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7/28/2019 Construct a Fold Cross-Section Using the Arc Method
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Construct a Fold Cross-Section Using the Arc Method
Construct a Fold Cross-Section Using the ArcBusk) Method
even Dutch, Natural and Applied Sciences, University of Wisconsin - Green Bay
rst-time Visitors: Please visit Site Map and Disclaimer. Use "Back" to return here.
ow the Arc (Busk) Method Works
his method approximates folds as a series of circular arcs. This method was published by H.G. Busk
929, so it is sometimes called theBusk Method.
1. Given the two d
shown, how do we
approximate the fo
as circular arcs? W
cannot assume the
measurements are
the same bed - thealmost certainly ar
not.
2. The problem is
find concentric
circles tangent to t
two dip
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Construct a Fold Cross-Section Using the Arc Method
measurements.
3. Radii of circles
always perpendicu
to the tangent whe
the radius hits the
circle.
4. Therefore, we
construct
perpendiculars to
each dip, and the
intersection of the
two perpendicular
the center of the
desired arcs.
e find the centers of curvature between adjacent dip measurements and construct the arcs for each.
he arcs are bounded by the perpendiculars for each pair of dip measurements.
A Common Problem
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Construct a Fold Cross-Section Using the Arc Method
1. It's quite comm
in this method for
perpendiculars to
measurements to
intersect far off th
diagram.
2. Locate the
bisector of the ang
between the
perpendiculars. On
way is to construc
lines parallel to ea
side the same
distance in, so tha
the lines intersect.
Then bisect thatangle.
3. From each dip
datum, draw a line
perpendicular to th
bisector and exten
to the opposite sid
This locates the ot
end of the arc.
4. Construct the di
on opposite sides
the sector. Dips
along any one side
the sector are all
equal and parallel
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Construct a Fold Cross-Section Using the Arc Method
5. If you extend th
dips in to the
bisector, the arcs
must lie within the
yellow triangles.
6. Sketch the arcs.
They will
approximately bis
the center line of
each triangle. A
good visual
approximation is
sufficient.
7. The completed
arcs.
8. Data from
adjacent sectors ca
be carried across
(tick marks in red)
by measuring
distances relative
the already plotted
arcs .
he earth will not fall out of orbit if the arcs in a sector like that shown above are approximate. What
atters most is the end points of the arc, because they determine relative stratigraphic position from
de to the other. Within the sector, between the dip datum points, there is no data, and the arc is only
proximation to the true (and unknown) exact shape of the fold.
the dips are exactly equal, then the perpendiculars will be parallel, and the center will be at infinity
o problem - the "arcs" become straight lines.
xample
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Construct a Fold Cross-Section Using the Arc Method
In the example at
left, dip data are
shown. We want t
construct a cross-
section that satisfi
the data.
The stratigraphic
units are colored
here but will not b
colored for most o
the remaining
diagrams. It is ofte
better notto consi
stratigraphy until
after the cross-section is drawn.
We first find the
center for concent
circles tangent to
dips 1 and 2.
All the circles
tangent to dip 1 ha
their centers on a
line perpendicular
dip 1. All the circl
tangent to dip 2 ha
their centers on a
line perpendicular
dip 2
Therefore, the
intersection C12 i
the center of
concentric circles
tangent both to dip
and to dip 2.
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Construct a Fold Cross-Section Using the Arc Method
Using C12 as a
center, draw arcstangent to dips 1 a
2 as shown. Draw
the arcs only
between the two
perpendiculars.
Now locate center
C23, the center of
concentric circles
tangent to dips 2 a
3. You already hav
a line perpendicul
to dip 2, so you on
need to draw a lin
perpendicular to d
3.
Note that, as often
happens, the cente
is off the diagram
Draw the arcs
tangent to dips 2 a
3. Again, draw the
only between the t
perpendiculars.
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Construct a Fold Cross-Section Using the Arc Method
We can now
exchange
information with
sector 1-2. Extend
the arc from dip 1
into sector 2-3, us
C23 as a center
(lower red arc).
Extend the arc fro
dip 3 into sector 1
using C12 as a cen
(upper red arc).
In general, as we
complete the cross
section, we will
extend data from o
sector to the next
like this.
