Geology Reference
In-Depth Information
Fig. 4.16.
Dip map of data from Fig. 4.14a
interpreted as isocore thick-
nesses measured in a folded,
constant-thickness unit. True
stratigraphic thickness is 150,
dips in degrees
4.4
Derivation: Map-Angle Thickness Equations
The traditional method for determining thickness based on data from a geologic map on
a topographic base results in two equations, depending on the relative dip of topography
and bedding. The following derivations are after Dennison (1968). If the ground slope
and the dip are in the same general direction, Fig. 4.17 shows that
t
= ah = the true thick-
ness, bc = fe =
v
= the vertical elevation change, ac =
h
= the horizontal distance from the
upper to the lower contact, angle cae =
= the angle between the measurement direction
α
and the true dip, and angle aej = feg =
δ
= the true dip. The thickness is
t
= aj - hj = aj - eg ,
(4.19)
where
eg =
v
cos
δ
,
(4.20a)
aj = ea sin
δ
,
(4.20b)
ea =
h
cos
α
.
(4.20c)
Substitute Eqs. 4.20 into 4.19 to obtain
t
=|
h
cos
sin
-
v
cos
| .
(4.21)
α
δ
δ
