Geology Reference
In-Depth Information
x =( x 2 - x 1 ) ,
(2.9a)
y =( y 2 - y 1 ) ,
(2.9b)
and L is given by Eq. 2.4. Division by zero is not allowed in Eq. 2.7. The preliminary
azimuth,
', calculated from Eq. 2.7, is always in the range of 000 to 090°. The angle
must be converted to the true azimuth,
θ
, in the range of 000 to 360° using Table 2.1.
As an example of the calculation of the orientation of a line, find the trend and
plunge of the well between points P 1 and P 2 from the example in Sect. 2.2.3.2. The lo-
cations of the two points are found from the deviation survey to be P 1 : z = -540 ft, 50 ft
northing, -1 050 ft easting and P 2 : z = -740 ft, 150 ft northing, -1 150 ft easting. The
preliminary plunge and trend of the line, from Eqs. 2.7 and 2.8, is 55, -045. The sign of
θ
x is negative (
x = (-1 150 - (-1 050) = -100) and
y is positive (
y = 150 - 50 = +100),
and so from Table 2.1, the true azimuth is
= 360 + (-45) = 315.
The orientation of a line can also be represented by its pitch or rake, r , which is the
angle measured in a specific plane between the line and the strike of the plane (Fig. 2.12).
Both the rake and the attitude of the plane must be specified. This form is convenient
for recording lines that are attached to important planes, like striations on a fault plane.
Alternatively the orientation of a line in a plane can be represented by its apparent dip
and bearing (Fig. 2.12). Apparent dip,
θ
', is the orientation of a line that lies in a plane
in some direction other than the true dip (Fig. 2.12). An apparent dip can be written
as a plunge and trend or as a rake in the plane. Apparent dips are important in drawing
a cross section that is in a direction oblique to the true dip direction of bedding.
It is possible to represent the three-dimensional orientations of lines and planes
quantitatively on graphs called stereograms and tangent diagrams. The graphical tech-
niques aid in the visualization of geometric relationships and allow for the rapid so-
lution of many three-dimensional problems involving lines and planes.
δ
Table 2.1.
True azimuth, θ , determined
from preliminary azimuth,
θ
'
based on the signs of x and
y (Eq. 2.9) or cos
α
and cos
β
(Eq. 2.14)
Fig. 2.12.
True dip,
δ
, apparent dip,
δ
',
and rake (or pitch), r
 
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