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What features should I look for to determine each of these kinds of waves in a seismogram? What signal processing methods (filters, transforms, etc...) should I use to determine them?

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There are two important ways to recognize different types of waves in seismic records:

  1. Their velocity. These waves travel at different speeds: P-waves are fastest, then S-waves, then Love waves, then Rayleigh. Since seismic recordings are measures of earth displacement, particle velocity, or water pressure over elapsed time, this means the waves show up at different times in the record. If we know or guess their velocities, then we can model the arrival times at various stations and try to recognize the different wavefronts. Here's one example of a shot record (distance x on the horizontal axis, time t on the vertical) where you can see reflected P-waves and Rayleigh waves: the slope of the arrivals is a function of wave speed. Once we can discriminate them in some domain (commonly tx, fx, or taup), we can design filters that exploit this fact.
  2. Their mode of oscillation. The waves are distinguished by different types of particple motion. For example, P-waves are longitudinal, S-waves are transverse, Rayleigh waves are circular. So if we have a sensor that can detect particle motion in three dimensions, we can recognize waveforms that way. In the oil & gas industry, where seismic reflection data is an important tool, so-called multi-component (or three-component, or 3C) sensors are now widespread; here's one example. I'm afraid it's beyond me, but I know one of the methods they use to unpack the different waveform polarizations is singular value decomposition.

Reconciling P- and S-wave reflections is one of the great problems in reflection seismology today. Everything is made more complicated by the fact that these waves can convert from one to the other. For example, when P-waves reflect from an elastic interface, like rock broundaries, some energy is converted into S-waves. Furthermore, some recording equipment is more sensitive to vertical ground motion than to horizontal (e.g. single component geophones), so our records are often strongly filtered. The result is that unpeeling multiple wave types is not easy.

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You can automatically detect the P and S waves for an event but I don't know of a way to automatically extract the Rayleigh and Love waves directly from the seismograms.

As @kwinkunks points out things are complicated in the real world. Understanding an event is an iterative bootstrapping process that is best done by looking at recordings from several stations and preferably with multi-component recordings.

My experience is with regional scale earthquake seismology where the signal amplitude is also a powerful discriminator - the fast, low amplitude P wave arrives first. Then the slower, higher amplitude S wave comes in later. You can see this happening on the seismogram that you originally linked to or you can watch this somewhat relevant video of a dog.

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    $\begingroup$ It's true that the S-wave arrival is often stronger than the P-wave; surfaces waves are usually stronger still. But this is not always true (for example this record and this record), and amplitude is therefore not a reliable indicator of wave mode. The absolute and relative amplitudes depend on lots of other things — the type of source, its focal mechanism, the distance and direction of the sensor, the medium, and the elastic impedances of any reflectors. $\endgroup$ – kwinkunks Apr 22 '14 at 0:05
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To supplement the current and very good answers , we can look at a seismogram:

enter image description here

from (http://www.bgs.ac.uk/discoveringGeology/hazards/earthquakes/images/dia_seismogram.jpg)

As you can see, we know that P-waves(compressional) will generally arrives before S-waves(shear). Also, in general, S-waves will arrive before the much stronger in response body waves. To distinguish which waves are which, we use a three directional seismometer, which will record three different seismograms: Radial, North-South, and East-West. Notice that all these directions are perpendicular to each other. The characteristic wave motion of the specific wave you are analyzing will cause stronger or weaker perturbations on each of the different directional seismographs depending on how the wave arrives. For example, if a shear wave arrives directly beneath a the seismometer, because of the wave motion, it will show up most on the East-West and North-South seismograms and less so on the radial seismogram where there is no deformation caused in that direction.

Suffice to say, there are a lot of factors and "tricks" that seismologists use to distinguish these waves from one another. Becoming a master at this takes years of doing this, and being good at this could also result in a very nice paycheck.

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