seismic surface waves In addition to P-waves and S-waves which penetrate deeply into the Earth (see
seismic body waves), a seismic source such as an explosion or earthquake also generates waves which travel along the surface of the Earth. The most commonly observed waves are called Rayleigh waves, after Lord Rayleigh who predicted their existence in 1887. These waves are analogous to waves travelling across the ocean. A swimmer is not only pitched up and down, but also to and fro as a wave passes. The actual movement of the swimmer describes an ellipse. In a Rayleigh wave, the motion of a point in the Earth as the wave passes is also elliptical (Fig. 1a). The motion of waves in the ocean dies out quickly with depth, and this is also the case with Rayleigh waves. On the land, these waves spread out in only two dimensions, compared to three for body waves. Thus, their amplitudes diminish with distance more slowly than do those of body waves. Surface waves are usually a prominent feature on seismograms; when particularly large earthquakes occur, the surface waves can propagate so as to encircle the Earth several times. The mathematical treatment of surface wave propagation is complex, but Rayleigh waves can be thought of as arising from the constructive interference of multiply reflected P-waves and S-waves (S
v) travelling in a vertical plane. Seismic surface waves of the second type are called Love waves, after A. E. H. Love, who developed a theory for their existence early in the twentieth century. These waves can be thought of as the constructive interference of multiply reflected S-waves whose particle motion is horizontal (S
H). In each case, the depth to which the waves penetrate is a function of their frequency. Lower frequencies have longer wavelengths, because of the relationship
v =
fl (where
v = velocity,
f = frequency, and
l = wavelength), and penetrate deeper into the Earth. Since velocity generally increases with depth in the Earth, the lower frequencies pass through material with higher average velocity. This gives rise to a major attribute of surface waves, which is that they are dispersed (i.e. velocity is a function of frequency). Thus, surface waves as seen on seismograms are not compact wavelets like body waves, but appear as long wave trains in which the frequency slowly increases (Fig. 1b). Surface waves are used to determine a general picture of Earth structure through the analysis of their dispersion. Since different regions of the Earth have different distributions of velocity with depth, each region is characterized by different dispersion curves (plots of the variation of velocity with frequency,
f, or period,
T, where
T = 1/
f). A typical dispersion curve for a continental region is shown in Fig. 1c. As shown in the plot, two velocities are associated with the propagation of surface waves. One is phase velocity, which is the velocity at which a particular feature on the wave train (i.e. a peak) or frequency component travels. The other is group velocity, which is the velocity at which a packet of energy or band of frequency travels. There is a mathematical relationship between these two velocities, but they are often treated independently in efforts to determine Earth structure from surface waves.
The analysis of the dispersion of surface waves has led to many important discoveries about the Earth. For example, the profound difference between the deep structure of the oceans and the continents, the existence of a widespread low-velocity layer in the upper mantle, and regional differences between the deep structure of continental features such as mountain belts and ancient cratons were all established on the basis of dispersion of surface waves. Although surface-wave dispersion yields average models for the region between two seismograph stations, it is capable of detecting low-velocity zones, and it is most sensitive to shear-wave velocity variations. These attributes are both advantageous to the seismologist in that they complement body-wave studies. Surface-wave studies are not limited to the analysis of deep structures. High-frequency surface waves can be used on a small scale in engineering studies. Because they are so near the surface, explosions generate surface waves strongly. This fact is a nuisance in seismic reflection studies (see
seismic exploration methods) and requires special measures to attenuate the large surface waves. On the other hand, part of the method for detecting nuclear explosions is based on the large surface waves they generate. In contrast, deep earthquakes can be recognized by the weak surface waves they generate. In general, the analysis of surface waves is a useful and cost-effective tool for determining Earth structure and seismic source characteristics. The Earth models derived from the analysis of surface waves are, however, more generalized than those obtained using most other seismic techniques.
G. R. Keller
Bibliography
Bullen, K. E. and and Bolt, B. A. (1985) An introduction to the theory of seismology. Cambridge University Press.
Lay, T. and and Wallace, T. C. (1995) Modern global seismology. Academic Press, San Diego.
