SGES 3371 STRUCTURAL GEOLOGY II

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SGES 3371STRUCTURAL GEOLOGY II
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2D Strain Analysis III

• Deformed fossils as strain indicators
• Fossils and other objects with know starting
  shapes can sometimes be used as strain indicators
• If the original undeformed size and shape is
  known, the the problem is merely one of measuring
  the extension/stretch and angular shear and the
  strain is determined by calculation or
  graphically (Mohr circle)
• However, it is impossible to reliably measure the
  original lengths of lines
• However, if several or many variously oriented
  individual fossils or objects are present the
  strain may be obtained by several methods
• Wellmans Method
• Center-to-center Method
• Frys Method
• Rf/f Method (Final ellipse/phi)

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2D Strain Analysis III - Wellmans Method

• Wellman (1962) has devised a relatively simple
  way to determine the shape and orientation of the
  strain ellipse from group of fossils with known
  original shape (volumetric strain cannot be
  determined).
• Fossils that are suitable for Wellman analysis
  are bilaterally symmetric and have orthogonal
  lines, such as brachiopods and trilobites.
• The fossils are preferably randomly oriented (at
  least show varied orientation)
• It is based on the fact that any angle drawn in a
  semicircle is a right angle (any triangle passing
  the center of a circle and intersect the
  circumference is a right triangle)

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2D Strain Analysis III - Wellmans Method

• In the circle below, red line is the diameter, L
  and M must be perpendicular.
• After homogeneous deformation, the circle becomes
  an ellipse, and the deformed lines (L L)
  still intersects the circumference of the ellipse
• Thus originally orthogonal lines can be used as
  reference lines where their angular distortion
  after deformation can be used to define the
  strain ellipse
• If enough pairs of lines (fossils) that are
  originally orthogonal, with different
  orientations are available, the strain ellipse
  can be drawn.
• Disadvantage the lines (fossils) must lie on a
  bedding surface, and for accurate results, 10 or
  more fossils occurring together are required

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2D Strain Analysis III - Wellmans Method

• There are 8 variously oriented brachiopods in the
  diagram below. We can use 2 perpendicular lines
  in each brachiopod, the hinge line the symmetry
  line
• Points A and B are arbitarily located on the
  diagram to represent the end of a reference
  diameter.
• Lengthen and translate both orthogonal lines to A
  and B, in doing so forming a rectangle. Repeat
  for all brachiopods.
• Join the corners of all the rectangles. It will
  form a circle reprensenting the strain ellipse of
  the undeformed brachiopods.

Hinge line
B
Symmetry line
A
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2D Strain Analysis III - Wellmans Method

• The diagram below shows the deformed state of the
  brachiopods. The 2 originally orthogonal lines
  are not orthogonal after deformation.
• Points C and D are arbitarily located on the
  diagram to represent the end of a reference
  diameter.
• Lengthen and translate pair of lines that were
  orthogonal before deformation to C and D, in
  doing so forming a parallelogram. Repeat for all
  brachiopods.
• Join the corners of all the parallelograms. It
  will form an ellipse reprensenting the strain
  ellipse of the deformed brachiopods.

Hinge line
Symmetry line
S1
D
S1 semimajor axis S3 semiminor
axis Ellipticity of the strain ellipse, RS1/S3
S3
C
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2D Strain Analysis III - Center-to-Center Method

• Ramsay invented this method in 1967. It is based
  on the principle that the distance and angular
  relationships between particles in an aggregate
  of objects (sand grains, pebbles, ooids) with
  statistically uniform initial distribution should
  help to determine the orientation of the strain
  ellipse in the deformed aggregates.

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2D Strain Analysis III - Center-to-Center Method

• This method involves measurement of the distances
  and angles between a reference grain and its
  nearest neighbours.
• Measurement of immediate neighbours only, the tie
  line should not cross any other grains.
• A plot may be made of d' versus values of a'
  ranging from 90 to 90
• A best-fit curve is constructed and then the
  maximum and minimum values and the symmetry axes
  of the curve is determined.

B, C D immediate neighbour
E, F, G, H, I far neighbour
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Deformed ooids
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Ooids centers plotted as points
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2D Strain Analysis III - Center-to-Center Method

• Arithmetric mean of the d values at certain a'
  interval (say 10) may be used to plot the
  best-fit curve.
• The ellipticity of the strain ellipse, R is
  obtained by Rdmax/dmin

d' versus a plot. Pointsmeasurements small
circlesaverage at 10 intervals
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2D Strain Analysis III - Frys Method

• Fry invented this method in 1979, which is a
  simplified version to Ramsays center-to-center
  method, which is time consuming to construct.
• Angular relationships and distances between
  particles are modified according to the nature
  and amount of accumulated strain.
• The result of the Fry technique is a diagram
  containing a set of points with a circular-to
  elliptical blank area of relative shape and
  orientation proportional to the shape and
  orientation of the strain ellipse. A circular
  area indicates that there is no strain in the
  rock.

Fry diagram of centers of ooids
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2D Strain Analysis III - Frys Method

• Procedure An overlay is made and a central
  reference point identified. A second overlay is
  made and the center of each particle is marked
  with a numbered point.
• The central reference mark on the first overlay
  is placed over a numbered point, and dots
  corresponding to all of the numbered centers of
  the particles are marked on the overlay. (It may
  be adequate to mark just the centers of the
  adjacent grains.)