Geology Reference
In-Depth Information
Wave amplitude, which is proportional to the square
root of the wave energy, therefore falls off as
r
-1
.
A further cause of energy loss along a ray path arises
because, even at the low strains involved, the ground is
imperfectly elastic in its response to the passage of seismic
waves. Elastic energy is gradually absorbed into the
medium by internal frictional losses, leading eventually
to the total disappearance of the seismic disturbance.The
mechanisms for the absorption of energy are complex,
but the loss of energy is usually regarded as being a fixed
proportion of the total energy, for each oscillation of the
rock particles involved, during which time the wave-
front will have moved forward one wavelength. The
ab-
sorption coefficient
a
expresses the proportion of energy
lost during transmission through a distance equivalent to
a complete wavelength
l
.Values of
a
for common Earth
materials range from 0.25 to 0.75 dB
l
-1
(for a definition
of decibels, dB, see Section 2.2).
Over the range of frequencies used in seismic survey-
ing the absorption coefficient is normally assumed to
be independent of frequency. If the amount of absorp-
tion per wavelength is constant, it follows that higher
frequency waves attenuate more rapidly than lower
frequency waves as a function of time or distance. To
illustrate this point, consider two waves with frequencies
of 10 Hz and 100 Hz to propagate through a rock in
which
v
p
= 2.0 km s
-1
and
a
= 0.5 dB
l
-1
. The 100 Hz
wave (
l
= 20 m) will be attenuated due to absorption by
5 dB over a distance of 200 m, whereas the 10 Hz wave (
l
= 200 m) will be attenuated by only 0.5 dB over the same
distance. The shape of a seismic pulse with a broad fre-
quency content therefore changes continuously during
propagation due to the progressive loss of the higher fre-
quencies. In general, the effect of absorption is to pro-
duce a progressive lengthening of the seismic pulse (Fig.
3.7).This effect of absorption is a familiar experience as
it applies to P-waves in air, sound. The sharp crack of a
nearby lightning flash is heard far away as the distant
'rumble'of thunder.
Input
spike
20 ms
After 1 s
After 2 s
After 3 s
After 4 s
After 5 s
Fig. 3.7
The progressive change of shape of an original spike
pulse during its propagation through the ground due to the effects
of absorption. (After Anstey 1977.)
of the two layers, and the angle of incidence on the
interface.
3.6.1 Reflection and transmission of
normally incident seismic rays
Consider a compressional ray of amplitude
A
0
normally
incident on an interface between two media of differ-
ing velocity and density (Fig. 3.8). A transmitted ray of
amplitude
A
2
travels on through the interface in the
same direction as the incident ray and a reflected ray
of amplitude
A
1
returns back along the path of the
incident ray.
The total energy of the transmitted and reflected rays
must equal the energy of the incident ray. The relative
proportions of energy transmitted and reflected are de-
termined by the contrast in
acoustic impedance Z
across the
interface.The acoustic impedance of a rock is the prod-
uct of its density (
r
) and its wave velocity(
v
); that is,
Zv
=
r
3.6 Ray paths in layered media
At an interface between two rock layers there is gen-
erally a change of propagation velocity resulting from
the difference in physical properties of the two layers.
At such an interface, the energy within an incident seis-
mic pulse is partitioned into transmitted and reflected
pulses. The relative amplitudes of the transmitted and
reflected pulses depend on the velocities and densities
It is difficult to relate acoustic impedance to a tangible
rock property but, in general, the harder a rock, the
higher is its acoustic impedance. Intuitively, the smaller
the contrast in acoustic impedance across a rock inter-
face the greater is the proportion of energy transmitted
through the interface. Obviously all the energy is trans-
mitted if the rock material is the same on both sides of the
