Logarithmic scale (Algebra 2 level)
Current time:0:00Total duration:11:19
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.