Geology Reference
In-Depth Information
Fig. 4.8.
Effect of attitude and angle
measurement errors on thick-
ness calculation. Normalized
error in thickness measure-
ment, in percent as a function
of the angle
(Eq. 4.1) for
angle errors of
ρ
= ±5°.
t
Tr u e
thickness of bed;
t
e
erroneous
thickness given the angle er-
ror;
ρ
angle between the pole
to the bed and direction along
which thickness is measured
ρ
-35% at 80 - 5°. This means that thickness measurements made at a low angle to the
plane of the bed may produce very large errors, with a strong bias toward overestima-
tion. At angles between the measurement direction and bedding of 10° or less (
= 80°
or greater), very large thickness errors will occur with very small orientation errors
and thickness determinations made from maps should be considered suspect.
From Fig. 4.8, a bed having a true thickness of 100 m measured at an angle of 10°
to bedding (
ρ
= 85°) will
yield a thickness of nearly 200 m. The same measurement with a 5° underestimate in
the angle will give a thickness of 65 m. The average thickness for these two measure-
ments is 132.5 m, still an overestimate. Thickness measurements made nearly per-
pendicular to bedding (
ρ
= 80°) for which the angle is overestimated by 5° (giving
ρ
= 20°
the error is about ±3%; a 100 m thick bed would be measured as being between 97
and 103 m thick.
Thickness calculations between two points on a map are very sensitive to the accu-
racy of the contact locations and the attitude of bedding, as illustrated by the data
obtained from Fig. 4.9a. The thickness of the Mpm from the seven locations a-g
(Table 4.1) ranges from 84 to 230 ft, as calculated from Eq. 4.1. This is an unreasonably
large variation in thickness at what is nearly a single location at the scale of the map.
What is the probability that the thickness variation is due to small measurement er-
rors? The bedding azimuth of 4, 125 represents the value determined from the struc-
ture-contour map (Fig. 4.9b). The difference in dip from 04° on the structure contour
map to 06° from the field measurement is responsible for a large variation in the cal-
culated thickness. For example, at point c, the thickness along a single line is 127 ft for
a 04° dip compared to 230 ft for a 06° dip (Table 4.1). However, the substantial differ-
ence in calculated thickness along lines a and g is not the result of uncertainty in the
dip, but must be attributed to the uncertainty both in the location of the lower contact
and in the exact dip direction. Changing the azimuth of the dip from 135 to 127 at
location a increases the thickness from 84 to 108 ft at a bed dip of 08°; at location g the
same change reduces the thickness from 173 to 159 ft. If we say that the thickness of
ρ
= 0°) are rather insensitive to errors in the angle. At
ρ
