Construct a Fold Cross-Section Using the Arc Method

7/28/2019 Construct a Fold Cross-Section Using the Arc Method

1/14

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

ttp://www.uwgb.edu/DutchS/STRUCTGE/SL161ArcMethod.HTM (1 of 14)8/5/2009 2:44:10 PM
http://weba.uwgb.edu/http://www.uwgb.edu/DutchS/sitemap.htmhttp://www.uwgb.edu/DutchS/sitemap.htmhttp://weba.uwgb.edu/


2/14


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



3/14


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



4/14


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



5/14


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.



6/14


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.



7/14


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



8/14


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



9/14


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).



10/14


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



11/14


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.



12/14


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.



13/14


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



14/14


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

Documents

Construct a Fold Cross-Section Using the Arc Method