SURFACE WAVES: CHARACTERISTICS, TYPES AND EXAMPLES - PHYSICAL - 2025

Surface waves are those in which the vibrating particles have motion in two dimensions, such as the waves that are produced when a stone is dropped into a pond or lake.

This type of wave occurs at the interface between two different media, such as the ocean and the air, or between the surface of the Earth and the air. These are waves in which the particles experience transverse combined with longitudinal displacements, that is, two-dimensional.

Figure 1. Surface waves in a pond. Source: Pixabay.

For example, the water particles on the ocean surface - waves - move in circular paths. When the waves break on the shore, longitudinal displacements predominate and so you see the algae or a piece of wood that is floating moving smoothly from front to back.

Waves also move on the Earth's surface in a manner analogous to ocean waves. They travel at a slower speed than the waves that move internally through the earth's volume, but they are capable of causing resonance in buildings more easily.

Since waves produce vibrations and carry energy, they have destructive effects during earthquakes.

Figure 2. Surface waves in the ocean. The water particles move in a clockwise direction when the movement of the wave is from left to right. At the highest point they are on the crest of the wave, while the lowest point is called the channel. Source of the left figure: F. Zapata. Right figure source: Giambattista, A. 2010. Physics. 2nd. Edition. McGraw Hill.

Types of surface waves

Any type of wave, whether superficial or not, is a solution of the wave equation, which applies to almost any type of wave motion, not only mechanical, as in the examples described, but also electromagnetic waves, which are a different kind of waves as they are transverse.

The wave equation, which is obtained considering Newton's second law, is written like this:

In the above equation, u is the wave function that depends on the three spatial coordinates x, y, and z plus time t: u = u (x, y, z, t). Furthermore v is the velocity of the disturbance. The wave equation can be stated in other coordinate systems depending on the geometry required.

To find the solution of the equation, it is adjusted to the problem conditions, in which, for example, the geometry is delimited and the properties of the medium through which the disturbance moves are established.

There are many types of surface waves, such as:

-Gravitational waves (gravity waves) like ocean waves described at the beginning, in which gravity provides a restoring force that allows transversal movement.

-Surface swell in a pond, here is the surface tension of the water that exerts as a restoring force.

-Surface elastic waves that move on the Earth's surface during an earthquake.

-Electromagnetic waves, which despite being transversal, can be properly guided to move on a surface.

-Some types of waves that are produced in the strings of a guitar when the strings are struck with force.

Superficial elastic waves on the earth's surface

Figure 3. Surface wave on the earth's surface. The motion of the particles is a combination of transverse and longitudinal displacements. Source: Giambattista, A. 2010. Physics. 2nd. Edition. McGraw Hill.

When solving the wave equation, the solutions, as we have said, correspond to different types of waves. When the disturbance moves in a solid medium such as the earth's crust, it is possible to make some assumptions about it that simplify the process.

For this reason, the medium is considered to be perfectly elastic, homogeneous and isotropic, which means that its properties are the same regardless of position or direction.

With this in mind, two of the solutions to the wave equation in an elastic medium correspond to surface waves:

- Waves of Rayleigh, named after Lord Rayleigh (1842-1919), the British physicist who first described them.

-Waves of Love, by Augustus Love, British geophysicist and mathematician (1863-1940) who developed the theory of these waves in his works on elasticity.

In seismic, these waves are called L waves, to differentiate them from P waves and S waves, both considered volume waves (body waves) that are also a solution to the wave equation with the conditions described above. P waves are longitudinal and S waves are transverse.

Examples of surface waves

Rayleigh waves

In a Rayleigh wave, the wavefront particles vibrate in the vertical plane, therefore they are said to be vertically polarized. The particles move in an ellipse, unlike the waves on the surface of the ocean, whose motion is circular, as was said at the beginning (although near the coast they are rather elliptical).

The major axis of the ellipse is vertical and the minor axis follows the direction of propagation, as shown in the figure. There it is also noted that the movement is retrograde, that is, it is carried out in an anti-clockwise direction.

Figure 4. Rayleigh wave. Source: Lowrie, W. 2007. Fundamentals of Geophysics. 2nd. Edition. Cambridge University Press.

Another important difference with water waves is that Rayleigh waves can only propagate in solid media, since there is a shear force that does not occur in liquids.

The amplitude of the particle displacement decreases exponentially with depth, since the wave is confined to the surface, although if it is a high intensity earthquake, the waves can circle the Earth several times before vanishing completely..

Waves of Love

In Love waves the particles are horizontally polarized and have a large amplitude of motion parallel to the surface. They move at a slightly slower speed than Rayleigh waves, although the speed in these types of waves depends on the wavelength (dispersive wave).

For these waves to propagate, there must be a low-speed layer superimposed on at least one higher-speed layer in the middle. Like Rayleigh waves, Love waves produced during an earthquake can circle the Earth several times before dispersing their energy.

Figure 5. Waves of Love. Source: Wikimedia Commons. Nicoguaro

Ground roll

It is common to find this variant of Rayleigh waves, called ground roll, in seismic exploration records. It is considered noise and must be avoided, because due to its great amplitude, it sometimes masks the reflections that you are looking to see.

Ocean waves

At great depth, ocean waves are longitudinal waves, like those of sound. This means that its direction of propagation is the same as the direction in which the particles vibrate.

However, the wave, near the surface, has both longitudinal and transverse components, causing the particles to follow an almost circular path (see figure 2 right).

Figure 6. Ocean waves are surface waves. Source: Pixabay.

References

1. Figueroa, D. 2005. Waves and Quantum Physics. Physics Series for Science and Engineering. Edited by D. Figueroa.
2. Giambattista, A. 2010. Physics. McGraw Hill.
3. Lowrie, W. 2007. Fundamentals of Geophysics. 2nd. Edition. Cambridge University Press.
4. Wikipedia. Waves of Love. Recovered from: es.wikipedia.org.
5. Wikipedia. Rayleigh waves. Recovered from: es.wikipedia.org.
6. Wikipedia. Surface waves. Recovered from: en.wikipedia.org.