Geology Reference
In-Depth Information
Fig. 4.3.
Equal-area stereogram show-
ing the angle between two
lines. Angle
is the great
circle distance between the
points giving the pole to bed-
ding and the orientation of
the apparent thickness mea-
surement. Lower-hemisphere
projection
ρ
the overlay to its original position. Plot the line of measurement (or well bore) by simi-
larly marking the trend of the measurement on the outer circle, bringing the mark to
the east-west axis and measuring the dip inward from the outer circle if given as a
plunge, or outward from the center of the graph if given as a hade or kickout angle.
Rotate the overlay until the two points fall on the same great circle (Fig. 4.3). The angle
ρ
is measured along the great circle between the two points.
As an example of the thickness calculation based on the universal thickness equa-
tion, find the true thickness of a bed that is
L
= 10 m thick in a well. The well hades 10°
to 310° and the bed dip vector is 20, 015. Plot the bed on the stereogram and find its
pole. Then plot the well and measure the angle between the two lines (
= 27°). Equa-
ρ
tion 4.1 gives
t
= 8.9 m.
4.1.1.2
Angle between Two Lines, Analytical
Method 1. Using bed dip vector and well dip vector
To find the angle between the bed pole and the well, both given as bearing and plunge,
substitute well dip vector (Eq. 12.3) and the bed pole from the dip vector (Eq. 12.13)
into the equation for the angle between two vectors (Eq. 12.25) to obtain
=cos
-1
ρ
ρ
=-cos
δ
w
sin
θ
w
sin
δ
b
sin
θ
b
-cos
δ
w
cos
θ
w
sin
δ
b
cos
θ
b
+sin
δ
w
cos
δ
b
,
(4.3)
where
ρ
= angle between bed pole and fault dip vector,
δ
w
= dip of well,
θ
w
= azimuth
of well dip,
δ
b
= dip of bed,
θ
b
= azimuth of bed dip.
