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the top of the unit containing the contact) which are separated by a known distance in
the well. Solve Eq. 2.11 for
h
(Fig. 2.21b):
h
=
v
/tan
δ
,
(2.13)
where
h
= distance from the well bore to the intersection with a dipping bed and
v
= vertical distance in the well between the intersection of the dipping horizon and
the horizontal horizon.
2.4.2
Analytical Three-Point Problem
The attitude of a plane is given by the trend and plunge of the dip vector (Fig. 2.22). The
dip vector can be determined analytically from the
xyz
coordinates of three non-colinear
points (derived in Sect. 12.3). The preliminary trend and plunge of the dip vector is
θ
'=arctan(
A
/
B
) ,
(2.14)
δ
= arcsin {-cos [90 + arccos (
C
/
E
)]} ,
(2.15)
where
θ
' = the preliminary azimuth of the dip,
δ
= the amount of the dip, and
A
=
y
1
z
2
+
z
1
y
3
+
y
2
z
3
-
z
2
y
3
-
z
3
y
1
-
z
1
y
2
,
(2.16a)
B
=
z
2
x
3
+
z
3
x
1
+
z
1
x
2
-
x
1
z
2
-
z
1
x
3
-
x
2
z
3
,
(2.16b)
C
=
x
1
y
2
+
y
1
x
3
+
x
2
y
3
-
y
2
x
3
-
y
3
x
1
-
y
1
x
2
,
(2.16c)
D
=
z
1
y
2
x
3
+
z
2
y
3
x
1
+
z
3
y
1
x
2
-
x
1
y
2
z
3
-
y
1
z
2
x
3
-
z
1
x
2
y
3
,
(2.16d)
E
=(
A
2
+
B
2
+
C
2
)
1/2
.
(2.16e)
Fig. 2.22.
Three points on a plane and
the dip vector of the plane
