Ground deformation reveals the scale-invariant conduit dynamics driving explosive basaltic eruptions

Explosive volcanic eruptions can occur suddenly on timescales of seconds to minutes, often without recognized precursors, posing significant hazards to populations and complicating risk management. Despite advances in monitoring, forecasting such blasts remains difficult due to incomplete understanding of short-term conduit processes. Open-vent basaltic volcanoes like Stromboli typically exhibit regular Strombolian activity but are intermittently punctuated by violent major explosions and paroxysms that disperse tephra widely and generate pyroclastic flows and tsunamis. These larger events differ in erupted mass, eruption rates, and magma properties (gas-rich, low-viscosity, deeper-sourced magmas) compared to regular Strombolian activity. The study aims to analyze high-resolution ground tilt data to identify and model systematic pre-blast deformation patterns and to link them to underlying conduit dynamics, with the goal of improving short-term eruption forecasting.

Previous studies have documented inflation–deflation cycles associated with explosive activity at various volcanoes and highlighted the utility and challenges of tilt measurements for eruption precursors. At Stromboli, regular Strombolian explosions are linked to shallow, volatile-poor, crystal-rich magmas, whereas major/paroxysmal events involve deep-derived, volatile-rich, low-viscosity magmas. Very-long-period seismicity and GPS have previously constrained shallow deformation sources during past paroxysms. Models of ground deformation from vertical conduits and of magma ascent driven by gas slug dynamics indicate that gas expansion and conduit overpressure can produce measurable surface tilt. However, capturing subtle pre-eruptive deformation in real time remains difficult due to noise and the short duration of processes.

Data: The team analyzed two decades of ground deformation (tilt) records from Stromboli, focusing on the paroxysms of 3 July and 28 August 2019 and earlier events (5 April 2003; 15 March 2007), along with 39 major explosions (2005–2019) and thousands of regular Strombolian explosions. Ground tilt data were recorded by borehole tiltmeters (Pinnacle T5000, 1 nrad sensitivity, 1 Hz sampling) installed at ~6 m depth. Broadband seismic stations (Guralp CMG-40T, 30 s natural period, 100 Hz, 24-bit) were used to derive tilt components at additional sites. The monitoring network also included acoustic sensors, thermal/visible/UV cameras, and multigas sensors. Analysis and source localization: Surface tilt amplitude decays rapidly with distance from the craters, suggesting a shallow source. A cylindrical open-conduit deformation model was used to relate observed surface tilt to overpressure and volumetric change within a conduit segment. A search over possible conduit top (h1) and length (L) positions (h1 from 0–10,000 m, step 10 m; L from 10–1000 m) identified the best-fitting source geometry by least-squares comparison of Green’s function ratios to observed tilt ratios among stations. Finite element checks indicated topography affects tilt amplitude by <15%. Modeling conduit dynamics: Ground inflation preceding explosions is interpreted as due to increased pressure on conduit walls from rapid volumetric expansion of gas in a vesiculated magma batch rising into the shallow conduit. An expansion-driven ascent model based on Stokes-type relations was used, where ascent velocity depends on gas bubble growth with depth due to magmastatic decompression (assuming ideal gas behavior). The normalized observed tilt inflation was fit to normalized volumetric expansion ratios V/V0 over the measured inflation durations (≈540–720 s for paroxysms). Early warning algorithm: A pattern-matching system compares real-time tilt in a 350 s backward window to a theoretical template of exponential inflation induced by gas expansion. The algorithm triggers an alert when the best-fit correlation R(t) > 0.85 and the tilt variation exceeds 0.3 µrad. Historical tilt records (2006–2020) were tested to evaluate performance.

