## Seismic Waves and Earth’s Interior

The are many different seismic waves, but all of basically of four types:

• Compressional or P (for primary)
• Transverse or S (for secondary)
• Love
• Rayleigh

An earthquake radiates P and S waves in all directions and the interaction of the P and S waves with Earth’s surface and shallow structure produces surface waves.

Near an earthquake the shaking is large and dominated by shear-waves and short-period surface waves. These are the waves that do the most damage to our buildings, highways, etc. Even in large earthquakes the intense shaking generally lasts only a few tens of seconds, but it can last for minutes in the greatest earthquakes. At farther distances the amplitude of the seismic waves decreases as the energy released by the earthquake spreads throughout a larger volume of Earth. Also with increasing distance from the earthquake, the waves are separated apart in time and dispersed because P, S, and surface waves travel at different speeds.

Seismic waves can be distinguished by a number of properties including the speed the waves travel, the direction that the waves move particles as they pass by, where and where they don’t propagate. We’ll go through each wave type individually to expound upon the differences.

The first two wave types, P and S , are called body waves because they travel or propagate through the body of Earth. The latter two are called surface waves they the travel along Earth’s surface and their amplitude decreases with depth into Earth.

Seismic Wave Speed

Seismic waves travel fast, on the order of kilometers per second (km/s). The precise speed that a seismic wave travels depends on several factors, most important is the composition of the rock. We are fortunate that the speed depends on the rock type because it allows us to use observations recorded on seismograms to infer the composition or range of compositions of the planet. But the process isn’t always simple, because sometimes different rock types have the same seismic-wave velocity, and other factors also affect the speed, particularly temperature and pressure. Temperature tends to lower the speed of seismic waves and pressure tends to increase the speed. Pressure increases with depth in Earth because the weight of the rocks above gets larger with increasing depth. Usually, the effect of pressure is the larger and in regions of uniform composition, the velocity generally increases with depth, despite the fact that the increase of temperature with depth works to lower the wave velocity.

Compressional or P-Waves

P-waves are the first waves to arrive on a complete record of ground shaking because they travel the fastest (their name derives from this fact – P is an abbreviation for primary, first wave to arrive). They typically travel at speeds between ~1 and ~14 km/sec. The slower values corresponds to a P-wave traveling in water, the higher number represents the P-wave speed near the base of Earth’s mantle.

P-waves are sound waves, it’s just that in seismology we are interested in frequencies that are lower than humans’ range of hearing (the speed of sound in air is about 0.3 km/sec). The vibration caused by P waves is a volume change, alternating from compression to expansion in the direction that the wave is traveling. P-waves travel through all types of media – solid, liquid, or gas.

S-Waves

As a transverse wave passes the ground perpendicular to the direction that the wave is propagating. S-waves are transverse waves.

Secondary , or S waves, travel slower than P waves and are also called “shear” waves because they don’t change the volume of the material through which they propagate, they shear it. S-waves are transverse waves because they vibrate the ground in a the direction “transverse”, or perpendicular, to the direction that the wave is traveling. Even though they are slower than P-waves, the S-waves move quickly. Typical S-wave propagation speeds are on the order of 1 to 8 km/sec. The lower value corresponds to the wave speed in loose, unconsolidated sediment, the higher value is near the base of Earth’s mantle.

An important distinguishing characteristic of an S-wave is its inability to propagate through a fluid or a gas because a fluids and gasses cannot transmit a shear stress and S-waves are waves that shear the material.

In general, earthquakes generate larger shear waves than compressional waves and much of the damage close to an earthquake is the result of strong shaking caused by shear waves.

Love Waves

Love waves are transverse and restricted to horizontal movement – they are recorded only on seismometers that measure the horizontal ground motion.

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. In general, earthquakes generate Love waves over a range of periods from 1000 to a fraction of a second, and each period travels at a different velocity but the typical range of velocities is between 2 and 6 km/second.

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

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. Typical speeds for Rayleigh waves are on the order of 1 to 5 km/s.

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.

Seismic Wave Propagation
Waves on a Seismogram

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.e. the rocks) are commonly observable on seismograms

• Refraction
• Reflection
• Dispersion
•  Diffraction
•  AttenuationWe can examine the two simplest types of interaction refraction and reflection.
RefractionAs 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. This speed decrease bends waves backwards and creates a “P-wave Shadow Zone” between about 100° and 140° distance (1° = 111.19 km).

### Reflection

When a wave encounters a change in material properties (seismic velocities and or density) its energy is split into reflected and refracted waves.

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. And your reflection in a mirror or pool of water is composed of reflected light waves. In seismology, reflections are used to prospect for petroleum and investigate Earth’s internal structure. In some instances reflections from the boundary between the mantle and crust may induce strong shaking that causes damage about 100 km from an earthquake (we call that boundary the “Moho” in honor of Mohorovicic, the scientist who discovered it).

A seismic reflection occurs when a wave impinges on a change in rock type (which usually is accompanied by a change in seismic wave speed). Part of the energy carried by the incident wave is transmitted through the material (that’s the refracted wave described above) and part is reflected back into the medium that contained the incident wave.

The amplitude of the reflection depends strongly on the angle that the incidence wave makes with the boundary and the contrast in material properties across the boundary. For some angles all the energy can be returned into the medium containing the incident wave.

The actual interaction between a seismic wave and a contrast in rock properties is more complicated because an incident P wave generates transmitted and reflected P- and S-waves and so five waves are involved. Likewise, when an S-wave interacts with a boundary in rock properties, it too generates reflected and refracted P- and S-waves.

Dispersion

A dispersed Rayleigh wave generated by an earthquake in Alabama near the Gulf coast, and recorded in Missouri.

It is mentioned above that surface waves are dispersive – which means that different periods travel at different velocities. The effects of dispersion become more noticeable with increasing distance because the longer travel distance spreads the energy out (it disperses the energy). Usually, the long periods arrive first since they are sensitive to the speeds deeper in Earth, and the deeper regions are generally faster.

### P-Waves in Earth

The paths of P-wave energy for a shallow earthquake located at the top of the diagram. The main chemical shells of Earth are shown by different colors and regions with relatively abrupt velocity changes are shown by dashed lines. The curves show the paths of waves, and the lines crossing the rays show mark the wavefront at one minute intervals.

The mathematics behind wave propagation is elegant and relatively simple, considering the fact that similar mathematical tools are useful for studying light, sound, and seismic waves. We can solve these equations or an appropriate approximation to them to compute the paths that seismic waves follow in Earth. The diagram below is an example of the paths P-waves generated by an earthquake near Earth’s surface would follow.

Note the curvature of the rays in the mantle, the complexities in the upper mantle, and the dramatic impact of the core on the wavefronts. The decrease in velocity from the lower mantle to the outer core casts a “shadow” on the P-waves that extends from about 100° to 140° distance. Other waves such as surface waves and body waves reflecting off the surface are recorded in the “shadow” region, but the P-wave “dies out” near 100°. Since the outer core is fluid, and S-waves cannot travel through a fluid, the “S-wave shadow zone” is even larger, extending from about 100° to 180°.

I am Rashid Aziz Faridi ,Writer, Teacher and a Voracious Reader.
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### 3 Responses to Seismic Waves and Earth’s Interior

1. abul hasan says:

good.

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