地震波的折射

I want to do a quick primer on refraction and our focus here is going to be on a 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 doing 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 a slow medium right over here and let's say I have a fast medium right over here and let's say just for the so that we can travel through both solid and liquid let's think about maybe P waves and a slow medium could be maybe some type of liquid in our fast way and our fast medium could be some type of solid so let me draw the boundary right over here and let's say so if I have something that goes that come o P wave 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 if it goes right at the boundary if it goes 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 more molecules kind of the chain reaction is going to be able to travel further because they're 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 a reminder in general refraction is when a wave gets deflected reflection is when it bounces back or 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 a reflection but if the wave goes through the boundary and just gets bent a little bit its direction changes that is a refraction and 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 come in at an angle what's going to happen is and the way you should think about it it's 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 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 can kind of view it 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 can move faster so what's gonna 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 gonna 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 you know they're kind of hitting each other well I won't go into that because that can kind of get a little confusing depending on the different cases and the different boundaries but this is the easiest way to think about in which direction it'll 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 would kind of its angle would accentuate in that direction if you went from 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 is gonna get stuck in the mud because now we're going from this it was on the road now this top left 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 gonna 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 of 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 you had an earthquake right here on earth maybe a little bit below the surface so like you know where it's in the 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 how would those let's just think about the p-waves how it cuz P waves can travel in anything let's think about how those P waves would travel well they were just going straight lines there's nothing that would refract the P waves it would just go in straight lines radially outward radially outward from where the earthquake occurred 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 how would so this is a uniform earth this is a uniform 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 and before we go into the continuous case because we're talking about the density as you go deeper it's it's it's just getting continuously more dense let's think about the discrete case where we have 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 and this is least dense least dense then let's say you have another layer over here that is more dense so this is more dense more dense let's say you have another layer that's even more dense so you have another layer over here that's even even more more dense and then let's do one more layer let's let's do this layer here that this is the densest layer densest so in general in general your P wave your seismic wave is going to travel faster and denser materials so it's going to travel the fastest here then here then here it's gonna travel the slowest and thus least dense material so if you're coming in at an angle 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 what's gonna happen when it goes into the let me do slightly shallower angle so let's say it's like that what's gonna happen when it goes into the more dense material so once again let's imagine our little car so this tire is 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 gonna 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 in to go to the densest material once again the tires on kind of the bottom side when we look at it this we're gonna be able to get move faster before the other tire so we're gonna get deflected even more so you see as you go from least dense material to more dense mature you're kind of curving outward so if this was continuous if you had a continuous kind of a continuous structure where as you go down it just gets more and more dense as you go so this is less less dense and then it just continuously it 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 your P wave would constantly be refracted out like that it would curve outwards so if we if earth so this was a simplest example where earth is uniform and you know that's pretty easy to dismiss that you know 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 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 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 gonna 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 in this angle is gonna be refracted outward like that if they go here they're gonna be refracted outward like that they're gonna 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 that 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 in this video and how it would refract as we're going through ever-increasing denser material we're going to use that that information to essentially try to figure out the composition of the earth based on based on what we've actually observed