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Waves

A wave is some sort of movement that travels through space and time. Some common waves we hear of or experience everyday are: ocean waves, sound waves, light waves, radio waves, microwaves, etc. Seismology focuses primarily on waves that travel through the Earth, which are called body waves, and to a lesser extent, surface waves. Surface waves do not provide an aid in determining the structure of the Earth due to the fact that they stay on the surface and their amplitude decreases sharply with depth. Two types of surface waves are Love waves and Rayleigh waves. Body waves make their way through the Earth and are generally called P-waves and S-waves.

ã Copyright 2004. L. Braile. Permission granted for reproduction and use of animations for non-commercial uses.

How Waves Propagate

There are many ways for waves to travel, but the ways we are most concerned with are the way body waves travel. P-waves will travel similar to a spring being pushed back and forth. S-waves travel up and down like a rope attached to a wall that is being jerked up and down. The wavelength is the distance or time between two crests or compressions of a wave. The opposite of the crest or compression is the trough or dilatation. Amplitude (a) is the maximum displacement from the stationary position (Mussett, 25). The velocity or speed of the wave is measured in meters/second and is equal to the frequency times wavelength. Frequency (f) is the amount of crests or compressions that pass a fixed point in one second.

ã Copyright 2004. L. Braile. Permission granted for reproduction and use of animations for non-commercial uses.

P-waves and S-waves

P- and S-waves are also known as longitudinal waves and transverse waves. As mentioned before, P-waves act like a spring and can be remembered as pressure or push-pull waves. Also, when moving through an object, P-waves will compress and change the shape and size of that object. S-waves act like the rope attached to the wall and, when moving through an object, only change the shape of that object. S-waves can be remembered as shear or shake waves. Both waves will decay over volume.

Velocity of Body Waves

P-waves will always travel faster than S-waves due to the way they deform the material they are traveling through and the restoring forces of that material. Its also important to understand that S-waves can’t travel through liquids. This is due to the fact that liquids have no shear strength and tend not to restore their shape. So for the S-wave that only changes the shape of the object it travels through, there would be no effect on liquids. Because liquids do resist compression, P-waves easily travel through them.

The velocity of a wave depends on two factors: the stronger the object, or increase in restoring force, the greater the propagation velocity, and the larger the mass, or density, the slower the propagation velocity.

Attenuation

Waves lose their energy through a process called attenuation, which occurs in three different ways:

  1. Intrinsic Attenuation: water content can increase S-wave attenuation compared to P-waves, and energy can transfer to material as heat.
  2. Geometric Spreading: there is less energy per surface area, due to the surface area increasing as a wave front spreads, moving further from the source.
  3. Scattering Attenuation: redistribution of energy as waves are reflected, absorbed by rock that is not fully elastic, or dispersed in less consolidated material.

Refraction and Snell’s Law

Waves travel outwards from their source along paths called wave fronts. Rays are a small portion of the wave fronts that have been emitted in all directions from their source. Rays are always perpendicular to wave fronts and are simpler to examine than wave fronts in seismology.

When rays are traveling through the Earth they go through different layers. If the wave happens to hit a layer with a different velocity, the wave is refracted. If that velocity is greater, the ray will speed up. An example would be playing with a toy truck in some sand next to pavement. If the truck is being driven from the sand to the pavement, the wheels hitting the pavement will speed up and will be turned a certain way depending on the initial direction the toy truck was traveling.

Snell’s law can help us determine the amount of change in direction, or how much the ray was refracted. As the waves propagate through the layers (the first with a slower velocity), there will be two parallel waves and their rays will be perpendicular to them. The time between the wave fronts stays the same and wavelength increases in the second rock layer. So we find:

It should be noted however that this version of Snell’s Law will only work for a flat earth, and in order to adjust for circular layering, it is necessary to each side of the equation by it’s section’s radius.

In the ray path figure, i1 and i2 are the angles between the rays and are normal or perpendicular to the interface, or the place where the ray enters the second layer. i1 is the angle of incidence and i2 is the angle of refraction.

Reflection

The reflection of seismic waves is extremely useful for imaging layers in the subsurface, and can reveal faulting, folding, and a variety of other structural features. The main concept of reflection seismology is that when a seismic pulse is emitted, it will travel outwards and some of the waves are bounced back towards the surface upon reaching a reflector. Snell’s Law is also applicable to reflection.

 

References

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