Geoscience Reference
In-Depth Information
Figure 4.45.
(a) A plane wave propagating vertically downwards. Each point on the
wavefront acts as a point source and generates spherical waves. The next
wavefront, which is the sum of all these spherical waves, is also a plane wave. All
the lateral disturbances cancel each other out. (b) A plane wave travelling vertically
downwards is reflected at an interface (lower material is shaded). Each point on the
interface acts as a point source and generates spherical waves. Thus, the reflected
wave is a plane wave travelling upwards (all lateral disturbances again cancel out).
(c) A plane wave reflected from an interface that terminates at a corner, P. The
reflected wave well to the left of P is unaffected. Since there are no point sources to
the right of P, the reflected wave close to P is reduced in amplitude. In addition, the
spherical wave generated by P is not cancelled out. It is called the diffracted wave.
4.4.4 Diffraction and migration
All the preceding sections have dealt with a horizontally layered model. Although
some structures can be approximated by horizontal layers, structures such as
faults, dykes and intrusions cannot. It is also necessary to allow for the effects
of dipping layers. These complications bring into question the minimum size or
contrast in physical properties which can be resolved by using the reflection-
profiling method.
Diffraction
Huygens' principle states that every point on a wavefront acts as a point source
generating spherical waves. The wavefront at a later time is then the sum of all
the waves from these point sources. The case of a plane wave is illustrated in
Fig. 4.45(a): the new wavefront is also planar because the lateral disturbances
from the point sources cancel each other out. When a plane wave is reflected
from an interface, the same principle applies: each point on the interface acts
as a point source and generates spherical waves. When summed together, these
spherical waves give a reflected plane wave (Fig. 4.45(b)). When an interface is
not infinitely long but terminates at a point P (Fig. 4.45(c)), the reflected wave
fartothe left of P is not affected. However, since there are no more point sources
