Refraction of seismic waves

I want to do a quick primer on refraction. And our focus here is going to be on the seismic waves, but the principles, how things refract when they go from a fast to a slow medium or a slow to a fast medium, It's actually the same as you would see when you're studying light waves or actually any type of wave. So let's think about it a little bit. So let's say I have a slow medium right over here. And let's say I have a fast medium right over here. And let's say, just so we can travel through both solid and liquids, let's think about maybe P-waves. And a slow medium could be maybe some type of liquid, and our fast medium could be some type of solid. So let me draw the boundary right over here. So if I have a P-wave. Let's say it's going through the water, and it's going right perpendicular to the boundary. It will then just continue to travel in the faster medium in the same direction if it's going right at the boundary. And it'll just travel faster in the faster medium. And that's because that faster medium is going to be more dense, and the molecules are going to bump into each other faster. In the same amount of time kind of the chain reaction is going to be able travel further because they are more closely packed and they rebound faster than it would in the slow medium. So that's obviously no refraction is going on. It has not been deflected. And just as a bit of reminder, in general, refraction is when a wave gets deflected. Reflection is when it bounces back. Refraction is when it gets deflected a little bit. Let me just make that clear. So if I have some type of boundary here, and I have a wave that bounces off, that's reflection. But if the wave goes through the boundary and just gets bent a little bit, its direction changes, that is refraction. That's what we're talking about. So clearly so far this P-wave has not been refracted. But if this P-wave comes in at an angle-- so let's make this P-wave wave come in at an angle-- what's going to happen is, and the way you should think about it-- and it's the easiest way to think about which direction will be refracted, or at least the way I think about it, is literally I imagine some type of vehicle with wheels on it. So this is the top view of my vehicle. So if I have some type of vehicle, and the wheels will be able to move slowly in this medium. You could kind of view it as it's kind of on mud so it doesn't get good traction, and then the fast medium maybe it's a road so it gets good traction, it could move faster. So what's going to happen when the vehicle gets to the boundary? Well, this bottom right wheel is going to go on the fast medium before any of the other wheels do. So it's going to get the traction first. These wheels on the left side of the vehicle, these wheels right here, these are still going to be stuck in the mud. So what's going to happen is this wheel right over here is moving faster, so it's essentially going to be able to turn the vehicle. These guys are still stuck in the mud. And so you fast forward a little bit, the direction of the vehicle will change. And so the vehicle will now move in a direction something like this. The same thing would happen in a wave. If the P-wave is approaching the boundary like this, and something analogous to this is happening at the molecular level. You can kind of view it as even billiard balls, and maybe they're kind of hitting each other. Well, I won't go into that, because that can kind of get confusing depending on the different cases and the different boundaries. But this is the easiest way to think about it, and which direction it will refract. And hopefully it makes a little bit of intuitive sense. And so when you go from a slow to a fast medium our P-wave its angle would accentuate in that direction. If you went from the fast medium to the slow medium, once again, you can just go through the same thought experiment. So let's say you have our wave coming in like that. Draw the car. Visualize the car here. Visualize the car right here. And you'd say, well, look, this tire's going to get stuck in the mud, because it was on the road. Now, this top tire right over here is get stuck in the mud first. So it's going to be moving slower. So these tires are going to be able to move faster. So the vehicle is going to turn. So you'll be refracted in a direction like that when you're going from the fast to the slow medium. So that's just a primer on refraction generally. Now, let's think about what would happen when sound waves are traveling through the Earth. And this will help inform us of, essentially, how do we figure out what the actual structure of the Earth is. So if the Earth was just made up of some uniform material and you had an earthquake right here on Earth, maybe a little bit below the surface. So it's happening in the crust, but a little bit below the surface of the Earth. If Earth was of uniform density, if it was all the same material, let's just think about the P-waves. Because P-waves can travel in anything. Let's think about how those P-waves would travel. Well, they would just go in straight lines. There's nothing that would refract the P-waves. They would just go in straight lines radially outward from where the earthquake occurred. Now, at a first approximation, we know that as we go deeper and deeper into Earth there's more and more rock above that. The weight of that rock is kind of compressing the rock below it. So you get higher and higher pressures and higher and higher densities. So this is a uniform Earth. But let's imagine an Earth that's made up of uniform material, that's all solid, a completely solid Earth, but one where the density is constantly increasing as you go down. So let's just think about it before we go into the continuous case. Because we're talking about the density as you go deeper, it's just getting continuously more dense, let's think about the discrete case, where we have the least dense layer. So let me draw it right over here. So let's say this is the surface of the Earth. This is least dense. Then let's say you have another layer over here that is more dense. So this is more dense. Let's say you have another layer that's even more dense. So you have another layer over here that's even more dense. And then let's do one more layer. Let's do this layer here, this is the densest layer. So in general, your P-wave, your seismic wave, is going to travel faster in denser material. So it's going to travel the fastest here, then here, then here. It's going to travel the slowest in this least dense material. So if you're coming in at an angle let's think about what's going to happen. So let's say you have your P-wave coming in at an angle like this. So it's going straight through the least dense material. Let me do a slightly shallower angle. So let's say it's like that. What's going to happen when it goes into the more dense material? So once again, let's imagine our little car. So this tire's going to be able to go faster before the tires on the other side. So the car is going to be deflected to the left, to the down left. So now it's going to travel like this. So it's now going to travel something like this. Now, what's going to happen at this boundary? Once again, imagine the car. This tire right here is going to be able to travel faster before the other tire, so it'll be deflected even more in that direction. Then we go, and we go to the densest material. Once again, the tires on kind of the bottom side when we look at this way are going to be able to move faster before the other tire. So we're going to get deflected even more. So you see, as you go from least dense material to more dense material you're kind of curving outward. So if this was continuous, if you had a kind of a continuous structure, where as you go down it just gets more and more dense as you go. So this is less dense, and then it just continuously gets more dense. So this is the most dense down here. How would the refraction look? Well, then it would just be a continuous curve. It would look like this. Your P-wave would constantly be refracted out like that. It would curve outwards. So this was the simplest example where Earth is uniform. And that's pretty easy to dismiss, that obviously things will get denser because of more pressure down. So let's say we assume another thing. We have a uniform Earth in terms of composition, but let's say it gets denser. So denser at the center. Then how would the P-waves travel, or how would any seismic waves travel? Well, then if you have your earthquake right over here, the ones that are going straight down still would go straight down. Because we know that we won't get refracted if we're kind of going perpendicular to the change in medium, or the change in boundaries. But things that are coming at a slight angle, as they get deeper they're going to get deflected more and more and more, and they're going to be refracted outward just like we saw in this example here. If they go on this angle they're going to be refracted outward like that. If they go here they're going to be refracted outward like that. They're going to be refracted outward like that. If you're here you're going to be refracted outward like that. If you're here you're going to be refracted outward like this. Now, what we're going to do in the next few videos is use what we just learned about refraction in the case of seismic waves-- and hopefully we learned it in this video-- and how it would refract as we're going through ever increasing denser material. We're going to use that information to essentially try to figure out the composition of the Earth based on what we've actually observed.