The 2015 Pertusillo Lake study established, via a robust periodogram and Singular Spectrum Analysis (SSA) of 132 monthly earthquake counts, an annual periodicity matching the reservoir's loading cycle and a significant correlation with annual lake-level fluctuations, and concluded that the seismicity is effectively induced by the time-varying water level. Such statistical association falls short of conclusive attribution, as the wider induced-seismicity literature recognizes, and the robustness of SSA-based identification on short series remains unquantified. Building on that study, this problem record asks for: (i) a comprehensive quantitative diagnostic framework combining periodicity, rate-change statistics, source mechanisms, spatial patterns, and magnitude-frequency characteristics into calibrated discrimination between reservoir-induced and natural tectonic seismicity; (ii) systematic quantification of the sensitivity of SSA-based periodicity identification and its statistical confidence in short catalogs to window length, preprocessing, and temporal aggregation; and (iii) validated transferability across reservoirs with different operational schedules and catalog qualities. All three strands remain open: existing tools are subjective expert questionnaires, scenario-specific physics-based probabilistic models, or region-specific machine-learning classifiers, and no systematic SSA sensitivity study for short seismic catalogs has appeared.

Background

Reservoir-induced seismicity (RIS) is earthquake activity triggered by the impoundment or seasonal operation of large artificial water reservoirs, caused by changes in crustal stress and pore fluid pressure acting on pre-stressed faults. A canonical Italian case is the Pertusillo artificial lake in the High Agri Valley (Val d'Agri) of southern Italy, a seismically active region where swarms of small earthquakes (magnitude below roughly 3) accompany large seasonal water-level oscillations. Telesca, Giocoli, Lapenna and Stabile (2015) analyzed the monthly number of earthquakes from 2002 to 2012 (a series of N=132N=132 points, short by the standards of time-series statistics) with two methods suited to short series: the robust periodogram (a frequency-domain estimator in which periodic components are assessed against confidence bands constructed robustly, so that a few large events cannot masquerade as periodicity) and Singular Spectrum Analysis (SSA; a technique that decomposes a series into trend, oscillatory components, and noise by diagonalizing the trajectory matrix formed from lagged windowed copies of the series). SSA requires choosing a window length MM (here M=24M=24 months, fixed by heuristic trade-offs: the window must be long enough to resolve the longest period of interest yet short relative to the series length), and the identified components depend on this choice. They found an annual periodicity in the seismicity that matches the yearly reservoir loading cycle, along with a significant correlation with annual fluctuations in the lake level, and concluded that the seismicity is effectively induced by the time-varying water level.

The open question sits at a wider unsolved problem. Distinguishing human-induced from natural tectonic earthquakes has been addressed since Davis and Frohlich (1993) proposed a checklist of yes/no questions about timing, spatial, and mechanistic plausibility. A German expert working-group recommendation (Dahm et al. 2013) systematized such criteria; Cesca, Rohr and Dahm (2013) explored full moment tensor inversion (recovering the radiation pattern of the seismic source and decomposing it into isotropic and deviatoric parts, where anomalous isotropic or shallow sources can hint at fluid involvement) as a discriminant; and Dahm et al. (2015) built a quantitative probabilistic framework that compares the probability of induced versus natural occurrence using modeled Coulomb stress changes (the combined effect of shear and normal stress on a fault) from reservoir depletion, a rate-and-state seismicity model (in which earthquake nucleation rates depend on stressing history), and observed source parameters — but only for events close to hydrocarbon reservoirs and under explicit modeling assumptions. Reviews (Grigoli et al. 2017; Foulger et al. 2018) list discrimination as a still-open challenge. Questionnaire-style schemes remain the operational default: Foulger et al. (2022) showed empirically that such schemes are subjective, analyst-dependent, and 'cannot be assumed to give the right answer in a scientifically rigorous sense', and the E-PIE generic grading tool (Evaluate Proposals of Induced Earthquakes) of Foulger et al. (2023) still produces opinion-weighted plausibility grades. Recent machine-learning classifiers (e.g., a vision transformer — a deep-learning architecture originally developed for image recognition — applied to raw waveforms (Song et al. 2025); spectral-amplitude decomposition in Utah (Hutchings et al. 2026)) achieve high within-region accuracy separating natural earthquakes from explosions or mining-induced events, but they are region- and dataset-specific event-type classifiers, not transferable attribution frameworks for reservoir-induced versus tectonic seismicity at a given site. A further confound is that natural seismicity can itself be seasonal (e.g., snowmelt- or groundwater-modulated loading), so matching periodicities are evidence of forcing but not proof of causation. In parallel, the statistical-seismology toolkit for RIS has deepened around Pertusillo itself — high-precision template-matching catalogs (built by cross-correlating waveform templates against the continuous recordings to detect many additional small events below the standard detection threshold) and b-value mapping (Valoroso et al. 2023; the b-value is the slope of the Gutenberg-Richter frequency-magnitude distribution, often elevated in fluid-driven swarms), ground-motion intensity and source-property contrasts (Picozzi et al. 2022), poroelastic stress (stress changes coupled to diffusing fluid pressure) and rate-and-state nucleation modeling (Rinaldi et al. 2020), and dynamic-triggering statistics modulated by the seasonal load (Barkat et al. 2025) — yet each contributes association- or mechanism-level evidence at one site rather than a general, calibrated discrimination methodology.

Problem Statement

The overarching objective is to convert statistical association between reservoir operation and seismicity into defensible quantitative attribution, with known methodological robustness. Three jointly supporting research results are posed:

  1. Construct and validate a comprehensive quantitative diagnostic framework that discriminates reservoir-induced from natural tectonic seismicity by combining, in a single calibrated procedure, the indicator families established in the discrimination literature: periodicity of the event sequence, rate-change behavior, source mechanisms (e.g., focal mechanisms and moment-tensor characteristics), spatial patterns (clustering and migration relative to the reservoir), and magnitude-frequency characteristics (e.g., the b-value), reporting calibrated probabilities or decision confidence for induced versus natural classification rather than a single yes/no verdict. Validation must test discrimination against ground-truthed or independently established induced and natural populations (e.g., synthetic catalogs from physics-based models, or well-documented case studies), not merely correlation with water level.

  2. Quantify the robustness of SSA-based periodicity identification and its statistical confidence in short seismic catalogs (on the order of N=132N=132 monthly points, as at Pertusillo): how do identified components, their periodicities, and significance levels vary with the window length MM, with alternative preprocessing choices, and with temporal aggregation (monthly versus other binning)? The dependence of identified components, their periodicities, and significance levels on these axes is to be characterized across their ranges rather than at isolated single alternatives.

  3. Establish transferability: does the combined methodology generalize across reservoirs with different operational schedules, geology, catalog lengths, and noise levels, and across different temporal aggregations, with performance bounds rather than isolated case-by-case demonstrations?

These three results are linked: (2) and (3) quantify the reliability of the evidence that (1) integrates.

References

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