Geoscience Reference
In-Depth Information
It is possible to determine correctly the velocities and thickness of all layers in
an
n
-layer structure solely by using the first-arrival travel times if refracted arrivals
from each interface are first arrivals over some distance range. If this is not the
case and the refractions from a particular layer are always second arrivals, that
layerisa
hidden layer
, and first arrivals alone will not give the correct structure
(Figs. 4.33(a) and (b)). Another structure that cannot be determined uniquely by
using first arrivals alone is illustrated in Figs. 4.33(c) and (d).Alow-velocity
layer cannot give rise to any head wave at its upper surface because the refracted
ray bends towards the normal (
α
j
−
1
>α
j
) rather than away from the normal. The
only indications that a low-velocity layer is present come from the reflections
from its upper surface, and the reflections and head wave from its lower surface.
The critical distance for this lower interface is less than expected, and arrivals
are larger in amplitude due to the large velocity contrast occurring there. This is
exactly the same as the shadow-zone effect illustrated for the spherical Earth in
Fig. 8.2.
Dipping layers
Real strata are far more complex than Fig. 4.32(a).Ifweallow the first interface
to dip at an angle
δ
(Fig. 4.36) instead of being horizontal (
δ
=
0) as in Fig. 4.34,
then the travel time for the head wave is
1
2
z
d
α
1
−
α
1
x
α
1
t
d
=
2
+
sin(
i
c
+
δ
)
(4.42)
2
α
where
z
d
is the perpendicular distance from the shotpoint S to the interface. This
is called shooting
down-dip
. Equation (4.42)isthe equation of a straight line, but
in this case the apparent head-wave velocity is
α
d
:
α
1
sin(
i
c
+
δ
)
α
d
=
(4.43)
α
d
is less than
=
α
1
/sin
i
c
). The fact that the interface is dipping cannot be
determined from this time-distance graph alone. However, if the refraction line
is 'reversed', that is, the shotpoint is placed at R and the receiver positions from
Rtowards S, the travel times are
α
2
(
1
−
α
2
1
2
z
u
α
1
x
α
1
Figure 4.36.
Ray paths
for seismic energy
travelling from source S
to receiver R in a
two-layer model in which
the interface between the
two layers dips at an
angle
δ
. The P-wave
velocity for the upper
layer is
α
1
, and that for
the lower layer is
α
2
,
where
t
u
=
2
+
sin(
i
c
−
δ
)
(4.44)
2
α
S x R
a
1
A
C
B
a
2
d
α
2
>α
1
.
