Week 2
Kinematic Analysis I. Read pages 38-66 in
Chapter 2: Kinematic Analysis.
- You are expected to read all the
sections listed below. Information from the sections in
italics will be discussed
- in class. You are expected to read the other sections and
you may be called on in class to answer questions
- based on that material.
- Strategy p.38-41
- Translation p.41-47
- Rotation p.47-50
- Strain p.51-66
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You should become familiar with the
following terms during this weeks lectures and readings:
| angular shear |
aspect ratio |
axis of rotation |
crystal fiber vein |
displacement vector |
| extension (e) |
heterogeneous deformation |
homogeneous deformation |
non-rigid body deformation |
rigid body deformation |
| sense of rotation |
shear strain |
(fault) slip |
strain |
strain ellipse |
| stretch (S) |
You should be able to answer the
questions below following this week:
- Identify the following figures from Chapter 1 as examples
of rigid body or non-rigid body deformationand (where
possible) determine if translation, rotation, dilation or
distortion occurred: Figures 1.1, 1.2, 1.3, 1.7, 1.10A,
1.13, 1.14B, 1.15, 1.16, 1.29, 1.34, 1.37.
- Determine the magnitude of extension of: a) the white
layer in the final stage of Figure 1.39; and, b) the
upper black layer in Figure 1.40B.
- Assuming no change in area, determine the percent
lengthening and shortening of the long and short axes
respectively, of the strain ellipses represented in the
distorted sample of lapilli tuff in Figure 2.5.
- A series of deformed worm burrows were examined to
determine strain on a horizontal bedding surface.
Stretches measured parallel to the principal axes of the
calculated strain ellipse were S1 = 2, S3
= 0.5. The S1 axis had a plunge an daximuth of 0, 330o.
Determine: a) the orientation of two lines relative to S1
that underwent no finite
stretch; b) the plunge and aximuth of those lines; c) the
angular shear values for the lines.
- The strain ellipse on the right was generated when a
circular strain marker was deformed. Assume no volume
loss during deformation and construct the original
circular marker centered over the ellipse. Determine the
extension and stretch values for the principal strain
axes of the ellipse.
- Draw a two-inch square. Assume the square undergoes the
deformation described below and redraw the figure to
illustrate the results of deformation. The deformation is
not cumulative.a) Show the square after non-rigid body
homogeneous distortion with an angular shear of +30o;
b) show the square after a positive dilation of 50%.
- What is the final length of a line of original length 6
cm that has experienced an extension of 0.4?
- What is the stretch of a belemnite that had an initial
length of 15 cm and a final length of 12 cm?
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Kinematic Analysis I
Reconstruction of movements that occurred during formation and
deformation of rocks.
Rigid vs. non-Rigid body deformation
- Is the relative arrangement of points in a body
maintained?
- Yes = rigid body deformation
- No = non-rigid body deformation: change in shape
and/or size of original object
Rigid Body Movements
Translation
- all points in a body move along parallel paths, e.g.
sliding book on desk
- sliding occurs on a discontinuity, e.g. fault, bedding
plane, desk top
- describe translation by a displacement vector with
components of:
- Examples?
Rotation
- rigid body rotation about an axis, e.g. rotation of pages
around spine of a spiral notebook
- describe rotation by:
- Examples?
Non-Rigid Body deformation
Dilation
- distance between internal points of reference increases
or decreases but shape remains uniform
Distortion
- non-uniform changes in distance between points within a
body results in a change in shape
dilation and/or distortion = strain
Homogeneous deformation: strain is constant throughout
a body
Heterogeneous deformation: strain is variable within a
body
Strain Analysis
- describe changes in shape and size of the original body
of rock using geometrical parameters (restricted to
homogeneous deformation or parts of heterogenously
deformed body that may be treated as homogeneous
deformation)
Rules for strain analysis:
- lines that were straight prior to deformation remain
straight after deformation
- lines that were parallel before deformation remain
parallel after deformation
i.e. strain is uniform throughout the deformed body of rock
Strain can be defined by measuring changes in line length
and orientation in:
- linear features that have been deformed, e.g. stretched
fossil
- geometric axes defined within elliptical markers that
were circular prior to deformation.
Line length changes
extension (e): the change in the length of a line relative
to its initial length
- e = (lf - lo)/lo where lf is the final length of an
object and lo is the original length
- % length change = e x 100
- +ve values = lengthening (what is the maximum possible
value?)
- -ve values = shortening (what is the minimum possible
value?)
stretch (S): final length of a line of unit length
- S = lf/lo = 1 + e
- maximum value is infinity
- minimum value is zero
Orientation Changes
- describe changes in the relative orientations of lines,
especially lines that were originally perpendicular
angular shear (psi)
- degree to which two originally perpendicular lines are
deflected from 90o
- +ve = clockwise deflection
- -ve = counter-clockwise deflection
- range = -90 to +90
shear strain (gamma)
- shear strain = tan (angular shear)
- relates change in orientation to distance moved by a
point along a reoriented line
strain ellipse
illustrates the magnitude and orientation of the distortion of
a geologic body
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