Both P and S waves travel outward from an earthquake focus inside the earth. The waves are often seen as separate arrivals recorded on seismographs at large distances from the earthquake. The direct P wave arrives first because its path is through the higher speed, dense rocks deeper in the earth. The PP one bounce and PPP two bounces waves travel more slowly than the direct P because they pass through shallower, lower velocity rocks.
Thus the simple rule of thumb for earthquakes in this distance range is the distance is about eight times the arrival time of S-wave less the arrival time of the P-wave. That means that we can estimate the distance an earthquake is from a seismometer. The earthquake can be in any direction, but must be the estimated distance away.
Geometrically that means that the earthquake must be located on a circle surrounding the seismometer, and the radius of the circle is about eight times the observed wave travel-time difference in kilometers. If we have two other seismometers which recorded the same earthquake, we could make a similar measurement and construct a circle of possible locations for each seismometer. Since the earthquake location since it must lie on each circle centered on a seismometer, if we plot three or more circles on a map we could find that the three circles will intersect at a single location - the earthquake's epicenter.
Using the "S minus P arrival time" to locate an earthquake. You need at least three stations and some idea of the P and S velocities between the earthquake and the seismometers. In practice we use better estimates of the speed than our simple rule of thumb and solve the problem using algebra instead of geometry. We also can include the earthquake depth and the time that earthquake rupture initiated called the "origin time" into the problem.
Love waves are transverse waves that vibrate the ground in the horizontal direction perpendicular to the direction that the waves are traveling. They are formed by the interaction of S waves with Earth's surface and shallow structure and are dispersive waves. The speed at which a dispersive wave travels depends on the wave's period. Love waves are transverse and restricted to horizontal movement - they are recorded only on seismometers that measure the horizontal ground motion.
Another important characteristic of Love waves is that the amplitude of ground vibration caused by a Love wave decreases with depth - they're surface waves. Like the velocity the rate of amplitude decrease with depth also depends on the period.
Rayleigh waves are the slowest of all the seismic wave types and in some ways the most complicated. Like Love waves they are dispersive so the particular speed at which they travel depends on the wave period and the near-surface geologic structure, and they also decrease in amplitude with depth. Rayleigh waves are similar to water waves in the ocean before they "break" at the surf line. As a Rayleigh wave passes, a particle moves in an elliptical trajectory that is counterclockwise if the wave is traveling to your right.
The amplitude of Rayleigh-wave shaking decreases with depth. As you might expect, the difference in wave speed has a profound influence on the nature of seismograms. Since the travel time of a wave is equal to the distance the wave has traveled, divided by the average speed the wave moved during the transit, we expect that the fastest waves arrive at a seismometer first.
Thus, if we look at a seismogram, we expect to see the first wave to arrive to be a P-wave the fastest , then the S-wave, and finally, the Love and Rayleigh the slowest waves. Although we have neglected differences in the travel path which correspond to differences in travel distance and the abundance waves that reverberate within Earth, the overall character is as we have described. The fact that the waves travel at speeds which depend on the material properties elastic moduli and density allows us to use seismic wave observations to investigate the interior structure of the planet.
We can look at the travel times, or the travel times and the amplitudes of waves to infer the existence of features within the planet, and this is a active area of seismological research. To understand how we "see" into Earth using vibrations, we must study how waves interact with the rocks that make up Earth. Several types of interaction between waves and the subsurface geology i. As a wave travels through Earth, the path it takes depends on the velocity.
Perhaps you recall from high school a principle called Snell's law, which is the mathematical expression that allows us to determine the path a wave takes as it is transmitted from one rock layer into another.
The change in direction depends on the ratio of the wave velocities of the two different rocks. When waves reach a boundary between different rock types, part of the energy is transmitted across the boundary.
The transmitted wave travels in a different direction which depends on the ratio of velocities of the two rock types. Part of the energy is also reflected backwards into the region with Rock Type 1, but I haven't shown that on this diagram.
Refraction has an important affect on waves that travel through Earth. In general, the seismic velocity in Earth increases with depth there are some important exceptions to this trend and refraction of waves causes the path followed by body waves to curve upward. The overall increase in seismic wave speed with depth into Earth produces an upward curvature to rays that pass through the mantle. A notable exception is caused by the decrease in velocity from the mantle to the core.
The second wave interaction with variations in rock type is reflection. I am sure that you are familiar with reflected sound waves; we call them echoes.
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