The structure of the Earth makes tracing raypaths more complicated than the simple layered models we considered in the problem set. For one thing, the Earth is round, not flat. This means that all waves that start at the surface return to the surface, whether they encounter velocity changes along their path or not. Also, the concentric layers of material that make up the Earth aren't necessarily homogeneous. This means that sometimes waves are transmitted faster in certain directions than others. Let's discuss how raypaths travel through a homogeneous spherical body and then add complexity to see how seismic waves travel through a more "Earth-like" structure of concentric shells. Then we'll check out some actual seismic data to see how well the Earth mimics our simple model.
If the Earth were a homogeneous sphere
The animation below shows a cross-section through a homogeneous sphere. In this case, an earthquake that occurs somewhere on its surface would send seismic waves out in all directions and these waves would travel straight through to the other side.
Hopefully you guessed that there was a point to all those refraction calculations you just did. What was that point? Well, the Earth is not a homogeneous sphere. It is composed of concentric shells of material and each one transmits seismic waves at a different velocity.
If the Earth had two layers over a homogeneous center
Let's consider a model like the sketch below, which is just a couple of spherical layers over a homogeneous center. This one is a little more Earth-like than the previous model we considered. When the incident ray strikes the boundary between the two layers, it will be refracted. It is refracted again at the next boundary, and then it happily travels along until it strikes the underside of that same boundary again and makes its way back up to the surface. In the animation below, note the shape of the ray paths through this model as opposed to the last model.
Earth model in which transmitting velocity increases smoothly with depth
Now what if you imagined a sphere composed of an infinite number of concentric layers, and let's say that each layer transmits seismic waves just a little faster than the layer above. This model in which velocity increases with depth is even more Earth-like than the previous model. At each local boundary, the ray still has to obey Snell's law, but since the layers are infinitely thin, the path ends up being a smooth curve. To see some of these curved ray paths, check out the animation below.
Now, armed with our model of a sphere in which velocity increases with depth, we should be ready to plop seismometers down all over the world, measure the P and S wave arrival times from earthquakes, and confirm our idea about how wave speed varies in the Earth. In fact, seismologists did do this, and when they did, they realized that at some distances away from earthquakes, they didn't get any P or S arrivals at the times they should have arrived. They realized that there had to be a major boundary inside the Earth where material properties changed drastically, thus altering the wave paths enough to create a "shadow zone" where there are no direct arrivals from P and S waves. This is how the Earth's core was discovered. Seismologists knew that seismic rays took a curved path through the Earth. As the distance between the source and the receiver increased, the "turning point" (the deepest point along the wave's path) got a little deeper. At the farthest distance direct body waves were recorded, the turning point corresponding to that raypath must have been the depth of the mystery boundary, because a ray that tries to turn at a deeper point will run into that boundary, get refracted, and follow a different path. The depth of the boundary between the mantle and the outer core was found to be about 2900 km. This corresponds to a shadow zone for direct arrivals of P and S waves beginning at about 104° from the source. The same method was used to discover the inner core of the Earth as well.
A Seismic Record Section from the 2004 Sumatra-Andaman Earthquake
Let's check out some actual seismic data to see if we can distinguish all the features of the raypaths in the Earth-like models we considered. Below is a record section from the 2004 26 December Sumatra-Andaman earthquake. Creating a record section means plotting a suite of seismograms that are arranged in order by their distance from the earthquake. In this record section, the closest station is CHTO, at about 16 degrees away, and the farthest station is PAYG, at about 173 degrees away (Can't get too much farther than that because 180 degrees would be exactly on the other side of the Earth!). Each seismogram has some colored bars on it. These colored bars are arrival time picks for various body waves. Watch the two screencasts below the figure to see me sketch the paths the seismic waves took through the Earth to produce each of these arrivals.
Seismogram arrivals explained!
First I'll single out station SBA and draw a cross-sectional sketch of the Earth that shows how each arriving wave gets from the earthquake to SBA.
There is also a transcript of the screencast demonstrating arrivals at SBA.
