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## Logarithmic scale (Algebra 2 level)

Current time:0:00Total duration:11:19

# Richter scale

## Video transcript

I've been doing a bunch of
videos about logarithmic scale. And we've also, unfortunately,
had many notable earthquakes this year. So I thought I would do a video
on the Richter scale, which is a way to measure
earthquake magnitudes. And just to be clear, although
we associate the Richter scale as the way we
measure earthquakes now, the one that we
actually use now is the moment of magnitude scale. And the reason why
most people don't make a huge differentiation
between the two, is that the moment
magnitude scale was calibrated to
the Richter scale. But the whole reason why we
moved to the moment magnitude scale is that the Richter
scale starts to kind of max out at around magnitude
7 earthquakes. So this gives us
a much better way to measure things that
are above a magnitude 7. So this right here is a
picture of Charles Richter. He's passed away. But this is from an
interview that he gave, and it's interesting
because it kind of gives the rationale for how he came
up with the Richter scale. I found a paper by Professor
K. Wadati of Japan, in which he compared large
earthquakes by plotting the maximum ground motion
against the distance to the epicenter. So this Professor K. Wadati
would, you could imagine, he did a plot like this,
where this is distance. So if you have an
earthquake someplace, you aren't always sitting
right on top of the epicenter, where you measure it. You might be sitting over here. Your measuring stations
might be some distance away. So he looks at how far
the measuring station was, and then he looks
at the ground motion at the measuring station. So that would be some
earthquake over there. Let's say that's a
relatively medium earthquake. This right over here would
be a weak earthquake, because you're close
to the earthquake, and it still didn't
move the ground much. This is the magnitude,
this axis is the magnitude, how much the ground is moving. And then, for
example, this would be a very strong earthquake. And then Charles Richter
said in the interview, I tried a similar
procedure for our stations. But the range between the
largest and smallest magnitudes seemed unmanageably large. So what he's saying
is, when he tried to plot it like
Professor Wadati, he found that OK, you
could get some earthquakes that you can plot around here. But no matter how you
create a linear scale, if you want any
resolution down here, the stronger earthquakes
just go off the charts. Or maybe off the page. So the stronger
earthquakes you might have to start plotting
here, or here. Or maybe they don't
even fit on the page. And so he says, Doctor
Beno Gutenberg-- and they were all working
at Caltech when they came up with the Richter scale--
Doctor Beno Gutenberg then made the natural suggestion
to plot the amplitudes logarithmically. I was lucky, because
logarithmic plots are a device of the devil. And I'm not really
sure what he means when he says that they
were a device of the devil. I'm assuming he means that
they're kind of magical. That all of a sudden, you
could take these things that you want your
resolution down here, you want to be able
to tell the difference between those weak earthquakes. But at the same
time, you want to be able to compare them to
the large earthquakes. And he thought, I
guess he viewed them as a bit of a
magical instrument. And we say that
they're logarithmic, or he plotted on a
logarithmic scale. What essentially
he's saying is, he's essentially taking the
logarithm of the magnitude of every one of
those earthquakes. So if you're measuring
the earthquake, maybe on a seismograph, so this
is before the earthquake, then the earthquake hits. And then the earthquake stops. And then you measure the
amplitude of this earthquake. If you just plotted
them linearly, you would have the
problem that he saw. Or if you try to plot them the
way Professor Wadati did it, you would have that problem. But what he does is
he measures this now, and he plots the
logarithm of that. And so what happens is that you
get a scale that is plotted-- or you get a logarithmic scale,
for lack of a better word. But what I want to
do in this video is think about what
implication that has for the magnitude
of earthquakes, especially some of the
earthquakes that we have seen recently. So this right here
is the earthquake that occurred August 23, on
the east coast of the United States. And it wasn't that
strong of an earthquake. It was a 5.8. That's not a small earthquake,
you would definitely feel it. It's a good bit of
shaking, it can even cause some minor damage. But the reason why
it's notable is it happened in a part of
the world that does not see earthquakes too frequently. So let's just take
that on our scale. I'm going to go down
all the way over here. So I'm going to
do our scale here. So let's just put that as a 5.8. And if you shake your
seat fairly vigorously, that'll give you a
good idea of what it might feel like on the
top of that earthquake. So this is 2011, east
coast earthquake. And then probably the
most famous earthquake in the United States
in recent memory was the one that
occurred at Loma Prieta. This is Loma Prieta
right over here, about 40 or 50 miles south
of San Francisco. And this is damage that was
caused in San Francisco, an actual freeway
collapsed right over here. And this whole area has
actually now become very nice, after they removed this freeway. But you can imagine
how powerful it was, that it was able to cause
this type of damage this far away. And actually I live
right over here, so I'm glad I wasn't around,
or I wasn't in the Bay Area, during that earthquake. But that earthquake,
depending on your measurement, but we'll just call it a 7.0. So that earthquake
