We sometimes hear news reports about a “once-in-a-century” earthquake in an active region or mentions of its “return period”. These terms often cause confusion: does “once-in-a-century” actually mean that an earthquake only happens once every hundred years? To explain the true meaning of “return period” and “probability”, let’s begin with a simple game of coin flipping.

Imagine you are flipping a coin with a friend. Let’s use a one-dollar coin. One side with the Bauhinia flower is “heads” and the other side with the number is “tails”. In an ideal situation, the probabilities of flipping heads or tails are both half, i.e. 50%. Therefore, the return period for flipping heads is two tosses. In other words, on average, you will get one “heads” every two flips.

But what could happen if you flip the coin twice?

Most of us might have experienced a similar game that, in most cases, you will get “heads” at least once. However, it is not hard to imagine that sometimes you indeed will not get “heads” at all in two tries. In an ideal situation where each flip is independent and does not affect the next, the probability of not getting “heads” in two flips is one in four, or 25%.

“Return period” is one way of expressing probability. The higher the probability, the shorter the return period; the lower the probability, the longer the return period. However, a “return period” does not mean an event is guaranteed to happen within that fixed time period, nor does it mean that the event will not happen more than once during that period. Instead, it should be understood as an “average” expected value of the time period.

Now, let’s apply this concept to earthquakes.

An earthquake return period is an estimate of the average time interval between earthquakes of a specific magnitude in a particular region. Because the occurrence of earthquakes is random, current technology still cannot precisely predict when, where, or how strong an earthquake will be. To estimate the probability of a specific magnitude earthquake occurring in a given area, we look at historical seismic data spanning decades or centuries in that region, count the number of occurrences of that specific magnitude, and calculate the average time interval. Because seismic activity itself is highly variable and historical records may be incomplete, we can also fit historical seismic data into statistical models to estimate the earthquake return period.

Major earthquakes are the result of the accumulation and release of energy along faults. Due to the relative motion of tectonic plates, stress builds up in the slower-moving sections of the Earth's crust. When this accumulated stress exceeds the limit of friction between the two plates, the stored energy can be abruptly released, causing an earthquake. While the process of stress accumulation and release is cyclical, earthquake cycles are not entirely regular.

Furthermore, an earthquake can sometimes trigger the release of accumulated stress in the vicinity, serving as a precursor to another earthquake event. Therefore, whether a major earthquake has occurred can influence the likelihood of another earthquake happening shortly after, in statistics, we say that earthquake events are not independent. Let’s take an example, say the chance of a magnitude 6 earthquake occurring in a certain region in a year is 1%. We would call this event has a return period of 100 years, or a “once-in-a-century” event. If we assume these earthquakes in this region are independent events (which is not actually the case, but can serve to illustrate the concept), the probability of no earthquake occurring within a century is about 37% (see Note below). This demonstrates that a “once-in-a-century” event does not mean the event must happen once within 100 years; the return period merely expresses the probability of occurrence. Commonly used return periods in seismology include approximately 475 years (a 10% probability of exceedance in 50 years) and around 2,475 years (a 2% probability of exceedance in 50 years).

Hong Kong is located within the Eurasian Plate, and is located rather far away from the nearest plate boundary. According to the study of earthquake hazards in Hong Kong by the Geotechnical Engineering Office of the Civil Engineering and Development Department, there are no obvious signs of recent fault activity in Hong Kong or its offshore, meaning the chance of a major earthquake is relatively low. However, people may travel to or work in places with higher seismic activity, it is essential to acquire disaster preparedness and prevention knowledge and know how to respond to hazards.

Note: Based on the multiplication rule for the probability of independent events, the detailed calculation is given as follows: