Civil Engineering Reference
In-Depth Information
Figure 1.11
Travel path mechanisms of surface waves: Love (
left
) and Rayleigh waves (
right
) (
adapted from
Bolt,
1999 )
LR-waves are caused by constructive interference of body waves, such as P and SV. As they pass
by, particles of soil move in the form of a retrograde ellipse whose long axis is perpendicular to the
Earth ' s surface (Figure 1.11). R-waves exhibit very large amplitude and regular waveforms.
LR-waves are slower than S-waves. As an approximation, it may be assumed that the velocity of
LR - waves
v
LR
is given by the equation (Bolt, 1999 ):
v
≈
092
.
v
(1.4)
LR
S
For a layered solid, LQ- wave velocity
v
LQ
generally obeys the following relationship:
vv v
S1
<<
(1.5)
LQ
S2
with
v
S1
and
v
S2
as the velocities of S-waves in the surface and deeper layers, respectively.
Surface waves are slower than body waves and LQ-waves are generally faster than LR-
waves. Moreover, the amplitudes of P- and S-waves show amplitudes linearly decreasing with the
increase in distance
x
, while the amplitude of surface waves attenuates in inverse proportion to the
square root of distance
x
. S-waves damp more rapidly than P-waves; attenuations increase with the
wave frequencies. Amplitude attenuation is caused by the viscosity of the Earth's crust; seismic waves
also change in form during their travel paths for the same reason (Kanai, 1983). Amplitudes and periods
are of great importance because they infl uence the energy content of seismic waves as discussed in
Section 1.2 .
Body waves are refl ected and refracted at interfaces between different layers of rock according to
Snell's law of refraction. When refl ection and refraction occur, part of the energy of one type is trans-
formed in the other. Regardless of whether the incident wave is P or S, the refl ected and refracted
waves, also termed ' multiple phase waves ', each consists of P- and S -waves, such as PP, SS, PS and
SP. Their name indicates the travel path and mode of propagation (Reiter, 1990). For example, SP starts
as S and then continues as P. The phenomenon known as the 'Moho bounce' is due to the simultaneous
arrival at the surface of direct S- waves and S - waves refl ected by the so- called ' Mohorovicic discontinu-
ity' - or 'Moho' in short - at the boundary between the crust and the underlying mantle in the internal
structure of the Earth. The latter discontinuity may be responsible for signifi cant strong motions leading
to damage far from the source as illustrated in Section 1.2.1 .
Multiple phase waves do not possess signifi cant damage potential. However, when P- and S-
waves reach the ground surface, they are refl ected back. As a result, waves move upwards and
downwards. Such refl ections may lead to signifi cant local amplifi cation of the shaking at the surface.
It has been shown that seismic waves are infl uenced by soil conditions and local topography (e.g.
Kramer, 1996), as further discussed in Section 1.3.2 .
