Geoscience Reference
In-Depth Information
depending on the nature of the bottom. The obvious
implication from this is that seismic waves generated in
the water will tend to stay in the water, reverberating in the
water body rather than entering the underlying sediments
or rocks (see Multiples in
Section 6.5.1.1
).
It is common, although something of a generalisation, to
refer to these and headwave arrivals simply as
'
refractions
'
.
Total reflection
When the angle of incidence is greater than
θ
Crit
, the wave
does not cross the interface and is totally re
ected
(
Fig. 6.9e
), i.e. there is no transmitted wave. These are
known as post-critical re
ections and, since no energy is
'
to a transmitted wavefront, they can have relatively
high energy and hence large amplitude. Total reflection is an
important phenomenon for the in-seam surveys described
in
Section 6.8.1
.
For these surveys, the seismic source is
actually located within a coal seam. The seam forms a
waveguide because the energy cannot pass through its upper
and lower boundaries, being totally reflected by the bound-
aries, so the waves are trapped within the seam. The wave is
guided by the seam and is known as a guided wave.
lost
'
θ
Inc
) increases the angle of transmission (
θ
Trn
) and, even-
tually, a critical angle of incidence (
θ
Crit
) is reached where
along the interface. This is a phenomenon known as
critical refraction and can only happen if the velocity
below the interface is greater than that above, i.e. V
2
>
V
1
. From Snell
'
s Law (
Eq. (6.8)
), and since the sine of 90°
is 1, then
V
1
V
2
sin
θ
Crit
¼
ð
6
:
14
Þ
Wavefronts at an interface
Following on from the description of re
ection and trans-
mission, given mostly in terms of rays, we now illustrate
the phenomenon using wavefronts. Consider
first an inter-
face where the acoustic impedance changes owing to the
velocity below the interface being lower than that of the
layer above. The wavefront snapshot images in
Fig. 6.10
show how, on encountering the interface, the incident
wavefront is partitioned into two separate wavefronts.
Note that because the velocity below the interface (V
2
)is
lower than that above (V
1
), the wavelength of the trans-
mitted wave in the lower layer is less than that of the
incident wave (see
Appendix 2
for the relationship between
frequency, velocity and wavelength). The upward travelling
reflected wave travels at the same speed as the incident
wave so its wavelength is unchanged, but its polarity is
reversed as shown by the relative locations of the darker
and lighter regions in the images. From a physical perspec-
interchanged.
We now change our model of the subsurface so that the
velocity and acoustic impedance increase below the inter-
face, i.e. V
2
is greater than V
1
. This model allows the
downward moving wavefront to return to the surface via
critical refraction. Referring to the wavefronts in
Fig. 6.10b
,
again the incident wavefront is partitioned into re
ected
and transmitted wavefronts, but with some important dif-
ferences from the example shown in
Fig. 6.10a
. Firstly, the
increase in acoustic impedance at the interface produces a
positive reflection coefficient (see Energy partitioning in
Critical refraction is important because it represents a third
way that the down-going waves created by the seismic
source can be returned to the surface. Recall that a seismic
wave is a packet of strain energy which deforms the rocks
as it passes through them. The critically refracted wave is
travelling at the higher velocity of material below the
interface. Although it is within the underlying higher-
velocity region (V
2
), it still affects the lower-velocity region
(V
1
) above the interface. The two regions are physically
continuous, so deformation associated with the wave in the
area immediately below the interface must affect the adja-
cent area immediately above. An important consequence
of this is that the wave, and its associated deformation, is
travelling
for the lower-velocity upper region.
This causes the disturbance at the boundary to act as a
mobile source of seismic waves as it travels along the
interface at the (higher) velocity of the underlying region.
The resulting upward travelling wavefront in the lower-
velocity layer is planar and the associated raypaths are at
the critical angle. Seismic waves created in this way are
known as headwaves.
The concept of critical refraction and headwave arrivals
is a simpli
cation. In reality, and especially in the near-
surface, velocities are rarely constant nor are interfaces
planar. Instead velocity varies continuously and increases
with depth. In these circumstances, transmitted waves may
penetrate a short distance into the deeper higher-velocity
region following curved raypaths roughly parallel to the
'
'
too fast
'
refracting
'
interface. These are referred to as diving waves.
Search WWH ::
Custom Search