equivoluminal waves. P-waves travel at speeds ranging from 300


m/s in shallow soils to 8 km/s deep in the Earth’s crust. Tey can propagate in solid materials, water and air. S-waves travel more slowly, at 60% to 70% of the speed of P-waves. Te exception is just beneath the seabed, where the S-wave velocity varies strongly with the sediment type. In higher-porosity muds, the S-wave velocity can be less than 30 m/s. Fluids do not support S-waves so they can only propagate in solids. As a consequence, S-waves are only sensitive to the rock matrix, and relatively insensitive to the rock’s fluid content. A good illustration of an S-wave is the


Mexican wave, which was initiated during the soccer World Cup in in 1986 (Figure 1.32). Te phenomenon of creating a human shear wave is probably older, since it is also demonstrated in a film from 1963 (Son of Flubber).


1.3.3.2 Surface Waves


In the theory of elasticity, surface waves have been given names after their discoverers. In 1885, Lord Rayleigh published a paper where he described


a wave – now called the Rayleigh wave – that propagated along the free surface of a solid half-space (which means the Earth’s surface, in practice). Te wave includes both longitudinal and transverse motions which decrease exponentially in amplitude with distance from the surface. Te motions are part of the seismic waves that are produced on the earth by earthquakes, and are used in seismology to characterise the earth’s interior. Tey can also be generated by explosions, railway trains, traffic, ocean waves, etc. Rayleigh waves are used in geophysics and geotechnical engineering for the characterisation of the near subsurface. Tey have a speed slightly less than shear waves by a factor dependent on the elastic constants of the material. In


the ground, the speed depends on frequency, and is of the order of 50–300 m/s. Typically, the Rayleigh velocity is Vr < 0.92 Vs. Being confined near the surface, their amplitude decays at the rate of 1 over the square root of the radial distance travelled. Surface waves thus decay more slowly with distance than do P- and S-waves. Low velocity, low frequency and high amplitude Rayleigh


waves are frequently present in land seismic records and can obscure the seismic reflections, degrading the overall data quality. Within the industry, the waves are called ‘ground roll’. In 1911, Love considered pure shear wave motion in an


elastic layer bounded by vacuum and with a higher velocity elastic half-space below. Te Love wave, being a horizontally polarised surface wave, is a result of the interference of many S-waves guided by the elastic layer. Tese waves propagate


Figure 1.33: (a) John William Strutt, 3rd Baron Rayleigh (1842–1919) was an English physicist and Professor of Physics at the University of Cambridge (following James Clerk Maxwell). He predicted the existence of the surface waves now known as Rayleigh waves. His textbook, The Theory of Sound, is still referred to by acoustic engineers today. (b) Augustus Edward Hough Love (1863–1940) was a British geophysicist and mathematician famous for his work on the mathematical theory of elasticity. He was appointed Professor of Natural Philosophy at Oxford University. He developed a mathematical model of surface waves known as Love waves. (c) Robert Stoneley (1894–1976), British seismologist and Professor of Seismology at the University of Cambridge. Although he did not write any text books, it was standard in advanced courses in seismology to study his papers. (d) J. G. J. Scholte (1907–1987) worked at the Royal Netherlands Meteorological Institute as a seismologist 1950–1970 and was at the same time Professor of General Geophysics at Utrecht University 1957–1970. He made a number of contributions to theoretical seismology. Scholte (1958) wrote a treatise on Rayleigh waves in elastic media.


Figure 1.32: The Mexican wave is an illustration of a shear wave propagating perpendicular to the movement of each spectator.


a


b


c


d 25


FlorianK/wikipedia.


Prof. dr. J.G.J. Scholte (object number: 0285-4202), from the collection of the University museum Utrecht, The Netherlands


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