I don't think the above kind of analysis applies very well to quakes, for the following reasons:

- Energy release in a quake is proportional to length of fault rupture, which can be very large w.r.to the other relevant dimensions - for instance the great 1960 Chile earthquake had a rupture zone over 1000km long. For quakes this large, that also means it takes a significant time for the rupture to spread out from the original break location [the proverbial straw that broke the camel's back] in both directions along the fault, like a 2-way zipper. The resulting wavelength spectrum may thus be more determined by local fault-zone relaxation times than anything having to do with overall quake magnitude. [This also explains why local shaking amplitude scales typically far sublinearly with overall quake energy release.]

- On top of the above non-point-source aspect there may be a significant small-scale granular aspect, due to local asperities interacting with the propagating rupture, and all the vagaries of local fault geology and geography.

Any geologists around here?

[QUOTE=davieddy;117804]Calling Cambridge and its environs the UK's "Silicon Valley" is one thing.
Trying to compete with "Tornado Alley" is quite another. And as for
earthquakes, I don't think the English Channel is much competition
for San Andreas.

David:smile:

(St. Catz 1972)[/QUOTE]I never said the fault under the Channel was anything like as serious a cause of earthquakes as the SA fault. Quite the reverse.

However, Tornado Alley gets several hundred tornados per annum in an area which is perhaps a hundred times that of southern England. The latter gets 30 - 40 tornados esentially every year, and over a hundred every now and again.

Go dig out the records if you don't believe me.

Paul

[quote=ewmayer;117822]
Any geologists around here?[/quote]

I think we have enough variables as it is:lol:

David

[quote=ewmayer;117822]I don't think the above kind of analysis applies very well to quakes, for the following reasons:

- Energy release in a quake is proportional to length of fault rupture, which can be very large w.r.to the other relevant dimensions - for instance the great 1960 Chile earthquake had a rupture zone over 1000km long. For quakes this large, that also means it takes a significant time for the rupture to spread out from the original break location [the proverbial straw that broke the camel's back] in both directions along the fault, like a 2-way zipper. The resulting wavelength spectrum may thus be more determined by local fault-zone relaxation times than anything having to do with overall quake magnitude. [This also explains why local shaking amplitude scales typically far sublinearly with overall quake energy release.]

[/quote]

This line of argument would maintain that
"volume ~ L^3" was falsified by the example of a pencil.

When I said "picture an earthquake" I was expecting its
shape to remain the same when scaling by L. (I was
picturing a sphere of stressed rock not particularly close to the surface,
but the details shouldn't matter).

I was only trying to justify the genralization asserted in
Wikipedia as the reason for for "Richter = log32(energy)~log10(amplitude)+c".

But I do see that, since speed at which rupture propagates is
presumably comparable to wavespeed, the Huygen's Principle argument
is complicated.

David

Can I have some marks for ingenuity anyway? ;-)

Whatever the Chile quake of 1960 was deemed to be
on the Richter scale, I don't see how that value could be
particularly meaningful, for the reasons you stated.

David

Although we are in the "Lounge", I would like to point out that
we use Huygen's Principle to derive diffraction patterns, and that
these are intimately connected with Fourier analysis. So we are not
as "off topic" re prime searching as you might think.

[quote=xilman;117829]I never said the fault under the Channel was anything like as serious a cause of earthquakes as the SA fault. Quite the reverse.

However, Tornado Alley gets several hundred tornados per annum in an area which is perhaps a hundred times that of southern England. The latter gets 30 - 40 tornados esentially every year, and over a hundred every now and again.

Go dig out the records if you don't believe me.

Paul[/quote]

I didn't say you did say it.
Having lived in SE England for 57 years I have to say
I have never witnessed a tornado, although I have seen
numerous news bulletins on them. Occasionally the tornado
was 20 miles away.
How many others have been similarly (un)lucky here and
in Tornado Alley?

David

[QUOTE=davieddy;117890]How many others have been similarly (un)lucky here and
in Tornado Alley?[/QUOTE]

I spent most of my youth in Ohio - not sure if that's officially considered part of Tornado Alley, but it is in the wild-weather US Midwest. Never saw one touch down [on land - did see a spectacular waterspout, a.k.a. tornado-over-water on Lake Ontario one summer], but saw several funnel clouds, and had at least one a year touch down somewhere within a 20 mile radius. However, ones that caused widespread damage were relatively rare - maybe every decade within a 20-to-50-mile radius you'd get a trailer park destroyed[sup]*[/sup]. The most-famous killer tornado that hit Ohio in my lifetime was one of the 1974 [url=http://en.wikipedia.org/wiki/Super_Outbreak]super outbreak[/url] that [among other things] destroyed Xenia, Ohio.

