Both the now-superseded Richter scale, and the currently used Moment Magnitude Scale are logarithmic, with each full point (i.e 7.0 to 8.0) disposing of approximately 31.6 times power of the next lower.
So yes, the 8.8 quake that hit Chile this morning is hundreds of times more powerful than the 7.0 quake that hit Haiti.
31.6 is (about) the square root of 1000. While the math was a bit over my head, I don't quite understand how it is logarithmic with 1=31.6 and 2=1000, unless the base number is 31.6 and not 10.
ReplyDeleteWhat I could gleam out of that is that there is a difference in what is measured, necessitating a slight modification of the numbers. In electronics, for example, differences in power are compared as
10 * Log (P1/P2)
whereas voltages compared as
20 * Log (V1/V2)
and currents are compared as
20 * Log (C1/C2)
But I am not an expert.
However, that would explain the 500 and 1000 descriptions. 1000 would be correct if the difference between Haiti and Chile was rounded to 2. 500 would be correct would be correct if the difference was rounded to 1.7 (a difference of .3 would be a difference by a factor of two -- at least in base 10).
It would also explain the discrepancy in the news reports.
ReplyDeleteI skimmed the mathematics behind the computations, but I'd like to sit down with a pencil and work through it.
^^^MY BRAIN IS BLEEDING^^^
ReplyDelete^^^MY HEAD JUST EXPLODED^^^
ReplyDeleteInteresting; I was going to ask whether the log scale was really base 10 or not.
ReplyDeleteApparently it uses base sqr(1000) = 31.6 or so.
I think the trick is to remember that _any_ number raised to the zero'th power is _one_.
31.6 ^ 0 = 1
31.6 ^ 1 = 31.6
31.6 ^ 2 = 1000
So if you have a magnitude N earthquake, then a magnitude N+2 quake is a thousand times more powerful, for all N.
^^^MY BRAIN IS BLEEDING^^^
^^^MY HEAD JUST EXPLODED^^^
I am a terrorist.
"I am a terrorist."
ReplyDeleteLMAO!
I've sent my British Mossad agents out to whip your butt.
But isn't 31.6 (more like 36.162 -- and I figured that out by hand!)an odd number to have as the base?
ReplyDeleteIf we really want to make people's brain hurt, I could explain how to figure out square roots by hand.
ReplyDelete31.62277660168... I figured that out by hand, too... I punched the calculator buttons with the index finger of my right hand...
ReplyDelete...I guess I cheated... I mean...
I didn't use a _real_ calculator, just the virtual one on my computer... ;)
LMAO at all of you!
ReplyDeleteCalculating a square root by hand is similar to division. Since we have been talking about the number 1000, I will use it to explain the process.
ReplyDeleteFirst, set up the process similar to division, splitting up the number in groups of two, going right to left from the decimal point (if there is an even number of numbers, then the left most one is a single digit) and going left to right in groups of two.
/ 10 00. 00 00
Start by figuring out what number, when squared, will be equal to or less than the first set of two (which, in this case, is the number 10). That would be 3:
3
3/10 00. 00 00
1
Then drop down the second set of two numbers.
3
3/10 00. 00 00
1 00
Then it begins to get a bit confusing. You double the previous working number, in this case three, and you double it. You then put an underscore after it:
3____
3/10 00. 00 00
6_ 1 00
Then you need to figure out what number when put in the ones column (in this case, consider the 6 as being in the tens column) AND multiplied by that number will be equal to or less than the “dropped down number. In other words, using our example, what number N will give you N((6*10)+N) that is equal to or less than 100. In this case, that number is 1: 61*1 is equal to or less than 100, whereas 62*2 is larger than 100.
3 1___
3/10 00. 00 00
61 1 00
39
Now you do that step one more time:
3 1.___
3/10 00. 00 00
61 1 00
62_ 39 00
What number when put in the ones position added to (64*10) and then multiplied by that number (((64*10)+N)*N) will be equal to 3900? This may take some trial and error, but let’s try 6.
3 1. 6___
3/10 00. 00 00
61 1 00
626 39 00
37 56
1 44
Now we drop down two more zeros and carry on as before:
3 1. 6____
3/10 00. 00 00 00
61 1 00
626 39 00
37 56
632_ 1 44 00
In this case, let’s just figure 2”
3 1. 6___2
3/10 00. 00 00 00
61 1 00
626 39 00
37 56
6322 1 44 00
1 26 44
17 56
Just keep going on as far as you want to carry it.
Aren’t you glad you asked?
Oh well, that didn't quite turn out right, but hopefully you can follow it. That is if you have any interest in following it.
ReplyDeleteOkay Matt.
ReplyDeleteMy eyes are crossed, and I just drooled a little....I'm gonna go sit in the kitchen with the other EWOKS...:)
Stop encouraging him people.
ReplyDeleteI have to live with it!
I wonder how they figured out logorithms. But my Holy Grail is to find an equation to figure out N! -- that is to multiply every number from 1 to N. Obviously that can get long if N is a large number, so there must be an equation.
ReplyDeleteI do have an equation for adding every number from 1 to N. That equation is:
((N*N)+N)/2
Oh, hello Sweetie!