IRSFPThe manuscript PSI: A Relaxation-Based Framework for Critical Volcanic Transitions (Martin Petrásek, 18 May 2026) introduces the Planetary Stability Interface as a theoretical and diagnostic framework for studying critical geophysical transitions. It investigates whether a system's ability to damp perturbations may weaken before an eruption, and whether this appears in the seismic time series. This is not a validated operational eruption-forecasting system.
Abstract and research question
Volcanic unrest is usually described through combinations of mechanical stress, magma movement, deformation, seismicity, and changes in gas or heat flux. The study adds the question of whether geophysical transitions may also involve deteriorating dynamic relaxation: disturbances persist longer, autocorrelation increases and the system becomes more sensitive to further perturbations. This relates to critical slowing down in nonlinear dynamical systems; the proposed PSI is a model application of that concept, not new evidence of a universal law.
Model definition
The principal indicator is Rgeo = σinstability / λstability2. The numerator models effective perturbation amplification, while the denominator is the effective relaxation rate squared. With the numerator held fixed and λ positive, the metric increases as the relaxation rate decreases. The manuscript treats it as a phenomenological quantity: estimates of σ and λ depend on the geophysical system measured and the chosen observation channel.
The retrospective Fagradalsfjall 2021 case
The empirical section describes the seismic swarm preceding the 2021 Fagradalsfjall eruption in Iceland. It uses relocated hypocentre catalogues and focal-mechanism information attributed to the Icelandic Meteorological Office. For the pre-eruption period, the author reports an increase in lag-one autocorrelation to ρ1 ≈ 0.934. For the effective relaxation parameter expressed per sampling interval, it uses the relation λstability = −ln(ρ1) ≈ 0.068. According to the text, the PSI proxy increased rapidly and nonlinearly approximately three weeks before the eruption began. These figures are reproduced from the author's preprint; this web page is not an independent reprocessing of the seismic catalogue.
From one case to broader diagnostics
The proposed state vector may include seismicity, ground deformation, gas emissions, thermal anomalies, hydrothermal dynamics and other measurable quantities. The text develops concepts of metastable states, stronger coupling and stochastic transitions. Applying the framework to hydrothermal instability or tectonic changes is presented here as a proposed possibility, not empirically established transferability of the model.
What a retrospective result does not establish
An indicator rising before an eruption in one known case does not establish operational success rates or false-alarm counts. Seismic-catalogue evaluations may be affected by changes in detection sensitivity, aftershock clustering, window selection, non-stationarity and missing measurements. Critical slowing down is not exclusive to future eruptions. The author therefore explicitly rules out interpreting PSI as a validated deterministic forecast or a means of controlling geophysical processes.
Validation criteria stated in the manuscript
The text calls for comparison with standard indicators: autocorrelation, variance, earthquake frequency, deformation and tremor amplitude. Tests should include eruptive and non-eruptive episodes; sensitivity to window length, missing stations and catalogue-completeness thresholds; null models; and temporally separated test data. As a proposed minimum criterion for future added value the manuscript specifies an improvement of ΔAUC ≥ 0.05 over the best simple indicator, at an acceptable false-alarm rate and with a nonzero median lead time. This is a proposed criterion, not an assertion that it has already been met.
Publications and related studies
Martin Petrásek (2026), PSI: A Relaxation-Based Framework for Critical Volcanic Transitions, a preprint by the author. DOI: 10.5281/zenodo.20277063 ↗. Public full text ↗. The text sets out a research hypothesis and a preliminary retrospective analysis; publication alone is not independent confirmation of the findings.
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