Seismo Blog

Lord Rayleigh and the Love Waves

Categories:   Surface Waves  |  Seismic Waves

July 27, 2009 

Figure 1: Diagram showing retrograde, elliptical particle motion of Rayleigh waves.

Figure 1

When you read the headline and notice the words "Love Waves", please don't think the Seismo Blogger is diverging into the X-rated territory of the web. Instead, he is delivering on the promise made two weeks ago, to explain more about surface waves (see blog July 15, 2009). These waves, which in contrast to P- and S-Waves do not travel through the interior of the Earth, race along its surface instead. They also come in two flavors which differ in at least two aspects: the particle motion they generate and the speed with which they circle the globe.

Diagram showing back-and-forth particle motion of Love waves perpendicular to the direction of propagation.

Figure 2

One type of surface wave was first mathematically described by John William Strutt, a young British physicist. He later not only followed his father into nobility as the third Baron Rayleigh, but also became one of the most prominent researchers of his time (1842-1919) and was honored for his work with the Nobel prize in 1904. At first glance, the Rayleigh waves look like the surface waves in the water (see blog July 15, 2009), but when observing carefully, one will notice that their respective particle motions are different. In a water wave, each particle makes a circular motion in the direction of the propagation of the wave. In a Rayleigh wave, the particles make an elliptical movement against the propagation direction. Hence, their motion is retrograde (see Figure 1). A very nice animation of the difference in particle motion between a water and a Rayleigh wave can be found here.

Photograph of A.E.H. Love

Figure 3. [From left to right] Lord Rayleigh and A.E.H. Love

The second type of surface wave was discovered in 1911 by another Englishman, Augustus Edward Hough Love. Although not quite as famous as Lord Rayleigh, Love nevertheless held the position of Professor for Natural Philosophy at Oxford University for 41 years. Love found that the particles in the waves named after him do not move in a rotating fashion at all. Instead, they jerk back and forth perpendicular to the direction of wave propagation (see Figure 2). They are therefore similar to an S-wave (see blog September 10, 2008).

The speed with which both types of waves circle the globe is truly mind boggling. Love waves race around the Earth at almost 10,000 miles per hour. Their relatives, the Rayleigh waves, lag behind slightly, but still speed at about 7800 miles an hour. It seems that only the International Space Station is faster. As of this writing, the 13 astronauts aboard ISS plough through their orbit at 16,218 miles per hour (hra042).