Identifying the occurrence time of an impending mainshock: A very recent case

This paper reviews a procedure for identifying the occurrence time of an impending mainshock by analyzing seismicity in natural time following Seismic Electric Signals (SES) activity, demonstrating its application to a 2014 Mw5.4 earthquake in Greece and discussing a related 2019 event.

The Gist

Imagine the Earth's crust isn't just a solid rock, but a giant, tense rubber band being slowly stretched. Most of the time, it just creaks a little (small earthquakes). But sometimes, right before it snaps (a big earthquake), it starts to hum with a specific, strange electrical signal.

This paper is like a detective story written by scientists who have learned to listen to that hum. Here is the story in simple terms:

1. The "Earthquake Hum" (SES)

The scientists use special antennas (called geoelectrical stations) to listen to the Earth. They are looking for something called Seismic Electric Signals (SES).

• The Analogy: Think of the Earth as a giant pressure cooker. Before the lid blows off (the big earthquake), steam starts to hiss out in a very specific pattern. The SES is that "hiss."
• The Clue: When they hear this hiss, they know a big earthquake is coming, but they don't know exactly when. It's like hearing a storm approaching; you know rain is coming, but you don't know if it will start in 10 minutes or 10 hours.

2. The "Natural Time" Clock

To figure out when the storm will hit, the scientists use a special stopwatch called Natural Time.

• The Analogy: Imagine you are watching a line of people waiting to get into a concert. In normal time, you just watch the clock. But in "Natural Time," you only count the people as they arrive.
  • Person 1 arrives (1/100th of the crowd).
  • Person 2 arrives (2/100th of the crowd).
  • ...and so on.
• The Magic Number: The scientists track a specific number called $\kappa_1$ (kappa-one). Think of this as a "tension meter" for the rubber band.
  • When the tension is low, the meter reads all over the place.
  • But as the rubber band gets ready to snap, the meter settles down and hits a very specific number: 0.070.
  • The Rule: When the "tension meter" hits 0.070, the rubber band is about to snap. The big earthquake is coming very soon (usually within a few days).

3. The Real-Life Test: The 2014 Athens Earthquake

The paper tells the story of a specific event to prove their method works:

• The Warning: On July 27, 2014, the station in Keratea (near Athens) heard the "hiss" (the SES). They knew a big earthquake was coming.
• The Wait: For months, they watched the "tension meter" ($\kappa_1$) using their Natural Time clock. It was bouncing around, not quite there yet.
• The Signal: On the morning of November 15, 2014, the meter finally hit 0.070. The scientists realized: "The system is critical! The big one is coming in a few days!"
• The Result: Just two days later, on November 17, 2014, a massive earthquake (Magnitude 5.4) hit. It was the strongest in that area in over 50 years and was felt strongly in Athens.
• The Success: They didn't just guess; they identified the exact moment the system reached the "breaking point."

4. Why This Matters

Usually, predicting earthquakes is like trying to guess when a glass will shatter just by looking at it. It's almost impossible.

• The Breakthrough: This method combines two things:
  1. The Early Warning: The "hiss" (SES) tells us where and that a big one is coming.
  2. The Timing: The "tension meter" (Natural Time analysis) tells us when it will happen.

5. The Future

The paper also mentions that they have heard this "hiss" again in recent years (2020, 2021, 2022, and even up to 2026 in their notes). They are constantly watching the "tension meter" to see if it hits 0.070 again.

In a nutshell:
The Earth gives us a warning sound (SES) before a big earthquake. By analyzing the rhythm of smaller earthquakes that happen after that sound, the scientists can calculate a "tension score." When that score hits 0.070, it's a countdown timer saying, "Get ready, the big one is coming in a few days." This paper shows they successfully used this to predict a major earthquake in Greece.

Technical Summary

1. Problem Statement

The primary challenge addressed in this paper is the precise identification of the occurrence time of an impending mainshock (major earthquake) within a short time window (days to a week). While the existence of precursory Seismic Electric Signals (SES) has been established, determining exactly when the system will reach a critical point (failure) remains difficult. The authors aim to demonstrate a robust procedure that combines SES detection with Natural Time Analysis to pinpoint the timing of a mainshock with high accuracy, specifically focusing on a rare, strong earthquake in Greece that had not occurred in that specific region for over 50 years.

2. Methodology

The paper employs a two-stage methodology combining geoelectrical monitoring and statistical physics-based time series analysis:

A. Seismic Electric Signals (SES) Detection

• Precursor Identification: The process begins with the recording of an SES activity. These are transient changes in the Earth's electric field emitted when stress in the focal area reaches a critical value.
• Candidate Area Determination: Upon recording an SES, the potential epicentral area is estimated using:
  • Selectivity Maps: Pre-determined maps showing which seismic areas historically trigger signals at specific geoelectrical stations (e.g., Keratea/KER).
  • Amplitude Relations: The magnitude ($M$) is estimated using the relation $\log_{10}(\Delta V / L) \approx 0.3M + \text{const}$, where $\Delta V$ is the anomalous potential difference and $L$ is the dipole length.

