Geology Reference
In-Depth Information
Fig. 4.2.
Data needed to determine
thickness of a unit from the
universal-thickness equation
(Eq. 4.1)
ness measurement and the pole to bedding (Fig. 4.2). The method is convenient for
data from a well or a map. It is here called the
universal
thickness equation because it
always works, regardless of the direction of the measurement or the dip of the bed.
The advantage of this method is that the thickness is given by a single, simple equa-
tion, eliminating most potential sources of error. The disadvantage for hand calcula-
tion is the need to determine an angle in three dimensions, although this is easily done
with a stereogram or spreadsheet. The apparent thickness is measured along the
direction
L
. In the plane defined by the line of measurement and the pole to bedding
t
=
L
cos
ρ
,
(4.1)
where
t
= the true stratigraphic thickness and
L
is the straight-line length between the
top and base of the unit (MD), measured along a well or between two points on a map.
The angle
= the angle between
L
and the pole to the bed. If the acute angle is used
in the equation, the thickness is positive. If the obtuse angle is used the thickness will be
correct in magnitude but negative in sign; taking the absolute value gives the correct result
for either possibility. If
L
is vertical, then the angle
ρ
, the dip of the bed. If the true
thickness is known, then the vertical thickness can be found by rewriting Eq. 4.1 as
ρ
=
δ
t
v
=
t
/cos
δ
,
(4.2)
where
t
v
= vertical thickness,
t
= true thickness, and
= true dip.
If
L
is not vertical, its inclination must be determined. For a well, a directional survey
will give the azimuth of the deviation direction and the amount of the deviation; the
latter which may be reported as the kickout angle, the angle up from the vertical. Al-
ternatively, the deviation of a well may be given as the
xyz
coordinates of points along
the well bore. The angle
δ
ρ
can be found graphically or analytically, as described in the
following two sections.
4.1.1.1
Angle between Two Lines, Stereogram
To find the angle
with an equal-area stereogram, on an overlay, plot the point repre-
senting the pole to bedding by marking the trend of the dip on the overlay, rotating the
overlay to bring this mark to the east-west axis, and counting inward from the outer
circle (the zero-dip circle) the amount of the dip plus 90°, and mark the point. Return
ρ