We can now
construct center C
by drawing a
perpendicular to d
4. We already havthe perpendicular
dip 3.
We extend the arc
from sector 2-3 in
sector 3-4 as show
Note that the arc t
starts at dip 2 passvery close to dip 4
We don't need an
through every dip
even though we m
use that dip to
construct a center
curvature. So we
won't bother draw
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Construct a Fold Cross-Section Using the Arc Method
an arc for dip 4.
Construct center C
by drawing a
perpendicular to d
5. We already hav
the perpendicular
dip 4.
Extend the arcs fro
sector 3-4 into sec
4-5 as shown.
Note that the arc t
starts at dip 1 pass
very close to dip 5
Again, we need no
bother drawing an
arc for dip 4.
ote that center C45 lies very near dip measurement 4. This is purely coincidental and has no
gnificance.
ector 4-5 presents a problem. The arc from dip 2 passes just about through C45, and the arc from disses on the opposite side of C45 than does the arc from dip 1. When concentric folds have tight
rvature, something has to give in the middle. If an arc passes on the wrong side of the center of
rvature, do not draw it.
Construct center C
by drawing a
perpendicular to d
6. We already hav
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Construct a Fold Cross-Section Using the Arc Method
the perpendicular
dip 5.
Note that the
intersection is now
beneath the surfac
This is no problem
It means the fold inow concave
downward (an
anticline)
Construct the arc
tangent to dip 6 as
shown. Since thispoint is
stratigraphically
lower than all the
other datum point
we continue the ar
back through all th
other sectors as w
(shown in red).
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Construct a Fold Cross-Section Using the Arc Method
Construct arcs toconnect with all th
previously-
constructed arcs a
shown in red.
ectors 6-7, 7-8, 9-9 and 9-10 are handled the same way, so the remaining illustrations simply show
sults for each sector.
Sector 6-7 comple
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Construct a Fold Cross-Section Using the Arc Method
Sector 7-8 comple
Sector 8-9
completed. Since
point 9 falls betwe
two already drawn
arcs, there is no reneed to construct
another arc for it,
least for now.
Note that centers
C67, C78 and C89
are all close togeth
This simply mean
the fold has fairlyuniform curvature
over that interval.
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Construct a Fold Cross-Section Using the Arc Method
Sector 9-10
completed. Sincepoint 10 falls very
close to an already
drawn arc, there is
no real need to
construct another
for it.
ying the Diagram to Reality
is virtually certain when you draw a cross section using strictly geometric methods that the contact
ill not match exactly with their predicted positions. There are many reasons why not:
q The units will not be uniform in thickness
q There are small construction errors
q Dips are not uniform from place to place
q Dip measurements have small errors
q Folds do not have ideal geometrical shapes.
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Construct a Fold Cross-Section Using the Arc Method
Here we have
indicated the
stratigraphy. It is
virtually certain
when you draw a
cross section using
strictly geometric
methods that thecontacts will not
match exactly with
their predicted
positions.
What we need to d
now is redraw the
folds so the cross-
section matches bothe dips and the
stratigraphy.
Here all the
construction has
been removed and
the arcs aresubdued.
Most of the time y
can modify the fol
shapes by hand to
match the
stratigraphy witho
too much trouble.
Modified contactsare in black.
o not get distracted by your dip symbols or stratigraphic colors. The only requirement is that the
ratigraphy and dips match on the surface. Be prepared to modify the colors and depart from the dip
low the surface if it's called for. Compare the two diagrams above to see that this was actually don
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Construct a Fold Cross-Section Using the Arc Method
eturn to Course Syllabus
eturn to Techniques Manual Index
eturn to Professor Dutch's Home Page
reated 18 October 2000, Last Update 20 October 2000
ot an official UW Green Bay site
http://www.uwgb.edu/DutchS/crustmvt.htmhttp://www.uwgb.edu/DutchS/STRUCTGE/labman.htmhttp://www.uwgb.edu/DutchS/index.htmlhttp://www.uwgb.edu/DutchS/index.htmlhttp://www.uwgb.edu/DutchS/STRUCTGE/labman.htmhttp://www.uwgb.edu/DutchS/crustmvt.htm