ± 4 MPa and dashed line ΔPcrit =10 MPa. Data below the grey area are in the viscous domain, promoting magma storage and plain unrest. Data above the grey area are in the elastic domain, promoting dyke nucleation.

Extended Data Fig. 3 Intruded volumes (V) as a function of the unrest duration (t).

Circles represent natural data (unrest nucleating dyke in less than 1 year) with t that should correspond to τe. All the points lie between the lower and higher values of V0, E and ΔPcrit used in our analysis (for the red line E=20 GPa, V0=20 km3 ΔPcrit=6 MPa, while for the yellow line GPa, E=60 GPa; V0=150 km3 and ΔPcrit=14 MPa).

Source data

Extended Data Fig. 4 Time (τe) to reach ΔPcrit as a function of Q and V.

Time required to reach the critical overpressure to nucleate a dyke in the elastic domain as a function of the inflow rates Q and the volume of the reservoir V, using a) ΔPcrit=10 MPa and E = 60 GPa, b) ΔPcrit=6 MPa and E = 30 GPa, c) ΔPcrit=10 MPa and E =20 GPa. The thicker line marks t=1 year.

Extended Data Fig. 5 Qmin for nucleating a dyke and viscoelastic relaxation time (τv).

Red and blue lines show the variation of the minimum rates (Qmin) for nucleating a dyke in the viscous regime as a function of τv. Triangles represents the plain unrest episodes in our dataset. Asterisks are the unrest episodes nucleating dykes in more than 1 yr.

Source data

Extended Data Fig. 6 Unrest outcome as a function of Q considering only the mean of the Krafla cases.

a Duration of unrest and corresponding inflow rate, Q, as a function of unrest outcome. The grey area highlights the zone with transitional rates (5 ± 4 ×10−2 km3/yr). The vertical dotted grey line separates the unrest episodes lasting <1 year from those lasting >1 year. Krafla data have been reduced to a single data point (mean value) above the transition zone and in the upper transition zone. b Histogram of frequency of the inflow rates. Tr. Q,, L. Tz. and U. Tz. in panel b refer to transitional, lower transitional and upper transitional rates, respectively.

Source data

Extended Data Fig. 7 Distribution of the analysed mafic calderas.

Red triangles point calderas in Fig. 1. Magenta triangles highlight the two additional calderas (Kilauea and Axial Seamount) considered in Extended Data Fig. 1. Blue circles highlight the location of other mafic calderas where our results (also calibrated to different inflow rates) could be applied, although the shallow depth of the magma reservoir should be verified.

Source data

Supplementary information

Supplementary Table 1

Geodetic data.

Supplementary Table 2

Data from Axial Seamount.

Source data

Source Data Fig. 1

Injection rates and times (duration of the unrest). Data used for generating Fig. 1.

Source Data Extended Data Fig. 1

Injection rates and times (duration of the unrest episodes) used in Extended Data Fig. 1. Data in Supplementary Table 2. Additional data are those coming from calderas not considered in Fig. 1.

Source Data Extended Data Fig. 3

In this table, we report the intruded volume (V) and the times of the considered unrest episodes.

Source Data Extended Data Fig. 5

In this table, we report the inflow rates (Q) and the times of the considered unrest episodes.

Source Data Extended Data Fig. 6

In this table, we report the inflow rates (Q) and the times of the considered unrest episodes.

Source Data Extended Data Fig. 7

Longitude and latitude of the calderas plotted in Extended Data Fig. 7. In the txt file named LonLatcaldereFig1 the longitude and latitude of the analysed mafic calderas are reported. In LonLatcaldereextraFigS1.txt there are the coordinates of the two calderas added in Extended Data Fig. 1. In LonLatcalderepotentialtarget.txt there are the coordinates of the additional potentially similar mafic calderas.

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Galetto, F., Acocella, V., Hooper, A. et al. Eruption at basaltic calderas forecast by magma flow rate. Nat. Geosci. 15, 580–584 (2022).

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