Generalizing and validating the spectral shape-factor ratio $k=\Omega/f_{p}$ as a precursor indicator of reservoir-induced seismicity

Fu et al. (2024) proposed the ratio $k=\Omega/f_{p}$ of the shape factor $\Omega$ to the peak frequency $f_{p}$ of P-wave power spectra (Welch estimation, 2–14 Hz band, 20 s windows) as a spectral precursor of reservoir-induced seismicity (RIS) at the Xiangjiaba reservoir, southwestern China: events with $k$ exceeding roughly 0.25 increased markedly after the second impoundment. The observation rests on one reservoir, one processing chain, an uncorrected site-effect treatment, and a shape factor with no quantitative physical model; the threshold itself shifts with the analysis band (about 0.25 at 2–14 Hz versus 0.37 at 1–40 Hz). The open problem is to establish whether $k$ is a robust, transferable, physically grounded RIS precursor, or to show that the indicator does not generalize.

Background

Reservoir-induced seismicity (RIS, also called reservoir-triggered seismicity) is seismicity causally influenced by the impoundment or operation of large artificial water reservoirs, driven mainly by stress changes on faults and by diffusion of pore pressure (the pressure of fluid in rock pores) into the crust. RIS is a practical hazard at large hydropower dams, so cheap waveform-based indicators that flag when a reservoir's seismicity is becoming induced are valuable for monitoring and early warning.

Fu et al. (2024) studied the Xiangjiaba (XJB) hydropower reservoir on the Jinsha River (upper Yangtze) in southwestern China, using M1.0+ earthquakes recorded by about 20 regional seismic stations from 2010 to 2015, spanning three impoundment periods. For each event they computed, from a 20 s window starting at the P-wave onset (the P wave is the first-arriving compressive seismic wave), the power spectrum $S(f)$ by Welch's method — an averaged-periodogram technique for estimating spectra with reduced noise. From each spectrum they extracted two parameters: the peak frequency $f_{p}$, the frequency of maximum spectral amplitude, and the shape factor $\Omega$, a dimensionless descriptor of spectral shape built from spectral moments over the 2–14 Hz analysis band:

$\Omega=\sqrt{1-\frac{m_{1}^{2}}{m_{0}m_{2}}},\qquad m_{i}=\int_{f_{1}}^{f_{2}}S(f)\,f^{i}\,df,$

with $f_{1}=2$ Hz and $f_{2}=14$ Hz. The shape factor was imported from volcanic seismology, where Galluzzo et al. (2020) classified volcanic event types from statistical moments of the power spectrum, and it echoes laboratory acoustic-emission work (acoustic emission, AE, is the high-frequency elastic radiation emitted by cracking rock specimens), in which spectral and dominant-frequency parameters track the fracture mode of water-bearing rock (e.g., Zhu et al. 2022).

Individually, the mean $f_{p}$ and $\Omega$ stayed roughly stable as reservoir water levels varied. Their ratio $k=\Omega/f_{p}$ behaved differently: before impoundment almost no events had $k$ above 0.25, a few appeared after the first impoundment, and after the second impoundment the number of events with $k>0.25$ increased pronouncedly — the observation the authors read as a candidate spectral precursor of RIS. They also documented strong site effects ($f_{p}$ varies with event azimuth, $\Omega$ with epicentral distance), mitigated only by selecting stations within 100 km (six such stations were used to display the joint distributions) and spatially/temporally averaging, and they showed that widening the analysis band from 2–14 Hz to 1–40 Hz shifts the critical $k$ value from about 0.25 to 0.37. The peak frequency has a qualitative physical reading through the standard corner-frequency relation of source spectroscopy (the corner frequency is where the source spectrum rolls off; it scales inversely with source size), but the shape factor $\Omega$ has no quantitative physical model at regional scale, and no causal link between elevated $k$ and specific RIS mechanisms has been demonstrated. An internal inconsistency worth noting: the paper's Discussion states the 2–14 Hz threshold as 0.15, while its Results and the Figure 6 caption use 0.25. Candidate mechanisms invoked for XJB seismicity include karst collapse (collapse of cavities dissolved in limestone), pore-pressure diffusion, and fault slip; the standard tools for adjudicating them are moment-tensor inversion (recovering the equivalent force system of a source from waveforms, distinguishing shear from tensile failure), high-precision relocation, and pore-pressure modeling.

Problem Statement

The problem, posed by Fu et al. (2024, Water 16:2217) in their own Discussion and Conclusions, is to establish whether the spectral ratio $k=\Omega/f_{p}$ is a robust and transferable precursor indicator of reservoir-induced seismicity — to turn a single-reservoir, single-processing-chain empirical observation into a validated (or refuted) monitoring metric. The following requested facets jointly serve that one objective:

(1) Transferability: test the indicator on at least one independent reservoir dataset with a different station network, re-estimating (not assuming) the threshold, and determine which processing choices carry over — specifying the independent dataset, the processing choices, and the decision rule. (2) Robustness: quantify the sensitivity of $k$ and of its threshold to the bandpass, power-spectrum-estimation, and P-window parameters, with uncertainty quantification, resolving the band-dependence already documented by Fu et al. (2024) (0.37 at 1–40 Hz versus the 2–14 Hz threshold, reported as 0.25 in the Results and 0.15 in the Discussion) — specifying the parameters varied and the uncertainty quantification. (3) Site and propagation effects: provide a standardized correction — or a demonstrated adequate mitigation — for azimuthal and distance-dependent site amplification across heterogeneous networks, beyond the current station-selection-plus-averaging heuristic — specifying the correction and the tolerance to which it removes the azimuthal and distance dependence, or bounds it within the measurement uncertainty. (4) Physical interpretation: either give a quantitative physical model linking $\Omega$ (and hence $k$) to source properties such as rupture mode or fluid content at regional scale, or show that the observed $\Omega$ changes are explainable without new source physics; a quantitative physical model must relate $\Omega$ (and hence $k$) to measurable source or path parameters and make at least one testable prediction. (5) Mechanistic validation: use the threshold to select candidate RIS events and test the proposed causal associations with specific mechanisms (karst collapse, pore-pressure diffusion, fault slip) through source studies — specifying the source-study inputs and the decision rule.

The overall question is whether, after these tests, $k$ can be endorsed as a physically grounded, cross-reservoir precursor and early-warning statistic for RIS — or is shown not to generalize.

References

1. Fu, Ziguo; Chen, Fei; Deng, Jianhui; Zhao, Siyuan; Dai, Shigui; Zhu, Jun (2024). A Spectral Precursor Indicative of Artificial Water Reservoir-Induced Seismicity: Observations from the Xiangjiaba Reservoir, Southwestern China. Water 16(16):2217. DOI 10.3390/w16162217. https://doi.org/10.3390/w16162217
2. Galluzzo, Danilo; Nardone, Lucia; La Rocca, Mario; Esposito, Antonietta M.; Manzo, Roberto; Di Maio, Rosa (2020). Statistical moments of power spectrum: a fast tool for the classification of seismic events recorded on volcanoes. Advances in Geosciences 52:67–74. DOI 10.5194/adgeo-52-67-2020. https://doi.org/10.5194/adgeo-52-67-2020
3. Zhu, Jun; Deng, Jianhui; Chen, Fei; Wang, Fei (2022). Failure analysis of water-bearing rock under direct tension using acoustic emission. Engineering Geology 299:106541. DOI 10.1016/j.enggeo.2022.106541. https://doi.org/10.1016/j.enggeo.2022.106541
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