• Pre-blast exponential ground inflation is a systematic feature across regular Strombolian explosions, major explosions, and paroxysms at Stromboli.
• 2019 paroxysms produced strong pre-onset inflation: 3 July ~14 µrad and 28 August ~9 µrad at tiltmeters, starting ~10 minutes prior to onset; deflation of similar amplitude followed the eruption, lasting 50–70 s.
• Source localization indicates shallow conduit segments inflated: for 3 July, uppermost ~380 m (750 to 370 m a.s.l.) with volumetric expansion ΔV ≈ 4.9 × 10^4 m^3; for 28 August, ~240 m (720 to 480 m a.s.l.) with ΔV ≈ 3.2 × 10^4 m^3. Overpressures inferred: ~5.9 MPa (3 July) and ~6.1 MPa (28 August), for conduit radius a ≈ 95 m and rigidity μ ≈ 1.3 × 10^9 Pa.
• Scale invariance: After normalization, inflation curves for regular, major, and paroxysmal events collapse onto the same exponential trend (best-fits 0.89–0.99), indicating a common conduit process operating at different scales.
• Scaling with magnitude: At ~800 m from vents, typical tilt amplitudes and lead times are: regular explosions ~0.1 µrad with ~150 s inflation; major explosions ~0.8 µrad with ~300 s inflation; paroxysms ~10 µrad with >600 s inflation. Tilt amplitude scales with erupted tephra volume across activity types.
• Conduit expansion model fits: Best-fit volumetric expansion ratios and durations are V/V0 ≈ 15.8 over tb ≈ 610 s (3 July) and V/V0 ≈ 12 over tb ≈ 590 s (28 August), with fits of 0.99 and 0.98, respectively.
• Depth constraints: If expansion begins at the base of the deformation source, fragmentation depths inferred are very shallow (~28 m for 3 July; ~16 m for 28 August). If fragmentation occurs at ~150 m depth (as inferred for 2007), gas expansion onsets deeper (~2.4 km and ~1.85 km), consistent with deepest slug source depths at Stromboli.
• Ascent rates of the gas-magma mixture inferred from the model: ~15.3 m/s (3 July) and ~9.5 m/s (28 August), consistent with independent petrological and modeling estimates.
• Early warning: The pattern-matching algorithm detected the 2007 and 2019 paroxysms 4–5 minutes before onset with no false positives over 14 years of data under the chosen thresholds; on 28 August 2019, an alert was communicated ~5 minutes before the explosion and ~9 minutes before a tsunami reached the coast.

The findings demonstrate that explosive eruptions at Stromboli, spanning nearly seven orders of magnitude in erupted volumes, are preceded by a scale-invariant exponential ground inflation, implying a common shallow conduit dynamics regardless of the event magnitude or the deeper magma source characteristics. Normalized inflation curves indicate that the temporal pattern is independent of explosion size and starting depth of the process, while amplitude and duration scale with magnitude. The inferred shallow pressure source (roughly 370–450 m a.s.l.) aligns with locations where tensile failure in a crystal-rich magma mush has been proposed for regular activity. Overpressure-driven upward migration of the magma column can explain observed pre-paroxysm lava overflows and increased effusion. Practically, the reproducible deformation pattern enables implementation of reliable short-term early warnings based on tilt pattern recognition, potentially improving hazard mitigation during violent explosive episodes and associated secondary hazards (e.g., tsunamis).

This study identifies a universal, scale-invariant pre-eruptive exponential inflation pattern in ground tilt at Stromboli across regular, major, and paroxysmal explosive activity. A shallow conduit expansion model, in which rapid gas expansion in vesiculated magma increases magmastatic pressure, quantitatively reproduces observed inflation with realistic parameters and ascent rates. The amplitude and duration of inflation scale with eruption magnitude, while the normalized temporal pattern is consistent across events. Leveraging this repeatable signal, a real-time pattern-matching early warning algorithm successfully detected past paroxysms minutes before onset without false positives in historical tests. Future work could refine source depth and fragmentation constraints (e.g., integrating high-rate GPS, infrasound, VLP seismicity, petrological constraints), incorporate topography more fully, and test generalization to other open-vent basaltic systems to develop robust multi-parameter forecasting tools.

• Fragmentation depth during the 2019 paroxysms is unconstrained; model solutions require assumptions (surface fragmentation vs fixed depth), leading to a range of inferred expansion onset depths.
• The conduit model neglects certain complexities: differences in viscosity between deep gas-rich and shallow degassed magmas are not explicitly modeled; gas density is neglected in parts of the derivation; and topography is not included in the primary tilt model (though FEM suggests <15% effect on amplitude).
• Early deformation at great depth may produce signals too small to detect at the surface, limiting the observable lead time to the shallow expansion phase.
• Tilt measurements are sensitive to environmental and anthropogenic noise; although the algorithm avoids pre-filtering and uses pattern matching, performance may vary with station conditions and network geometry.
• Assumes ideal gas behavior and simplified bubble growth relations; real magma–gas systems may deviate under certain conditions.