Geology Reference
In-Depth Information
mic case, and it passes up obliquely through the upper
layer towards the surface (Fig. 3.11). Any ray associated
with the head wave is inclined at the critical angle
i
c
.By
means of the head wave, seismic energy is returned to the
surface after critical refraction in an underlying layer of
higher velocity.
sin
sin
v
v
q
q
1
2
=
1
2
Note that if
v
2
>
v
1
the ray is refracted away from the
normal to the interface; that is,
q
2
>
q
1
. Snell's Law also
applies to the reflected ray, from which it follows that the
angle of reflection equals the angle of incidence (Fig.
3.10).
3.6.4 Diffraction
In the above discussion of the reflection and transmission
of seismic energy at interfaces of acoustic impedance
contrast it was implicitly assumed that the interfaces
were continuous and approximately planar. At abrupt
discontinuities in interfaces, or structures whose radius
of curvature is shorter than the wavelength of incident
waves, the laws of reflection and refraction no longer
apply. Such phenomena give rise to a radial scattering of
incident seismic energy known as
diffraction
. Common
sources of diffraction in the ground include the edges of
faulted layers (Fig. 3.12) and small isolated objects, such
as boulders, in an otherwise homogeneous layer.
3.6.3 Critical refraction
When the velocity is higher in the underlying layer there
is a particular angle of incidence, known as the
critical
angle
q
c
, for which the angle of refraction is 90°. This
gives rise to a critically refracted ray that travels along the
interface at the higher velocity
v
2
.At any greater angle of
incidence there is total internal reflection of the incident
energy (apart from converted S-wave rays over a further
range of angles).The critical angle is given by
sin
q
c
sin
90
∞
1
=
=
v
v
v
1
2
2
Head wave
generated
in overlying layer
Ray paths
so that
θ
c
)
(
q
c
= sin
- 1
v
1
v
2
v
1
v
2
> v
1
A
B
The passage of the critically refracted ray along the top
of the lower layer causes a perturbation in the upper layer
that travels forward at the velocity
v
2
, which is greater
than the seismic velocity
v
1
of that upper layer. The
situation is analogous to that of a projectile travelling
through air at a velocity greater than the velocity of
sound in air and the result is the same, the generation of a
shock wave.This wave is known as a
head wave
in the seis-
Wavefront
expanding in
lower layer
Fig. 3.11
Generation of a head wave in the upper layer by a wave
propagating through the lower layer.
Reflection
wavefront
Faulted layer
Fig. 3.12
Diffraction caused by the
truncated end of a faulted layer.
Diffraction
wavefront
