# Seismic wave

Seismic waves are the waves of energy caused by earthquakes, volcanic eruptions, magma movement, large landslides, and large man-made explosions that give out low-frequency acoustic energy. They are the energy that travels through the earth and is recorded on seismographs.

## Types of seismic wave

Seismic waves are elastic waves that propagate in solid or fluid materials. They can be divided into body waves that travel through the interior of the materials; surface waves that travel along surfaces or interfaces between materials; and normal modes, a form of a standing wave.

### Body waves

Body waves travel through the interior of the Earth along paths controlled by the material properties in terms of density and modulus (stiffness). The density and modulus, in turn, vary according to temperature, composition, and material phase. This effect resembles the refraction of light waves. There are two types of body waves, pressure waves or primary waves (P-waves) and shear or secondary waves (S-waves).

#### P-waves

P-waves can stand for either pressure wave or primary wave, are longitudinal waves that involve compression and expansion in the direction that the wave is moving and are always the first waves to appear on a seismogram as they are the fastest moving waves through solids. P-waves are pressure waves that travel faster than other waves through the earth to arrive at seismograph stations first, hence the name “Primary”. These waves can travel through any type of material, including fluids, and can travel nearly 1.7 times faster than the S-waves. In air, they take the form of sound waves, hence they travel at the speed of sound. Typical speeds are 330 m/s in air, 1450 m/s in water and about 5000 m/s in granite.

Almost all the information available on the structure of the Earth’s deep interior is derived from observations of the travel times, reflections, refractions and phase transitions of seismic body waves, or normal modes. P-waves travel through the fluid layers of the Earth’s interior, and yet they are refracted slightly when they pass through the transition between the semisolid mantle and the liquid outer core. As a result, there is a P-wave “shadow zone” between 103° and 142° from the earthquake’s focus, where the initial P-waves are not registered on seismometers. In contrast, S-waves do not travel through liquids.

#### S-waves

S-wavessecondary waves, or shear waves (sometimes called elastic S-waves) are transverse waves that move perpendicular to the direction of wave propagation, and the main restoring force comes from shear stress. S-waves are slower than P-waves. Following an earthquake event, S-waves arrive at seismograph stations after the faster-moving P-waves and displace the ground perpendicular to the direction of propagation. Therefore, they appear later than P-waves on a seismogram.

Therefore, S-waves can’t propagate in liquids with zero (or very low) viscosity; However, they may propagate in liquids with high viscosity. They can propagate through solid rocks because these rocks have enough shear strength. The shear strength is one of the forces that hold the rock together, preventing it from falling into pieces. Liquids lack shear strength. This is the reason why, if you take a glass of water and suddenly remove the glass, the water will not keep its shape. In fact, it is just a matter of rigidity: S-waves need a medium that is rigid enough for them to propagate. This is why S-waves cannot propagate through liquids.

Depending on the propagational direction, the wave can take on different surface characteristics; for example, in the case of horizontally polarized S waves, the ground moves alternately to one side and then the other. S-waves can travel only through solids, as fluids (liquids and gases) do not support shear stresses. S-waves are slower than P-waves, and speeds are typically around 60% of that of P-waves in any given material. Shear waves can’t travel through any liquid medium, so the absence of S-wave in earth’s outer core suggests a liquid state.

### Surface waves

Surface waves are the result of P- and S-waves interacting with the surface of the Earth. These waves are dispersive, meaning that different frequencies have different velocities. Surface waves travel more slowly than P-waves and S-waves because they are the result of these waves traveling along indirect paths to interact with Earth’s surface. Surface waves are strongly excited when their source is close to the surface, as in a shallow earthquake or a near surface explosion, and are much weaker for deep earthquake sources.

Because they travel along the surface of the Earth, their energy decays less rapidly than body waves (1/distance2 vs. 1/distance3), and thus the shaking caused by surface waves is generally stronger than that of body waves. The two main surface wave types are Rayleigh waves, which have both compressional and shear motions, and Love waves, which are purely shear.

#### Rayleigh wave

Rayleigh waves are a type of surface acoustic wave that travel along the surface of solids; result from the interaction of P-waves and vertically polarized S-waves with the surface and can exist in any solid medium. The existence of Rayleigh waves was predicted in 1885 by Lord Rayleigh, after whom they were named.

#### Love wave

Love waves, named after Augustus Edward Hough Love, are formed by horizontally polarized S-waves interacting with the surface, and can only exist if there is a change in the elastic properties with depth in a solid medium, which is always the case in seismological applications. Since Love waves travel on the Earth’s surface, the strength (or amplitude) of the waves decrease exponentially with the depth of an earthquake. Love waves are the most destructive outside the immediate area of the focus or epicentre of an earthquake. They are what most people feel directly during an earthquake.

### Normal modes

Free oscillations of the Earth are standing waves, the result of interference between two surface waves traveling in opposite directions. Interference of Rayleigh waves results in spheroidal oscillation S while interference of Love waves gives toroidal oscillation T. The modes of oscillations are specified by three numbers: $$_nS_l^m$$, where $$l$$ is the angular order number (or spherical harmonic degree). The number $$m$$ is the azimuthal order number. It may take on $$2l+1$$ values from $$-l$$ to $$+l$$. The number $$n$$ is the radial order number. It means the wave with $$n$$ zero crossings in radius. For spherically symmetric Earth the period for given $$n$$ and $$l$$ does not depend on $$m$$.

## References

1. Lowrie, William. The Fundamentals of Geophysics. Cambridge University Press, 1997, p. 149.
2. United States Geological Survey, SVG by Vanessa Ezekowitz. Wikimedia. https://commons.wikimedia.org/wiki/File:Earthquake_wave_shadow_zone.svg
3.  “Why can’t S-waves travel through liquids?”. Earth Observatory of Singapore. Retrieved 2019-12-06. https://www.earthobservatory.sg/faq-on-earth-sciences/why-cant-s-waves-travel-through-liquids
4. Greenwood, Margaret Stautberg; Bamberger, Judith Ann (August 2002). “Measurement of viscosity and shear wave velocity of a liquid or slurry for on-line process control”. Ultrasonics. 39 (9): 623–630. doi:10.1016/s0041-624x(02)00372-4. ISSN 0041-624X. PMID 12206629.
5. Seismic wave. Wikipedia. https://en.wikipedia.org/wiki/Seismic_wave
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