Geoscience Reference
In-Depth Information
expect from a first glance at Eqs. (4.4) and (4.5). This occurs because the elastic
moduli
K
and
(a)
x
=
vt
1.0
.A
linear relationship, termed
Birch's law
, between density and seismic velocity is
of the form
µ
are also dependent on
ρ
and increase more rapidly than
ρ
O
z
(b)
v
=
a
ρ
+
b
(4.6)
O
x
=
vt
where
a
and
b
are constants; it fits measurements from many crustal and mantle
rocks fairly reasonably. Figure 4.2 shows examples of such linear relationships.
The Nafe-Drake curve in Fig. 4.2(d) is another example of an empirical relation-
ship between density and seismic velocity. This shows clearly that igneous and
metamorphic crustal rocks generally have higher seismic velocities than those in
sedimentary rocks. The ability to estimate density at a particular depth from the
velocity (albeit with considerable uncertainty) can be useful when investigating
the isostatic implications of structures determined seismologically, or in attempt-
ing to make gravity models for regions where something is already known about
the seismic-velocity structure.
Figure 4.3.
Amplitudes of
surface waves and body
waves. (a) A surface wave
is travelling from a source
Oatspeed
v
. After a time
t the area of the
cylindrical wavefront is
2
πvtz
= 2
πxz
. The initial
energy in the wave is now
spread out over the area
of this wavefront. Energy
is proportional to the
square of amplitude
(Eq. (4.26)). Assuming that
energy is conserved, the
amplitude at a distance
x
is thus proportional to
x
−1/2
. (b) A body wave is
travelling from a source O
at speed
v
. After a time
t
the area of the spherical
wavefront is 4
4.1.3 Surface waves
Surface waves are seismic waves that are guided along the surface of the Earth
and the layers near the surface. They do not penetrate into the deep interior.
Surface waves are generated best by shallow earthquakes. Nuclear explosions,
although shallow, do not generate comparable surface waves. This fortunate fact
is the basis for one criterion of discrimination between earthquakes and nuclear
explosions (Section 4.2.4). Surface waves are larger in amplitude and longer in
duration than body waves, and, because their velocities are lower than those of
body waves, they arrive at seismographs after the main P- and S-waves. The
reason for the relatively larger amplitude of surface waves is easy to understand
(Fig. 4.3). The area of the cylindrical wavefront of a surface wave is proportional
to
x
, the distance from its source, which means that the amplitude of the surface
v
2
t
2
π
=
x
2
. Assuming
conservation of energy,
the amplitude at distance
x
is proportional to
x
−1
.
4
π
wave is inversely proportional to
√
x
.Incontrast, the wavefront of P- and S-waves
at any time is spherical; therefore, the area of the wavefront is proportional to
x
2
,
the square of the distance from the source. The amplitude of the body wave is
therefore inversely proportional to
x
.
There are two types of surface waves,
2
both named after famous physicists:
Rayleigh waves
, sometimes descriptively called 'ground roll' in exploration seis-
mology, are named after Lord Rayleigh, who predicted their existence in 1887;
Love waves
are named after A. E. H. Love, who predicted their existence in 1911.
2
A third type of surface wave, the Stoneley wave, propagates along an interface between two media
and is more correctly called an interface wave. Stoneley waves are not dispersive; they decrease in
amplitude with distance from the interface and have a velocity between the lesser S-wave velocity
and the greater Rayleigh-wave velocity.
