Lab_07_2010 - GG303 Lab 7 1 DOWN PLUNGE CROSS SECTIONS I Main Topics A Cylindrical folds B Downplunge cross-section views C Apparent dip II

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GG303 Lab 7 10/6/10 1 Stephen Martel Lab7-1 University of Hawaii 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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GG303 Lab 7 10/6/10 2 Stephen Martel Lab7-2 University of Hawaii 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: 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.

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Lab_07_2010 - GG303 Lab 7 1 DOWN PLUNGE CROSS SECTIONS I Main Topics A Cylindrical folds B Downplunge cross-section views C Apparent dip II

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