How strong can an earthquake be in measurement by the Richter scale in comparison to a weaker earthquake?

Question

I've seen that the Richter scale measures the strength of any earthquake from 1 to 10 and I've also learned that a 2 is 32 (not 2) times as strong as a 1. What other comparisons of these numbers can help me measure how many times stronger an earthquake can be in comparison to a smaller number down to 1? Have a good time answering and use your knowledge!

Answer 1

I don't know anything much about this, but my reading of the Wikipedia page is:

• "How much stronger" can mean at least two things. In an earthquake, the ground moves back and forth (or up and down) and you can measure how far it moves. (I suppose this is what a seismometer does.) Or you can measure how much energy is released by the movement. (I guess they don't measure the energy directly, but they have some argument from physics that relates the energy release to the size of the movements.)
• The Richter intensity scale is based on how far the ground moves: Each increase of 1 in the Richter scale means the ground moves 10 times as far. The ground moves 10 times as far in a Richter scale 2 earthquake as it does in a Richter scale 1 earthquake, and 10 times as far in a Richter scale 8 earthquake as it does in a Richter scale 7 earthquake.
• The energy released is closely related to the distance the ground moves. (More energy is required to move the ground farther.) This relationship is such that each increase of 1 in the Richter scale means that 31.6 times as much energy is released. 31.6 times as much energy is released in a Richter scale 2 earthquake than in a Richter scale 1 earthquake, and 31.6 times as much energy is released in a Richter scale 8 earthquake than in a Richter scale 7 earthquake.

To compare two earthquakes, with Richter magnitudes $r_1$ and $r_2$, one then has that the movements of the $r_1$ earthquake are $$10^{(r_1-r_2)}$$ times as large as the movements of the second earthquake, and the $r-1$ earthquake releases $$31.6^{(r_1-r_2)}$$ times as much energy.

So for example, we compare the 2007 Sumatra earthquake (Richter 8.5) and the 2007 Antofagasta earthquake (Richter 7.5) we have that the ground movements were $10^{(8.5-7.5)} = 10$ times greater in the Sumatra earthquake, and the energy release was 31.6 times as large. According to Wikipedia, the energy released was 360 PJ (petajoules) and 11 PJ, respectively, and the indeed $31.6\cdot 11 \approx 360$.

One thing to notice here is that you can pick any energy ratio or movement size ratio and translate it into a constant difference in Richter intensities. For instance, it is always the case that if one earthquake releases twice as much energy as another, it will have a Richter intensity that is greater by $0.2$, and if it has ground movements twice as large as another earthquakes, it will have a Richter intensity that is greater by $0.3$.