## Seismic waves

The strain energy released by an earthquake is transmitted through the Earth by several types of seismic wave (Fig. 2.2), which propagate by elastic deformation of the rock through which they travel. Waves penetrating the interior of the Earth are known as body waves, and consist of two types corresponding to the two possible ways of deforming a solid medium. P waves, also known as longitudinal or compressional waves, correspond to elastic deformation by compression/dilation. They cause the particles of the transmitting rock to oscillate in the direction of travel of the wave so that the disturbance proceeds as a series of compressions and rarefactions. The velocity of a P wave Vp is given by:

p where k is the bulk modulus, |l the shear modulus (rigidity), and p the density of the transmitting medium. S waves, also known as shear or transverse waves, correspond to elastic deformation of the transmitting medium by shearing and cause the particles of the rock

Figure 2.2 Focus and epicenter of an earthquake and the seismic waves originating from it (after Davies, 1968, with permission from Iliffe Industrial Publications Ltd).

### Figure 2.1 Illustration of epicentral angle A.

Figure 2.2 Focus and epicenter of an earthquake and the seismic waves originating from it (after Davies, 1968, with permission from Iliffe Industrial Publications Ltd).

to oscillate at right angles to the direction of propagation. The velocity of an S wave Vs is given by:

Because the rigidity of a fluid is zero, S waves cannot be transmitted by such a medium.

A consequence of the velocity equations for P and S waves is that the P velocity is about 1.7 times greater than the S velocity in the same medium. Consequently, for an identical travel path, P waves arrive before S waves. This was recognized early in the history of seismology, and is reflected in the names of the body waves (P is derived from primus and S from secundus). The passage of body waves through the Earth conforms to the laws of geometric optics in that they can be both refracted and reflected at velocity discontinuities.

Seismic waves whose travel paths are restricted to the vicinity of a free surface, such as the Earth's surface, are known as surface waves. Rayleigh waves cause the particles of the transmitting medium to describe an ellipse in a vertical plane containing the direction of propagation. They can be transmitted in the surface of a uniform half space or a medium in which velocity changes with depth. Love waves are transmitted whenever the S wave velocity of the surface layer is lower than that of the underlying layer. Love waves are essentially horizontally polarized shear waves, and propagate by multiple reflection within this low velocity layer, which acts as a wave guide.

Surface waves travel at lower velocities than body waves in the same medium. Unlike body waves, surface waves are dispersive, that is, their different wavelength components travel at different velocities. Dispersion arises because of the velocity stratification of the Earth's interior, longer wavelengths penetrating to greater depths and hence sampling higher velocities. As a result, surface wave dispersion studies provide an important method of determining the velocity structure and seismic attenuation characteristics of the upper 600 km of the Earth.