In our previous post, we described the use of decibels as a unit of ‘sound level’, and talked of it as a logarithmic scale, one in which equal increases represent equal multiplications of the quantity represented. In this post, we will look at another logarithmic scale, the Richter scale for earthquake magnitudes (seismologists may be disgusted at our use of the term ‘Richter scale’, but (a) we’ll come on to that, and (b) that’s what the media and general public routinely call it).
Here’s a graphic showing four earthquakes from the last 60 years. The magnitudes of the earthquakes range from 5.7 to 9.1. If you aren’t familiar with logarithmic scales, you won’t realise the difference contained in those numbers. You will be in 700 words time.
What does the Richter scale measure?
When measuring earthquakes, it would be useful to know either how much energy is released in the event, or how large the vibrations are (or both!). However, the nature of earthquakes means that it is not straightforward, to say the least, to measure either of those.
What we can measure is the size of the trace on a seismograph (how big the wiggle is on those graphs of seismic activity).
Seismograph photo by Flickr contributor Matt Katzenberger
for Creative Commons http://bit.ly/2y1m4zI
And so Charles Richter developed a scale based on that. He developed a scale that:
- Is logarithmic, so that each increase of one on the scale represents the same multiplication in terms of energy release or wave amplitude
- Has its zero at the limit of human perception (this is one of several similarities to the decibel scale in acoustics)
- Refers to a particular seismometer common at the time (and not to other seismometers)
Then the definition of the Richter magnitude was ’the logarithm of the maximum trace amplitude on a [specified type of] seismograph, expressed in microns, a distance of 100 km from the event’.
Now, most of the time, your seismometer is not 100 km away from the earthquake. And the closer you are, the larger the vibrations, generally. So you need distance curves that relate your seismometer trace at your actual distance to the trace size you would have measured if you had been 100 km away. But that’s OK because lots of seismologists spent a lot of time creating those graphs…
Getting a feel for the numbers
So, what does the definition of Richter magnitude mean in practice. Well, the logarithmic nature of the scale means that:
- Adding 1 to the (Richter) magnitude represents 10 times the size of trace on the seismograph
- Adding 2 to the magnitude represents 100 times the amplitude on the seismograph
In turn, the energy release is related to the (3/2)th power of the maximum amplitude. So:
- Adding 1 to the magnitude represents 103/2=31.6 times the energy release
- Adding 2 to the magnitude represents 1003/2=1000 times the energy release
That’s worth reiterating – a difference of 2 in magnitude is a difference of 1000 times the energy release. Another fact is that a doubling of energy release is represented by a shift of just 0.2 in the magnitude scale.
So, small differences in the scale can mean enormous differences in energy release. This is why logarithmic scales are useful – they are good for expressing quantities that can vary by enormous amounts. I’ve read that a magnitude 15 quake (‘only’ 6 above the Indian ocean event) would destroy the Earth! But if you weren’t familiar with logarithmic scales, it might not sound that much worse than a magnitude 9 event.
How do earthquakes compare?
The following table recaps the information in the diagram at the top of the post:
| Earthquake | Magnitude |
|---|---|
| Indian Ocean, 2004 | 9.1 |
| San Francisco, 1906 | 7.8 |
| Tangshan, 1976 | 7.6 |
| Agadir, 1960 | 5.7 |
Source: https://en.wikipedia.org/wiki/Lists_of_earthquakes
With our new-found understand of the scale, we can say that the San Francisco earthquake had double the energy release of the Tangshan event. And since 7.8 – 5.7 = 2.1, the energy release of San Francisco was over 1,000 times the energy of Agadir.
The Indian Ocean event was enormous. It’s energy release was 125,000 times that of Agadir, which itself was a destructive event with thousands of casualties. It’s hard to comprehend the scale of that.
In the UK, the largest recent earthquake, in 2008, had magnitude 5.2. I remember it – a picture fell off my wall (which probably says as much about my picture hanging skills as about the earthquake).
Other scales
There are several other magnitude scales in widespread use, due to shortcomings of the original Richter scale. One such shortcoming is that the seismometer specified by the Richter scale saturates somewhere around 7 or 8 on the scale. (‘Saturation’ means that further increases in earthquake magnitude do not produce a larger output from the seismometer).
Possibly the most common scale in use is the moment magnitude scale (MW), which is capable of assigning magnitudes above 8. You will hear the media describe ‘9.1 on the Richter scale’, which is technically meaningless, but for most people it isn’t a massive problem because the other scales have been devised so that the numbers coincide with the Richter scale.
Postscript – in recognition of Beno Gutenberg
And note that Richter didn’t name the scale after himself – at first, in the 1930s, he simply called it the ‘magnitude scale’. Then in the 1950s, he and Beno Gutenberg renamed it the Local Magnitude scale (ML) to differentiate it from other scales they had devised. Others insisted on calling it the ‘Richter magnitude’. This is a great example of how naming something can immortalise one person and leave another unrecognised (at least to the public at large). Have you heard of Beno Gutenberg? He played an enormous role in the development of seismology, but his name’s not on the scale…