Seismology is the science of studying earthquake waves as they propagate through the Earth. This tells us something about what the Earth looks like on the inside -- and hopefully, how it works.
I have made videos of wave propagation to visualise what kind of different waves exist and how these waves can travel throught the Earth.
Some examples:
Ripples in a pond (SH seismic wave propagation).
This first video shows the concept of a travelling seismic wave in its very simplest form. An 'earthquake' is excited at the source (x) after which the signal spreads out like ripples in a pond when a stone has been dropped into it.
Speaking in more technical terms, what you see is so-called SH seismic wave propagation in 2D through a homogeneous medium. In this setting, the particle motion is perpendicular to the screen that you're looking at -- the ripples move towards you when coloured red, and move away from you when coloured blue. In a 2D environment, this SH motion is completely decoupled from the other types of seismic wave propagation: P-SV motion, where the particles would move in the plane of the screen.
This video shows the concept of seismic waves. An 'earthquake' is started at the source (x) after which the signal spreads out. We see here that two sets of waves start spreading out from the source. One in the horizontal direction, going fast, and the other going in the vertical direction, going a bit slower. This is a very basic distinction in seismology: that between P-waves and S-waves.
P-waves are "pressure" or compressional waves. As a wave moves in a direction, the particles that are excited start vibrating in that same direction. This is exactly how sound works.
S-waves, on the other hand, are "shear" waves. In this case, the particles which make up the medium move _perpendicular_ to the direction in which the wave itself moves: if the wave goes up, the particles vibrate to the left and to the right.
The explanation for the fact that there is this distinction between P-waves and S-waves is a bit technical, and has to do with the particle motion. The source (x) is excited in the x-direction. That is, the 'x' is tugged to the left and to the right for a bit, and then left to itself to spread out. Since we move particles left and right, and waves start spreading out in all directions, you can maybe see that the waves that go in the same direction as the one in which the particles were excited will be P-waves, and the waves that go in the perpendicular direction (up and down) will be S-waves.
One thing I haven't explaine yet is why P and S go with different speeds. This has to do with very basic material properties. The S-wave is influenced by the resistance of a material to be 'sheared' (like when you rub your hands with something in between), while the P-wave is also influenced by the resistance of a material to be compressed. Because of the way these resistances are combined, the P-wave is always faster than the S-wave.
Wave propagation in 2D - simple radiation in a homogeneous medium.
This video shows the full spectrum of forms of seismic wave propagation that is possible 2D. Again, we have a homogeneous medium where an 'earthquake' is started off at the source x. Here, we see three different plots showing the particle motion in the three different coordinate directions x, z and y. The wave propagation in the first two plots is coupled (called 'P-SV propagation'), while the third (called 'SH propagation') is completely independent from the other two - the ripples in the pond again.
P-SV wave propagation, shown in the first and second plot, is a little more complicated. You now see the particle motion separately in the x-direction (first plot) and z-direction (second plot). Because the source was excited in the x-direction, the bulk of the signal is visible in the first plot. But because they are coupled, you will still get some particle motion in the Z-direction too.
This video shows what happens when one of the boundaries of the domain is reflecting. Both the original P-wave (the fast wave going to the left and right) and the original S-wave (the slow wave going up and down) eventually hit the top surface, and there reflections are excited.
You can see an interesting thing happening at this reflecting top surface. A single original P-wave excites a reflected P-wave but also a reflected S-wave. Likewise, the original S-wave results in a reflected P-wave and a reflected S-wave.
Although the waves can still be distinguished from one another by the fact that P-waves are fast and S-waves slow, the wavefield by now starts to look very complicated. Multiple sets of waves arrive at the receiver, and some even simultaneously (for example the P to S reflected wave and the S to P reflected wave, along with the direct S-wave)
The following video shows how the travel time sensitivity kernel of a P to S / S to P top surface reflection is calculated (the waves that arrive simultaneously - and along with the direct S wave - at the receiver o in the previous video). Input to this are the recorded seismogram at the receiver o, and the original wavefield as the signal travels from source x to receiver o - saved from the calculations made for the previous video. The kernel, however, is calculated in reverse time.
Calculating the 'seismic ray path'.
Seismology is closely related to optics. There is a source, there is a receiver, and in between we have the ray - a beam of light in the case of optics, a seismic wave in the case of seismology. This ray can go directly from source to receiver, it can reflect off a surface, it can bend, and in the case of seismology it can also convert from one type of wave to another (P to S, S to P...).
Usually, we just assume that this ray is super-narrow. So if a seismic wave arrives earlier or later than predicted, this has to have happened somewhere along this pencil-thin line between source and receiver. This, however, is a simplification of reality, and that is what this video tries to show. The lower the frequency is, the fatter the "ray" becomes, an effect that has to do with a physical principle called interference.
In this video, we show how we can calculate the fatness of the "ray". There are four panels, the last of which shows the actual extent of the ray as it is being calculated as time goes by. At the end of the video, this panel shows the actual ray fatness plot, more commonly called 'sensitivity kernel', 'travel time sensitivity kernel' or 'banana-doughnut kernel'.* The other three panels have to do with the way these kernels are calculated, a method called the 'adjoint method'. To explain this fully, one would have to go into more detail than the lenght of this description allows, but the basics are as follows:
1st panel: the forward field. this is the same wavefield that we also see in the 'reflecting top' video. The only peculiarity is that we are now playing it in REVERSE TIME. The reason for this is that we have to make it interact with the so called 'adjoint field' (panel 2).
2nd panel: the adjoint field. This field is generated as if there were a source at the original receiver, with the original seismogram that was recorded there as the seismic signal. This is calculated in reverse time.
3rd panel: the interaction field. This is the important bit: it shows how, at every time step, the forward and the adjoint field interact. You see that there is only interaction where both the forward and the adjoint are non-zero, and as time goes back to zero, this interaction goes from receiver to source.
4th panel: the resulting kernel. This is simply all the interactions from all the timesteps added up. At the end of the reverse time run, we have calculated the full sensitivity kernel.
Anyone wishing to know more about adjoint methods, sensitivity kernels, and the like, are welcome to e-mail me about it or read:
- en.wikipedia.org/wiki/Banana_Doughnut_theory (Wikipedia page on banana-doughnut kernels)
- geoazur.fr/GLOBALSEIS/nolet/BDdiscussion.html (Guust Nolet, a renowned seismologist, on kernels)
- Tromp et al, Seismic tomography, adjoint methods, time reversal and banana-doughnut kernels (Geophysical Journal International, 2005)
There are many more references which I'll be happy to supply you with.
* This name, banana-doughnut, is not the result of some seismologist with an excess of imagination, but of the way these kernels usually look in a 3D Earth. Because velocity mostly increases with depth in the Earth, the ray path is curved -- hence 'banana'. However, in cross-section, this banana is hollowed out and it is ring-shaped -- hence the doughnut. Because the calculations for this video were made in 2D, however, there is no cross-section and hence no hole.