use faux pas (killtacular) wrote,
use faux pas
killtacular

Why is the Richter scale a log scale? Or more precisely, cares about the Richter scale?

Can anyone tell me this? Log scales make sense when differences at the "normally" low end count more than differences at the "normally" high end. For example, if you are comparing ratios of substances in a mixture, then the difference between a ratio of 4 to 1 and a ratio of 3 to 1 for substance x as compared to substance y is obviously equivalent to a difference of a ratio of 1 to 4 and 1 to 3 for substance y as compared to substance x. But representing that by the straight difference between fractions doesn't represent that similarity (this is why solving the von Kries-style version of the water-wine paradox for the principle of indifference with the log uniform measure makes sense, but, whatever). So you should use a log scale. Similarly, if the "natural" way some quantity behaves that you are interested in is exponential, then again, a log scale makes sense (sometimes). Or I suppose if you want to squeeze big differences onto a graph, a log scale might also make sense. And I'm sure I'm forgetting others.

But what does any of that have to do with earthquakes? Why have the most salient representation of the physical force of an earthquake be represented by a log10 scale like the Richter scale? Why not focus on the destructive power itself? Isn't that more important for general news functions? Can't we leave the Richter scale to the geologists? What is wrong with taking the shaking amplitude, raise it to the power of 3/2 (which is a rough and ready way of correlating the energy released by the quake, and - at least according to Wikipedia! - its destructive power), and call that the magnitude of the quake? Am I totally missing something? If not, it seems a lot more accurate to describe the recent Japan earthquake as something pretty radically different in kind than, say, the most recent California earthquakes. I mean, this earthquake was much, much more like the historic Lisbon one than it was contemporary Japanese or American earthquakes. Not in terms of human consequences, but more "wrath of god" consequences (note, this earthquake was much, much bigger than Krakatoa, the largest hydrogen bomb, and the 1906 San Fran Earthquake, at least according to Wikipedia). Am I being stupid or is Wikipedia failing me here?
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