Geology Reference
In-Depth Information
(Table 4.1) or 108 ±12 ft based on the whole range of values. The SE lengths (Table 4.1)
are measured to a southeasterly position on the base of the Mpm, at the 600-ft contour,
which lies directly beneath the 700-ft contour on the top of the unit; the NW measure-
ments are from the more northwesterly position of the lower contact. Changing the
location of the structure contour of the base has only a small effect on the thickness.
The average thickness determined from the structure-contour-based measurements
falls within the range of the point-to-point measurements, but is much smaller than
the average of the point-to-point measurements, as expected from the behavior of the
thickness equation (Fig. 4.8). Thickness measurements between two points (Eqs. 4.10
and 4.11, or 4.1) exhibit a non-linear sensitivity to error at low angles between the dip
vector and the measurement orientation, leading to a high probability of an artificially
high average from multiple measurements. Smoothing of the attitude errors by struc-
ture contouring leads to a better average thickness.
Where the thickness is known accurately from a complete exposure or from well-
defined contacts in a borehole, the structure contours or bedding attitudes might be
adjusted to conform to the thicknesses. The thickness measured between structure
contours is the best approach at the map scale where there is uncertainty in the data.
4.2
Thickness of Folded Beds
In a folded bed, the dips of the upper and lower contact are not the same and the previous
thickness equations are inappropriate. The fold is likely to approach either the planar dip
domain or the circular arc form. Equations for both forms are given in the next two sec-
tions. For both methods it is assumed that the thickness is constant between the measure-
ment points and that the line of the thickness measurement and the bedding poles are all
in the plane normal to the fold axis. The latter condition is satisfied if the directions
of both dips and the measurement direction are the same. If the geometry is more
complex than this, then a cross section perpendicular to the fold axis should be con-
structed to find the thickness and projection may be required, as discussed in Chap. 6.
4.2.1
Circular-Arc Fold
The thickness of a bed that is folded into a circular arc (Fig. 4.10) can be found if the
dip direction of the bed and the well or traverse line are coplanar. In this situation the
bedding poles intersect at a point. Let
ρ
1
be the smaller angle between the well and the
pole to bedding, thus always associated with the longer radius,
r
1
. The thickness,
t
, is
t
=
r
1
-
r
2
.
(4.12)
From the law of sines:
r
2
=(
L
sin
ρ
1
)/sin
γ
,
(4.13)
r
1
=(
L
sin (180 -
ρ
2
)) / sin
γ
,
(4.14)
