Geology Reference
In-Depth Information
Fig. 7.25.
Displacement versus distance
plots for completely exposed
small normal faults.
a
Ap-
proximately circular-arc dis-
tribution.
b
Approximately
sinusoidal distribution.
c
Two overlapping faults
with D-shaped distributions.
VE:
vertical exaggeration.
(Schlische et al. 1996)
The change in displacement along the strike of a fault can be illustrated with a
displacement-distance graph. The displacement-distance curve typically ranges from
a circular arc (Fig. 7.25a) to sinusoidal (Fig. 7.25b) to D-shaped (Fig. 7.25c). All three
distributions in Fig. 7.25 come from one small area in a quarry and are completely
exposed. More complex displacement distributions (Fig. 7.24b) may be the result of
the coalescence of multiple faults, like the two faults in Fig. 7.25c.
The smooth variation of displacement along a fault in the style of Figs. 7.24a and
7.25 has been described as the bow and arrow rule (Elliott 1976). The trace of a
faulted horizon on one side of the fault (fault cutoff line) forms the bow and a straight
line joining the tips of the fault is the bow string. A line perpendicular to the bow
string at its center is the arrow. The distance along the arrow between the bow and
the bow string is an estimate of the displacement amount and the direction of the
arrow is an estimate of the displacement direction. These are reasonable first ap-
proximations for dip slip faults although they should be used with caution. If the
displacement distribution on the fault resembles that in Fig. 7.22, then the dis-
placement with respect to the correlative horizon across the fault is twice that given
by the bow and arrow rule because both hangingwall and footwall are displaced
from their original positions (the position of the bow string). The rule does not apply
to strike-slip faults.
The length of a fault in the strike direction is usually much greater than its maxi-
mum displacement. A comparison between the maximum displacement on a fault
and its length, down dip or along strike, shows that ratios of 1 : 8 to 1 : 33 are common,
regardless of location, size, or fault type (Table 7.1). The maximum displacement is
expected to occur near the center of the fault as in Fig. 7.24a and 7.25. Fault displace-
ments measured from maps or cross sections may not go through the point of maxi-
