An introduction to surface waves.

Surface waves versus body waves:

Waves that propagate through the earth as elastic waves are referred to as seismic waves. There are two broad categories of seismic waves: body waves and surface waves.

Body waves:

Body waves are elastic waves that propagate through the Earth's interior. In reflection and refraction prospecting, body waves are the source of information used to image the Earth's interior. Body waves propagate away from the source in all directions.

Seismic body waves can be further subdivided into two classes of waves: P-waves and S-waves.

• P-waves are also called primary waves, because they propagate through the medium faster than the other wave types. Material is being extended and compressed as P-waves propagate through the medium. P-waves are analogous to sound waves propagating through the air.

• S-waves are sometimes called secondary waves, because they propagate through the medium slower than P-waves. In S-waves, particles consistituting the medium are dispaced in a direction that is perpendicular to the direction that the wave is propagating.

Let's now introduce waves that only propagate near the surface.

Surface waves:

Surface waves are waves that propagate along the Earth's surface, where they are trapped.

Fig. 1: Trapped surface waves (in red).

The amplitude of surface waves at the surface of the Earth can be very large, but this amplitude decays exponentially with depth. If you consider the energetic point of view, surface waves are waves whose energy is concentrated near the Earth's surface. At large distances from the source, this type of waves is prominent as its energy decays with distance r from the source, as 1/r, whereas P and S wave-energy decays as 1/r². This type of waves can give us accurate information on the medium that the wave has travelled through.

The surface waves: Love and Rayleigh waves:

Love waves:

Love waves result from SH-waves trapped near the surface.

Fig. 2: Love wave motion process. (after Scientific American, 1978-1982).

They have the same propagation principle as S-waves that would stick to the surface and which would have no vertical motion. The particle motion is perpendicular to the wavefront, as is shown above.

Rayleigh waves:

Rayleigh waves are a combination of P-wave and SV-wave motion.

Fig. 3: Rayleigh wave motion process. (after Scientific American, 1978-1982)

The horizontal and vertical components of ground motion are out of phase. Because of that, the particle motion at a point of the free surface - here, the ground - is a counter-clockwise ellipse.

Fig. 4: Rayleigh wave particle motion (with a free surface at z=0).
The depths indicated with dotted lines are the original horizontal layers at z=0, z=-lambda/10, z=-lambda/5, z=-3*lambda/10, z=-2*lambda/5. The sine-like curves which move up and down show the particle motion.

Dispersion of surface waves.