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GG303 Lab 7
10/6/10
1
Stephen Martel
Lab71
University of Hawaii
DOWN PLUNGE CROSS SECTIONS
I
Main Topics
A Cylindrical folds
B Downplunge crosssection 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 twodimensional 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 crossproduct of the poles gives the
orientation of the fold axis.
III Downplunge crosssection views
A Downplunge crosssection 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 crosssection 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 endon, the fold axis will
appear as a point.
All the other lines lying in the surface of a
cylindrical fold will also be viewed endon, so the fold surface will
appear as a curve.
D Computerassisted technique using Matlab
1
Find threedimensional 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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View Full Document GG303 Lab 7
10/6/10
2
Stephen Martel
Lab72
University of Hawaii
2
Transform the coordinates of the digitized points by projecting them
onto a new set of righthanded reference axes aligned with the fold
axis.
a “Manual” procedure
i
Define the downplunge (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 downplunge 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:
X
1
X
2
...
X
n
Y
1
Y
2
...
Y
n
Z
1
Z
2
...
Z
n
⎡
⎣
⎢
⎢
⎤
⎦
⎥
⎥
=
a
Xx
a
Xy
a
Xz
a
Yx
a
Yy
a
Yz
a
Zx
a
Zy
a
Zz
⎡
⎣
⎢
⎢
⎤
⎦
⎥
⎥
x
1
x
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This note was uploaded on 12/05/2011 for the course GEOLOGY 300 taught by Professor Stephenmartel during the Fall '11 term at University of Hawaii, Manoa.
 Fall '11
 StephenMartel

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