How Much Temporal Information Does Earthquake Declustering Remove? An Entropy-Based Analysis of the Türkiye Catalogue

Earthquakes rarely happen in isolation. When one tremor strikes, it often triggers a chain reaction: a smaller foreshock might precede a main event, which is then followed by a swarm of aftershocks that can last for weeks or even years. To scientists trying to understand the Earth's deep-seated stress patterns, these clusters act like static on a radio, drowning out the steady, independent background noise of the planet's natural seismic activity. To get a clear signal, researchers use a process called declustering, which attempts to strip away these dependent events and leave only the "main shocks" that represent the true, underlying rhythm of the region. However, a lingering question has always been whether this cleaning process removes too much of the story, or if it leaves behind a predictable pattern that could help us understand how earthquakes behave over time.

A new study focusing on Turkey, a nation sitting atop some of the world's most active fault lines, tackles this question by measuring how much information is lost when we try to separate these seismic events. The researcher, Hakan Karaca, did not look for a crystal ball to predict exactly when the next quake will strike; such precise prediction remains beyond current science. Instead, he asked a more fundamental question: if we know how active the Earth was last month, does that tell us anything about how active it will be next month? To answer this, he applied three different, widely used methods for declustering a massive database of Turkish earthquakes spanning fifty years, from 1976 to 2025. He then used a mathematical concept known as entropy, which essentially measures how much uncertainty exists in a system, to see how much order remained in the data after the cleaning process.

The study began with a single, unified catalogue of nearly 40,000 earthquakes. The researcher then ran this data through three different filters. The first two methods, known as Gardner-Knopoff and Deniz-Yücemen, use fixed time and distance windows to decide which events are part of a cluster and which are independent. The third method, Reasenberg, uses a more complex, interaction-based approach where clusters grow and evolve as events link together. The results of this filtering were starkly different. The first two methods were aggressive, removing about 70 to 73 percent of the recorded events as dependent clusters, leaving behind roughly 11,000 events. The Reasenberg method was far more conservative, removing only about 32 percent of the events and retaining nearly 27,000. This difference in how many events were kept provided the perfect setup to test whether the way we clean the data changes the story the data tells.

When the researcher analyzed the monthly counts of these remaining earthquakes, he converted the raw numbers into four simple states: low, moderately low, moderately high, and high activity. He then looked at the sequence of these states month by month to see if knowing the state of one month reduced the uncertainty about the next. The results showed that the choice of cleaning method completely changed the outcome. For the two methods that removed the most events, the connection between one month and the next vanished. The data looked essentially random; knowing that last month was quiet told you nothing about whether this month would be quiet or loud. The statistical measures confirmed that these methods had stripped away nearly all detectable short-term dependence, leaving a sequence that behaved like a coin toss.

In contrast, the data processed by the Reasenberg method told a different story. Because this method kept more of the clustered events, the resulting sequence retained a significant amount of temporal organization. In the early years of the record and again in the most recent decades, the data showed a clear pattern where the activity level of one month provided real information about the next. The uncertainty about the future was measurably reduced when the present was known. This did not mean that the earthquakes were predictable in a deterministic sense, but it did mean that the "noise" of the clusters had not been fully removed, leaving behind a structure that the other two methods had successfully erased.

The study further broke the fifty-year timeline into three distinct periods to see if these patterns held up over time. The two aggressive methods consistently showed no significant connection between months, regardless of the era. The Reasenberg method, however, showed strong, statistically significant links in the first and final periods, while the middle period appeared more random. This suggests that the apparent predictability of seismic activity is not a fixed property of the Earth itself, but rather a feature that depends heavily on how the data is prepared. The researcher found that the more conservative approach left behind a "memory" of past activity, while the more aggressive approaches wiped that memory clean.

Ultimately, the paper demonstrates that the answer to how much temporal information earthquake declustering removes depends entirely on the tool used to do the removing. There is no single, objective truth about the remaining order in the data; there is only the order that survives the specific rules of the algorithm chosen. The findings suggest that if scientists use methods that aggressively strip away clusters, they will see a world of independent, unpredictable events. If they use methods that are more lenient, they will see a world with lingering patterns and short-term dependencies. This does not mean one method is right and the other wrong, but it does mean that any conclusion about the predictability of earthquakes must be understood in the context of the data cleaning process that produced it. The study serves as a reminder that the way we organize our observations can fundamentally alter the patterns we see in the natural world.