This is a record section from the 2004 Sumatra Andaman earthquake. A record section just means that I have taken a bunch of seismograms and arranged them in order of their distance from the earthquake. So on the x axis here is time. On the y axis is distance in degrees. Each of these seismograms is plotted with the name of its station and its distance away from the earthquake. What I'm going to do now is just focus on one of these stations. This station, SBA, here. I'm going to show you just by sketching that path that each of these arriving waves took to get from the earthquake to this station. These colored bars here are arrival time picks for various waves. This was probably done by an automatic picker that knows about how long it takes for each type of wave to get from one point to another on Earth. If I just make this little sketch right here of the Earth. I'm leaving out the crust here, but basically this is a cross section. Here's the mantle, and here's the outer core, and here's the inner core. And let us just pretend that my earthquake happened right up here at the top. We can pick any spot I guess. I'm going to choose this station SBA because it is handily almost exactly 90 degrees away and that is easy for me to freehand. So we'll draw a little house. That's our seismometer. The first arriving wave that gets from the earthquake to the seismometer is this one that is marked in green right here. It is the direct P wave. The path that the direct P wave takes through the mantle is kind of like that. Notice how it curves. It does not follow a straight line path. That is because seismic wave speed increases with depth. The next arriving wave is this arrival marked in red. That is PP. What PP does is it goes through the mantle and bounces once between the earthquake and the station, and then it continues on its way to the station. Each of these waves is a P wave in the mantle so we call it PP. The next arriving wave; well actually this orange one and this yellow one come practically on top of each other. The orange one is the direct S wave and the direct S wave follows the exact same path as the direct P wave only shear waves are slower so that is why it takes longer than the P wave to get from the earthquake to the station. The yellow one is a little more interesting. It is an S wave that bounces off the core mantle boundary and then gets to the station. So it is S and then that bounce point is called little c and then it is S again so the entire wave is called ScS. The next arriving wave is this pink one. The pink one is SS which follows the same path as PP only shear waves are slower so it takes it longer to get to the station. Those are all the waves marked here. We have this big high amplitude this coming in later on and those are actually surface waves. They travel along a path like this. Takes them longer to get there because the crust doesn't transmit waves as fast.
Now...Station PAYG is trickier! No direct P wave! No direct S wave! In fact, by looking at seismic records like this one, seismologists figured out that the Earth must have a core made of significantly different material than the mantle. Based on the "shadow zone," the distance range over which no direct mantle body waves are observed, seismologists also figured out the size of the core. The fact that no S waves could make it through the core showed scientists that at least part of it had to be a liquid. Watch my sketch of how this works for the arrivals at station PAYG.
There is also a transcript of the screencast of the sketched paths to PAYG.
Let us look at the same record section, but a different station. This time I am going to look at station PAYG, which is almost 180 degrees away from the earthquake. I have drawn it down here. What you will notice right away is that the number of arrivals is fewer. There is no direct P wave and there is no direct S wave. The reason for that is that the core gets in the way. Remember at the earlier station that P waves and S waves take a kind of curving path through the mantle that I'm showing you right now with the mouse. If you are farther away than about 104 degrees then these waves will bounce off the core or they will be refracted within the core as P waves and so you will not get a direct arrival. This is how the core was discovered. What are the arrivals that are coming in at this station? The first one is this one here and that one is labeled PKiKP. What that wave does is, it is a P wave in the mantle, it comes down here, it gets refracted in the outer core, and the inner core, and back through the outer core, and back out through the mantle to this station. The path is called a P wave when it is in the mantle, and then a P wave in the outer core is called K. I do not know why that is. In the inner core it is called i. And then it goes back out as K and P. The whole thing together is called PKiKP. The next arriving wave is PP. That is our old friend. We know how that works. It goes through the mantle and it bounces and it goes to the station. Each of these paths is a P wave in the mantle. It is called PP. The last arriving wave is SS. It follows the same path as PP except shear waves are slower so it takes it longer to get there.
Want to make your own record section of a recent earthquake?
Thanks to the good folks at IRIS, the Incorporated Research Institutions for Seismology, it is not too hard for anyone to do. I recommend letting your students play around with this!
Go to Wilber3, where you can request seismic data from recent earthquakes.
The default page has a map with recent (last month or so) earthquakes on it. The map is interactive, so you can draw a box to zoom in, and there are also some dialog boxes you can type into in order to narrow down the number of events in the list by date, location and magnitude.
The map locations are clickable colored circles. Clicking on one of them will highlight that event in the list on the same page.
After you've clicked on your selection in the list, the map will refresh and now show you all the stations that recorded data from your selected earthquake.
At this point you can click a button that says "Show Record Section"