Earthquake Early-Warning, the GR Law, P-waves, and S-waves

Out of the handful of catastrophic acts of God we experience from time to time, earthquakes are arguably the most terrifying. There are several reasons for this. They cannot be accurately predicted or “controlled”, and despite our best efforts in earthquake engineering to make earthquake-resistant buildings, we don’t stand a chance against a large enough earthquake whose epicenter is close enough.

The Gutenberg-Richter Law (GR Law) Broken Down

That’s the bad news. The good news is that earthquakes of catastrophic magnitude rarely happen. Going by the Gutenberg-Richter law, the number of earthquakes decrease exponentially as the magnitude increases. More specifically, the law describes the relationship between an earthquake’s magnitude and the total number of earthquakes in a given region over a given period of time with at least the same magnitude.

or

  • N is equal to the number of earthquakes M
  • a is a constant that equals the logarithm of the total number of events to base 10.


  • b is a constant that is typically equal to 1.0, although it can be as high as 2.5 or as low as 0.5, indicating a higher or lower proportion of smaller earthquakes to larger ones, respectively.
  • M equals the magnitude of the earthquake in question.

In a manner of speaking, it’s simply stating the obvious, in that the more earthquakes a given area has over a set period of time, the higher the chance of there being a big one. The law states that for every 10 earthquakes magnitude 4.0 and over, there are roughly 100 earthquakes magnitude 3.0 and over – and so on. However3 main earthquake fault types, although this law is based on empirical data and found to be quite consistent, it is by no means a method of accurate prediction.

It is simply a ball-park relationship that helps to give some general insight. This is the cornerstone for the “general predictions” seismologists sometimes make concerning high-seismic activity regions, such as “we can expect a mega-earthquake within the next 50 years” etc. They are usually careful to also mention that it could be significantly earlier or later.

One thing to remember about this exponential relationship, as good as it sounds, is that there are roughly half a million earthquakes recorded every year, 100,000 of which can be felt. Granted, 90% of these earthquakes occur within the infamous Ring of Fire, but we should remember that the regions most prone to high loss of life in such an event are those in which the people are least expecting it.

This “lack of expectation” is often reflected in the region’s building code. But as is now common knowledge, earthquake preparation starts with the building code. Earthquake engineering plays a significant role in constructing buildings and homes that can withstand moderate to large earthquakes without completely collapsing. The idea isn’t to construct a building that will come out unscathed, but to first and foremost ensure minimum human casualties.

Generally speaking, structures made of stone, insufficiently reinforced concrete, or earth-based materials such as adobe and sandbags, are most vulnerable to sudden and complete collapse. To add to this, these materials also have significant mass – when compared to materials like wood and composites – that will make escape and/or survival in such an event extremely unlikely. (See What makes a Structure Strong or Resistant to an Earthquake.)

Earthquake Early-Warning Systems – P-wave Vs. S-wave

Early-warning systems exploit the time-difference between the p-wave (primary wave) and the s-wave (secondary wave) of an earthquake. The p-wave travels considerably faster than the s-wave at an approximately 1.7:1 ratio. One can calculate the approximate distance of an earthquake (in kilometers) by multiplying the difference in seconds between the P and S wave by 8. Slight inconsistencies in this equation exist due to the nonuniform media the wave is passing through.

Although it’s nice to have an effective form of early-warning, we must understand that the amount of time between the first P-wave and the more damaging S-wave is dependent on the distance from the epicenter. The further the seismometer is from the epicenter, the longer the interval. Conversely, the closer it is to the epicenter, the shorter the interval. In other words, its effectiveness as an early-warning system decreases the closer the earthquake is to home – YIKES!

Here’s an interesting webpage that allows you to experiment with a P and S-wave displaying graphic, making the concept much easier to understand – Seismic Waves.


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