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

[killtacular]

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

Comments

[easwaran]

One of the other big uses of log scales is because of human perceptual abilities - a change of 10 deciBels sounds about the same, no matter what volume it's already at (I think). Perhaps there's something similar going on with earthquakes - humans are no better or worse at telling a 3.5 from a 4.0 by feeling the shaking than they are at telling a 4.0 from a 4.5 (perhaps). Of course, there's added complications given by distance to epicenter - I think I felt a 2.3 that was actually inside Berkeley, several in the 3.0 to 3.5 range in nearby towns, and a 5.4 that was several dozen miles away, and the only noticeable difference was that the first one was more of a single clean jolt while the others involved some shaking. Rather than human perception, it might also relate to damage - maybe it takes 10 times as much energy to damage things twice as much, no matter what energy you're already talking about

[killtacular]

Ya, the first two those explanations make sense. Again, I'm wondering if they are true! :). In any case, the first explanation doesn't really amount to a justification for using the Richter scale to report on earthquakes (other than in a "it was really scary for people around here" type of sense). The second explanation definitely does.

It could also be the frequency of occurrence thing, but again, I don't really see how that is amazingly relevant. I think I kinda see your point about using a doubly logarithmic scale, although, of course, that could be justified if (which, again, I am completely ignorant of), there is some sort of critical point at the high end that does, in fact, really magnify the scale of destruction (this does not seem intuitively implausible).

Finally, you are completely right that this cosmically unfair in the "god is a bastard" sense.

[easwaran]

I recently looked at the wikipedia pages about the Richter scale and the moment magnitude scale and was surprised to learn that for earthquakes above 7.0 they can't really use the Richter scale. (It was designed for Southern California earthquakes, and those almost never go above 7.0.) Fortunately, the two scales are calibrated so that they give pretty similar values in the range where both make sense. But after reading up on it, it really seems to me that they aren't measuring anything that real and important at all. They're approximating the total amount of seismic energy released, but that is extremely difficult to measure (was there additional energy released on side-faults or underground that either didn't register, or was somehow dissipated as heat?) and it doesn't really tell you about what we normally care about, which is the damage and shaking. I'm starting to think that what we really care about is the Mercalli intensity scale, which doesn't sound like it's very calibrated at all, but is pretty much just subjective.

[killtacular]

Ya, that was kinda the impression I was getting.

But I had not heard of the Mercalli intensity scale you mention. It does seem fairly subjective.

That doesn't mean it fails! But it does mean that there seems to be a good reason to get rid of the Richter scale (at least for journalism purposes) and figure out a "destruction" scale or something, which is what we care about non-qua geologists.

[airstrip]

A brief search of Wikipedia answers the question: Richter designed the scale after the stellar magnitude scale, which is logarithmic. Norman Pogson defined SMS scale logarithmically, believing that this best modeled human vision response (it doesn't, vision response is a power law).

Here's your jump list: Richter scale (Wiki) --> stellar magnitude (Wiki) --> fn. 42 (Wiki) --> abstract explains the situation.

[airstrip]

Here's my bet: every time you see a log scale being used, you can trace its development back to the Weber-Fechner law. It will either be modeled from it directly, or refer to something which is ultimately based on it either through inspiration or derivation.

[killtacular]

Ok, that seems to answer my question in something somewhat analogous to the "context of discovery" sense, but not in the "context of justification sense." (NOTE: not really analogous at all! But hopefully it makes sense).

[airstrip]

I'm not sure what the problem is. Scales are arbitrary and this one was justified at the time by the Weber-Fechner laws.