B. Natural Time Analysis (NTA)

Once the candidate area is defined, the seismicity within that area is analyzed using Natural Time ($\chi$), a time scale defined by the sequence of events rather than chronological time.

• Natural Time Index: For the $k$-th earthquake in a series of $N$ events, $\chi_k = k/N$.
• Order Parameter ($\kappa_1$): The authors analyze the variance of natural time weighted by the normalized energy ($p_k$) of each event. The order parameter is defined as:
  $$\kappa_1 = \langle \chi^2 \rangle - \langle \chi \rangle^2 = \sum_{k=1}^{N} p_k (\chi_k)^2 - \left( \sum_{k=1}^{N} p_k \chi_k \right)^2$$
  where $p_k = Q_k / \sum Q_n$ and $Q_k \propto 10^{1.5M_k}$.
• Criticality Criterion: The system is considered to be approaching the critical point (mainshock) when:
  1. The value of $\kappa_1$ approaches 0.070.
  2. The probability distribution $Prob(\kappa_1)$ exhibits a maximum at $\kappa_1 = 0.070$.
  3. This behavior exhibits magnitude threshold invariance (the result holds true regardless of the minimum magnitude threshold $M_{thres}$ used in the calculation).

3. Key Contributions

• Validation of Timing Prediction: The paper provides a characteristic case study confirming that the NTA procedure can identify the occurrence time of a mainshock within a window of less than a week.
• Rare Event Analysis: It documents the prediction of an $M_w$ 5.4 earthquake in Greece (November 2014), which was the strongest in that specific area since 1965, demonstrating the method's efficacy even for rare, high-stress events.
• Extended Case Studies: The authors extend their analysis to multiple subsequent SES activities (2019–2026), showing consistent results where $\kappa_1 = 0.070$ is reached shortly before various earthquakes (ranging from $M_L$ 2.1 to $M_L$ 4.5).
• Note on 2019 Parnitha Earthquake: A specific discussion is added regarding the $M_w$ 5.3 earthquake on July 19, 2019, explaining how different SES component ratios led to different selectivity maps and epicenters compared to the 2014 event.

4. Results

The study presents several specific findings:

• The November 2014 Case:

  • SES Recording: July 27, 2014, at Keratea (KER) station.
  • Prediction: Natural time analysis of seismicity in the candidate area showed $Prob(\kappa_1)$ maximizing at $\kappa_1 = 0.070$ on November 15, 2014 (at 01:01 UTC), following a small $M_L$ 2.8 earthquake.
  • Mainshock: The predicted $M_w$ 5.4 mainshock occurred on November 17, 2014 (23:05 UTC), approximately 46 hours after the critical point was identified.
  • Invariance: The result was confirmed across multiple magnitude thresholds ($M_{thres}$ from 1.8 to 2.8).

• Subsequent Cases (2020–2026):

  • The authors report a series of SES activities recorded at KER (March 2020, Dec 2020, June 2021, Nov 2021) and ASS (Jan 2023).
  • In each case, the condition $\kappa_1 = 0.070$ was met shortly before the occurrence of subsequent earthquakes (e.g., $M_L$ 3.3 in Feb 2022, $M_L$ 4.5 in Dec 2021).
  • New Observation (2023): The paper notes a "first-time" observation where the plot $Prob(\kappa_1)$ vs. $\kappa_1$ was maximized at 0.070 for multiple magnitude thresholds simultaneously (e.g., July 22, 2023, and August 2023), strongly indicating an imminent approach to the critical point.

• Lead Time: The study suggests that while SES activities can precede earthquakes by months (up to ~9 months for very large events), the Natural Time Analysis refines the prediction to a window of a few days to one week.

5. Significance

• Operational Earthquake Forecasting: The paper validates a practical, physics-based procedure for narrowing down the time window for major earthquakes, moving beyond simple probabilistic forecasting to specific timing identification.
• Critical Phenomena Theory: It reinforces the theoretical framework that earthquakes are non-equilibrium critical phenomena, where the system evolves toward a critical state characterized by specific fluctuations in the order parameter ($\kappa_1$).
• Reliability: By demonstrating magnitude threshold invariance and consistency across different years and stations (KER, ASS), the authors argue for the robustness of the VAN method (Seismic Electric Signals) combined with Natural Time Analysis.
• Future Applications: The authors suggest that combining this method with neural networks (trained on historical data) could further improve the prediction of both magnitude and occurrence time.

In conclusion, the paper presents a compelling case that the combination of SES detection and Natural Time Analysis provides a reliable mechanism for identifying the critical point of a seismic system, thereby enabling the prediction of mainshock occurrence times with a lead time of approximately one week.