Geoscience Reference
In-Depth Information
Figure 4.49.
(a) The
normal-incidence
reflection profile over an
interface that has a fault
with a vertical throw of
h
.
(b) The record section for
(a). The time difference
between the two-way
travel times on either side
of the fault is
t
. For the
fault to be resolved, its
throw
h
must be greater
than about
λ/
8to
λ/
4,
where
is the wavelength
of the signal. (In terms of
t
,
t
must be greater
than 1
/
(4 × frequency) to
1
/
(2 × frequency).)
λ
Figure 4.50.
(a) Spherical waves from a point source reflected from a plane
interface. The first Fresnel zone is that part of the interface which reflects energy
back to the receiver within one-half a cycle of the first (normal-incidence) reflection.
Because the wave must travel from source to interface and back to the receiver,
energy from the wavefront one-quarter of a wavelength behind the first wavefront
when reflected back to the receiver is delayed by half a cycle. (b) The geometry of
the first Fresnel zone. The width
w
of this zone can be calculated by applying
Pythagoras' theorem to the right triangle SOQ;
d
is the depth of the interface
beneath the source and
the wavelength of the signal. The upper material is
assumed to have constant P-wave velocity
λ
α
1
.
the same wave is travelling through material with a P-wave velocity of 7.2 km s
−
1
,
the wavelength is increased to 360 m.
Consider a fault with a vertical throw of
h
(Fig. 4.49). For the fault to be
detected, it must be greater than about one-eighth to one-quarter of the wavelength
of the seismic wave. This means that the reflected wave from the down-faulted side
is delayed one-quarter to one-half a wavelength. A smaller time delay than this is
