Determining strike and dip from geologic maps
(revisited)
75 m
This is a satellite photo of a
plunging anticline ("A" shape)
and syncline ("V" shape) pair.
Which direction is the
anticline plunging (to top or to
bottom of figure)?
Which direction is the
syncline plunging toward?
What is the name for these
fold shapes?
Are the apparent thicknesses
of the beds less than or
greater than the true
thicknesses of the beds?
What is it? (Quiz)
(D&R 51-97)
1. Definitions and strain quantities
2. Mohr circle strain diagram
3. Pure shear vs. simple shear
4. Strain rate
What is strain?
Strain is dilation (change in size) and/or
distortion (change in shape).
The Goal of strain analysis is to explain how
every line in a body changes in length and angle
during deformation.
How is this attempted?
Homogeneous deformation: systematic and uniform.
Test: straight lines in the body before deformation are
straight after deformation. Circles get deformed into ellipses.
We will assume that deformation is homogeneous!
Heterogeneous deformation: irregular and non-uniform. A
mess to work with, mathematically.
Some important quantities for describing strain
Extension (e): (Lf-Lo)/Lo, where Lf is the final length
of a line and Lo is the initial length of a line
Stretch (S): Lf/Lo, where 0 = severe shortening, 1 =
no shortening, and infinity = severe stretching
Quadratic elongation (l): = (1+e)2 = (Lf/Lo)2 = S2
Example of calculating
extension
(51.5 - 33)/33 = .56 = extension
multiply by 100 to give you 56% extension
A similar exercise can be performed for
calculating %shortening in a thrust belt
So far- we have only talked about changes in
lengths of lines- what about angles?
Angular shear (y, psi): degree to which 2 initially
perpendicular lines are deflected from 90 degrees
Shear strain (g, gamma): = tan (y)
Finite vs. Instantaneous strain
What does 'finite' mean? It is total strain, the final
result of deformation that we see as geologists
Instantaneous or infinitesimal strain describes a
tiny increment of deformation
As will become apparent when studying how
fabrics form in rocks, the orientation of finite
strain may be very different than that of
instantaneous strain
The "Magic" of
homogeneous
strain
Strain ellipse and ellipsoid for homogeneous
deformation:
Shows how circular reference object is deformed
3-D
2-D
Vs=4/3pr3
Ve=4/3pabc
Calculating strain
If the stretch values in the principal finite
stretching directions are known, it is possible to
determine the stretch and shear strain for any
line of any orientation in the strained body.
fundamental strain equations
g/l (for any line of orientation qd from S1) =
1/2(1/l3-1/l1)sin2qd
Strain can be calculated graphically in the Mohr
Strain Circle:
g/l = 1/2(1/l3-1/l1)sin2qd
l'1 = 1/l1
l'3 = 1/l3
Some more definitions
Plane strain: S1 is compensated by S3 so that
there is no change in S2- and no change in volume!
Noncoaxial strain: finite principal stretching axes
do not remain fixed in orientation during deformation
Coaxial strain: Finite principal stretching directions
have the same orientation before and after
deformation
2 end-member types of plane strain
Simple shear: Rock is
sheared like a deck of cards.
A square becomes a
parallelogram. **The finite
stretching axes rotate during
deformation. Distortion by
simple shear is the most
important process in shaping
shear-zone structures!
Pure shear: Rock is
shortened in one direction and
extended in the perpendicular
direction. A square becomes
a rectangle. **The finite
stretching axes do not rotate.
A better feeling for simple shear
lines in circle
brachiopod
A better feeling for pure
shear
lines in circle
brachiopod
Strain Rate
strain rate = extension (e) divided by time (t) = e/t
The rate at which a rock is strained has important
implications for the manner in which it deforms.
"Lab" Strain Rates
During 1 hour experiment, an initially 2.297 cm-long
sample is shortened to 2.28 cm. What is the average
strain rate during this experiment?
"Natural" Strain Rates
Basin and Range
extension:
present-day width = 600
km
initial width = 300 km
Extension occurred over
~20 m.y.
What was the strain rate?
How much does it differ
from laboratory
experiments?
What are the
implications?
Next Lecture: Stress!
Read D&R 98-122
Important terminology/concepts
dilation
distortion
homogeneous vs. heterogeneous deformation
extension- definition and calculation of
stretch
strain ellipse and ellipsoid- principle stretch directions
finite strain vs. instantaneous strain
Mohr strain diagram
plane strain
noncoaxial vs. coaxial strain
simple shear
pure shear
strain rate- definition and calculation of