Geoscience Reference
In-Depth Information
and
α
n
are known). Then, by using Eqs. (4.79) and (4.82), we can determine the
velocity of the
n
th layer
α
n
:
n
n
2
n
2
m
t
m
α
t
m
=
1
α
m
=
1
m
=
n
−
1
2
m
t
m
+
α
2
n
t
n
=
1
α
(4.84)
m
=
and
n
−
1
n
−
1
2
n
−
1
2
m
t
m
α
t
m
=
1
α
(4.85)
m
=
1
m
=
Subtracting Eq. (4.85) from Eq. (4.84)gives
n
n
−
1
2
n
2
n
−
1
2
n
t
m
α
t
m
−
α
t
m
=
α
(4.86)
m
=
1
m
=
1
or
2
n
t
0
,
n
−
α
2
n
−
1
t
0
,
n
−
1
=
α
2
n
(
t
0
,
n
−
t
0
,
n
−
1
)
α
(4.87)
Rearranging this equation gives
α
n
, the velocity of the
n
th layer (also known as
the
interval velocity
), in terms of the RMS velocities:
2
n
t
0
,
n
−
α
2
n
−
1
t
0
,
n
−
1
t
0
,
n
−
t
0
,
n
−
1
α
α
n
=
(4.88)
After
α
n
has been determined,
z
n
can be calculated from Eq. (4.79):
n
2
z
m
α
m
t
0
,
n
=
m
=
1
n
−
1
2
z
m
α
m
+
2
z
n
α
n
=
m
=
1
2
z
n
α
n
=
t
0
,
n
−
1
+
(4.89)
Thus,
α
n
2
z
n
=
(
t
0
,
n
−
t
0
,
n
−
1
)
(4.90)
Therefore, given the two-way normal-intercept times and corresponding stack-
ing (RMS) velocities from a velocity analysis, the velocity-depth model can be
determined layer by layer, starting at the top and working downwards.
Multiples
are rays that have been reflected more than once at an interface.
The most common multiple is the surface multiple, which corresponds to a ray
that travels down and up through the layers twice. Reflections with multiple ray
paths in one or more layers also occur. In marine work, the multiple which is
reflected at the sea surface and seabed is very strong (Figs. 9.23 and 10.10). The
periodicity of multiple reflections enables us to filter them out of the recorded
data by deconvolution.
