What's in a Magnitude

As mentioned some days ago, due to the Tohoku Earthquake, a lot of people visited my earthquake mashup. The number of visits have decreased since then, but levelled off at a significant higher level than before:



During this time, one (and only one...) person contacted me about the mashup. Andy Adamson noticed, that in the earthquake swarms that flooded the area off the coast of Japan, it is hard to distinguish the really big quakes from the somewhat smaller ones:



He suggested to size the icons not according to their magnitudes, but to their actual strength. Andy works for the Gemini Observatory, which operates telescopes in Chile and Hawaii. I wonder how many long exposure images get ruined by earthquakes in those locations...

And indeed, the magnitude scale is logarithmic, so what an increase by one magnitude really means is not easy to grasp. In our daily life, we are used to linear scales, and only very seldom we find logarithmic ones. I remembered something like "an increase of one magnitude means a tenfold increase of released energy". I started to calculate corresponding icon sizes and soon realized, that it would be impossible to cover the range of all earthquakes from magnitude 2.5 to 9.0 and above this way. And only then I actually looked up the real figures: An increase of one magnitude means an increase of about 32 times the energy! 10 to the power of 1.5, to be precise. It would be impossible to visualize one single magnitude this way: Everything weaker would be represented by icons of less than a pixel, everything stronger by icons that are larger than the average monitor resolution (even by todays HD standards).

So as a compromise, I settled for an increase of a factor of 10 instead of 32, and with this figure, it was possible to come up with somewhat reasonable sizes for icons:



Magnitude 5 is barely visible, the big circles in the image above are about magnitude 6.5. Just to give you an idea, how this scale continues: This is the icon for a magnitude 8.0 quake, and this for a magnitude 9.0 one, i.e. the one that hit Japan.

As everything below magnitude 5.0 is too small to be seen, instead of adding some sort of filter to my mashup, I simply used the USGS feed that only contains earthquakes of this magnitude and above. So if you select the "USGS 5+" feed in the mashup now, you get (nearly) linear scaled icons, representing the energy released by the corresponding earthquake.