Wave Propagation of Earthquakes

(Image courtesy sciencelearn.org.nz)

Wave Propagation

The focal point of an earthquake under the surface of the earth is called the hypocenter and its corresponding point on the surface the epicenter. It is customary to refer to earthquakes with relation to the epicenter.

When an earthquake hits the hypocenter, it sends out shock waves. There are two types of shock waves:

Push waves—denoted p
Shock waves or shear waves that produce transverse vibration with respect to the direction of travel, also named s waves The p waves are faster than s waves and arrive first, produce a relatively mild vibration, and cause less damage. They are messengers of the severe ground shaking that will follow. The moment the s waves arrive, seismographic diagrams start recording the magnitude of ground shaking (Figure 1).

If the distance from a given observation point to the hypocenter is s, the propagation velocity of the transverse waves is v_s and the propagation velocity of the longitudinal (push waves) is v_p. Then T, the time difference between the arrival of p and s waves, is given as,

where the distance s (1/v_s - 1/v_p) ^-1 T from simple arithmetic. We need three observation points to use triangulation and the geology of the ground, which determines vs and vp by measurement. The 1997 UBC gives some rough values for vs and vp. Nonetheless, it is advisable to have a good geotechnical report for accuracy.

Wave Velocities (Body Waves)

where,

E = Young’s modulus
σ = Poisson’s ratio (usually 0.25)
ρ = density

Figure 1 Seismograph reading of ground vibration caused by an earthquake.

Velocities vs of typical transverse waves to propagate through the ground for selected materials are as follows (in meters per second):

Sand	60
Reclaimed sand	100
Clay	250
Gravel	600
Tertiary rock	1000 and up