1

DOWN PLUNGE CROSS SECTIONS

I Main Topics

A Cylindrical folds

B Downplunge cross-section views

C Apparent dip

II Cylindrical folds

A Surface of a cylindrical fold is parallel to a line called the fold axis.

B Cylindrical folds maintain their shape for “long” (infinite) distances in the

direction of the fold axis (as opposed to folds bending in the shape of a

bowl); they are two-dimensional structures because they do not change in

shape along the dimension of the fold axis.

C Planes tangent to cylindrically folded beds intersect in lines parallel to the

fold axis.

D Poles to cylindrically folded beds are contained in the plane perpendicular

to the fold axis, so taking the cross-product of the poles gives the

orientation of the fold axis.

III Down-plunge cross-section views

A Down-plunge cross-section views can be obtained directly from a geologic

map by looking obliquely at the map down a fold axis.

B Beds appear in true thickness

C Graphical technique

1 Find orientation of fold axis

2 Draw a cross-section along a plane parallel to the fold axis. The fold

axis will be contained in this plane and the fold axis will appear "in true

length" and its plunge can be measured.

3 Take an adjacent view of the above cross section where the line of

sight is parallel to the fold axis. Viewed end-on, the fold axis will

appear as a point. All the other lines lying in the surface of a

cylindrical fold will also be viewed end-on, so the fold surface will

appear as a curve.

D Computer-assisted technique using Matlab

1 Find three-dimensional coordinates of points on the folded units. This

can be done be digitizing a geologic map, for example, by scanning a

map and using Matlab’s ginput function:

[x,y] = ginput

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2 Transform the coordinates of the digitized points by projecting them

onto a new set of right-handed reference axes aligned with the fold

axis.

a “Manual” procedure

i Define the down-plunge (e.g., X,Y,Z) reference frame in terms of

the geographic (e.g., x,y,z) reference frame.

For example, let the Y axis be the down-plunge direction, the X

axis be horizontal and 90° clockwise from the fold axis trend,

and the Z axis be “up” (but not vertical). This is the view one

would get if you point you right arm and right index finger down

the fold axis, with your thumb pointing to the right. and your

middle finger pointing “up”.

ii Transform the coordinates from the x,y,z reference frame to the

X,Y,Z reference frame using the matrix transformation equations.

For one point:

X

Y

Z

⎡

⎣

⎢

⎢

⎤

⎦

⎥

⎥

=

a

Xx

a

Xy

a

Xz

a

Yx

a

Yy

a

Yz

a

Zx

a

Zy

a

Zz

⎡

⎣

⎢

⎢

⎤

⎦

⎥

⎥

x

y

z

⎡

⎣

⎢

⎢

⎤

⎦

⎥

⎥

(3x1) = (3x3) (3x1)

For n points:

X1X2... Xn

Y

1Y2... Yn

Z1Z2... Zn

⎡

⎣

⎢

⎢

⎤

⎦

⎥

⎥

=

aXx aXy aXz

aYx aYy aYz

aZx aZy aZz

⎡

⎣

⎢

⎢

⎤

⎦

⎥

⎥

x1x2... xn

y1y2... yn

z1z2... zn

⎡

⎣

⎢

⎢

⎤

⎦

⎥

⎥

(3xn) = (3x3) (3xn)

iii Then prepare an (X,Z) plot using Matlab’s plot command:

plot(X,Z)

The Y (down-plunge) coordinate is irrelevant for this view.

b “Automated Matlab 3-D visualization technique”

i Use the Matlab command

plot3(x,y,z)

ii Then use the “view” command to look down the fold axis

view(-trend,plunge)

(Here the trend and plunge are in degrees, not radians)

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Upload date:
18/07/2013