measured at a 7.0. So let's call this 7. Let me do that in a color
you're more likely to see. So that earthquake was a 7.0. Loma Prieta, that was in
the San Francisco Bay Area. And this was in 1989. It happened right actually
before the World Series. And then of course 2011, a
very unfortunate earthquake in Japan. The Tohoku earthquake,
right over here, this circle shows the
magnitude of that earthquake. It was off the coast
of Japan, all of these were the aftershocks. And the real damage
it caused was really the tsunami and
the damage it did to the Fukushima
nuclear power plant. But that was an 8.-- well,
sometimes it's called 8.9, sometimes a 9.0, depending
on how you measure it-- let's just call it a
9.0 for simplicity. So let's say this is almost
6, and this would be 7, then an 8 would get
us right over there. So 9.0 is right over there. So this is 2011 the earthquake
in Japan, the Tohoku earthquake. And then the largest
earthquake ever recorded was the great Chilean
earthquake in 1960. And that was a 9.5. So 9.5 would stick
us right over, let's say right over here. And this is the 1960
earthquake in Chile. And just to give a sense,
when you look at this, if you thought this was a linear
scale you'd say, OK, the Chilean
earthquake, maybe that was a little bit
less than twice as bad as the east
coast earthquake. And it doesn't seem too bad. Until you realize that
it is not a linear scale. It is a logarithmic scale. And the way that
you interpret it is thinking about how
many powers of 10 one of these earthquakes
is from another. So you can view these
as powers of 10. So if you take, go
from 5.8 to 7.0, that was 1.2, a 1.2 difference. But remember, this is
a logarithmic scale. And I encourage you
to watch the videos we made on the
logarithmic scale. On a logarithmic
scale, a fixed distance is not a fixed amount of
movement on that scale. Or a change on that scale is
not a fixed linear distance. It is actually a scaling factor. And you're not scaling
by 1.2 over here. You're scaling by
10 to the 1.2 power. So this is times 10
to the 1.2 power. So I'll get my calculator
out right over here. And let's figure what that is. So you could imagine
what it's going to be. 10 to the first power is 10. And then you have 0.2. So it's going to be, let's just
do it, 10 to the 1.2 power. It's 15.8. So it's roughly
16 times stronger. So whatever shaking that was
just felt on the east coast, and maybe some of
you all watching this might have felt it,
Loma Prieta earthquake was 16 times stronger
than the earthquake-- let me write this-- this is 16
times stronger than the one that we just had
on the east coast. So that's a dramatic difference. Even though this caused
some damage, and this is kind of shaking on
a pretty good scale. Imagine 16 times
as much shaking. And how much damage
that would cause. I actually just
met a reporter who told me that she
was in her backyard during the Loma
Prieta earthquake, not too far from
where I live now. And she says all the cars
were like jumping up and down. So it was a massive,
massive earthquake. Now let's think about
the Japanese earthquake. We could think about
how much stronger it was than Loma Prieta. So remember, this
isn't, you don't just think of this as just
2 times stronger. It is 10 to the
second times stronger. And we know how to
figure that out. 10 to the second power is 100. So this right over here. So cars were jumping up and down
at the Loma Prieta earthquake. The Japanese earthquake
was 100 times stronger. 100 times stronger
than Loma Prieta. And if you compare it to
the east coast earthquake, it would be 1,600 times
the east coast earthquake that occurred in August of 2011. So massive, massive,
massive earthquake. And just to get a sense
of how much stronger the Chilean earthquake was in
1960-- and just to-- there's some fascinating outcomes
of the Japanese earthquake. It was estimated
that Japan, just over the course of the
earthquake got 13 feet wider. So this is doing something
to the actual shape of a huge island. And on top of that,
it's estimated that because of the shaking,
and the distortions in earth caused by that shaking,
that the day on earth got one millionth
of a second shorter. A little over a millionth
of a second shorter. So you might say, hey, that's
only a millionth of a second. But I'd say, hey,
look it actually changed the day of the earth. A very fundamental thing. It actually matters when
people send things into space, and probes into
Mars, is that they are to be able to
know that our day just got a millionth of
a second shorter. So this was already
a massive quake. And the Chilean
earthquake is going to be 10 to the 0.5
times stronger than that. So let's get our calculator out. So you really could view this
as the square root of 10. So 10 to the 0.5 is the
same thing as 10 to the 1/2, which is just the same thing
as the square root of 10. Which is 3.16. So the strongest
earthquake on record was 3.16 times stronger than
the Japanese earthquake. The one that shortened
the day of the planet. The one that made
Japan 13 feet wider. And so this was-- if you wanted
to compare it to the east coast earthquake-- this
would be almost, or about 5,000 times stronger. So massive, massive earthquake. So one, hopefully
that gives you a sense of what the Richter
scale is all about. And also gives you a
sense of how massive some of these super
massive earthquakes are. And you can also appreciate what
Charles Richter's first problem was. If you wanted to plot all of
these on the same linear plot, you would have to stick
this one 5,000 times further along an axis than you would
have to stick this one. And this one itself, this is
still a pretty big earthquake. So this would have to be
5,000 times further than some of the earthquakes at the
low end of the Richter scale.