I wonder if there could be a reporting bias at work here - in the US, tornados in Tornado Alley are so common that the news reporting thereof is roughly thus:

1) Funnel clouds [tornados that fail to fully coalesce and/or touch down] at best make the local news;
2) Tornados that touch down and cause at most modest property damage make the local news and maybe get a small 'pagefiller' mention in the national news;
3) Tornados that cause widespread property damage but cost no or very few lives make the national news and maybe get a small 'pagefiller' mention in the international news;
4) Only Tornados that level entire towns and kill tens of people, typically ones that are part of Super Outbreaks, make the international news in a meaningful way.

The fact that many non-Brits here apparently have never even heard of 'tornados in the UK' indicates to me that there may be a similar trend at work - since [acording to Paul] UK tornados rarely make it above the afore-defined step (2), news of them stays local and national.

=========

[sup]*[/sup][Aside: I have no explanation for the apparent predilection tornados have for trailer parks here in the US - is it part of as larger global 'shantytown' phenomenon?].

[QUOTE=ewmayer;117894]I spent most of my youth in Ohio - not sure if that's officially considered part of Tornado Alley, but it is in the wild-weather US Midwest. Never saw one touch down [on land - did see a spectacular waterspout, a.k.a. tornado-over-water on Lake Ontario one summer], but saw several funnel clouds, and had at least one a year touch down somewhere within a 20 mile radius. However, ones that caused widespread damage were relatively rare - maybe every decade within a 20-to-50-mile radius you'd get a trailer park destroyed[sup]*[/sup]. The most-famous killer tornado that hit Ohio in my lifetime was one of the 1974 [url=http://en.wikipedia.org/wiki/Super_Outbreak]super outbreak[/url] that [among other things] destroyed Xenia, Ohio.

I wonder if there could be a reporting bias at work here - in the US, tornados in Tornado Alley are so common that the news reporting thereof is roughly thus:

1) Funnel clouds [tornados that fail to fully coalesce and/or touch down] at best make the local news;
2) Tornados that touch down and cause at most modest property damage make the local news and maybe get a small 'pagefiller' mention in the national news;
3) Tornados that cause widespread property damage but cost no or very few lives make the national news and maybe get a small 'pagefiller' mention in the international news;
4) Only Tornados that level entire towns and kill tens of people, typically ones that are part of Super Outbreaks, make the international news in a meaningful way.

The fact that many non-Brits here apparently have never even heard of 'tornados in the UK' indicates to me that there may be a similar trend at work - since [acording to Paul] UK tornados rarely make it above the afore-defined step (2), news of them stays local and national.

=========

[sup]*[/sup][Aside: I have no explanation for the apparent predilection tornados have for trailer parks here in the US - is it part of as larger global 'shantytown' phenomenon?].[/QUOTE]I believe your conclusion about the newsworthiness of UK tornadoes is correct --- very few of them kill anybody or cause massive damage.

I suspect the shantytown phenomenon, as you term it, is related to the newsworthiness angle too. Shantytowns tend not to be physically robust and individual dwellings tend to be close together. Consequently, a tornado strike is more likely to cause more damage to more properties and to kill or injure more people in a shantytown than it would in a more prosperous area.

Paul

[quote=ewmayer;117894][sup]*[/sup][Aside: I have no explanation for the apparent predilection tornados have for trailer parks here in the US - is it part of as larger global 'shantytown' phenomenon?].[/quote]

I guess you see a caravan upsidedown more often than a house.

May I belatedly say how glad I am that you survived your recent
earthquake. I am sure the rest of the Forum would concur.

David

[quote=ewmayer;117894]
[Aside: I have no explanation for the apparent predilection tornados have for trailer parks here in the US - is it part of as larger global 'shantytown' phenomenon?].[/quote]

[URL]http://www.frankwu.com/tornado.html[/URL] :smile:

And more seriously:
[URL]http://www.newton.dep.anl.gov/askasci/gen99/gen99010.htm[/URL]

Which seems to support the news bias explanation.

[quote]...I spent most of my youth in Ohio...[/quote]
We did as well. We remember lots of tornadoes and have seen a few in action.

We now live in NC and have to deal with the occasional hurricane, which is worse in some ways, but at least gives you a warning.

Some opinions about trailer parks and tornadoes:

[url]http://ask.metafilter.com/26791/Trailer-parks-and-tornadoes[/url]

[SIZE=1]Gerbil1: How is a tornado and a divorce the same? Either way, somebody's gonna lose a trailer.
[/SIZE]