Determination of principal stresses from faults

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Determination of the directions of the principal stresses from faults
Given a single or a conjugate set of faults, we can determine the orientation of the principal stresses
using the stereonet (see problem on page 252 of the Lab manual).
Procedure when we have a conjugate set (two faults that form synchronously under the same state of
stress):
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Plot the two conjugate faults and mark their poles with the  symbol
The intermediate principal stress (2) lies at the intersection of the two faults.
Mark it with the 2 symbol
Plot a great circle perpendicular to the 2, by drawing the great circle whose pole is 2 (i.e., 2)
This is the 13 or Movement or ‘M’ plane.
The 13 or Movement or ‘M’ plane intersects the two faults along the slip lineations (SL).
Mark these with the SL symbol.
Notice that the pole of the two faults lie on the M-Plane!
Locate 1 on the M-Plane, along the acute bisector between the two slip lineations.
Measure the acute angle between the 1 and the two slip lineations. This is the angle .
Determine the angle of internal friction () from the 2+ = 90 equation!
Locate 3 at 90o to the 1.
If 1 is near (or at) the center, then the two faults are normal faults.
If 3 is near (or at) the center and If 1 is near (or on) the primitive, then the two faults are
reverse faults.
If 2 is near (or at) the center, then the two faults are strike-slip.
Read the pitch of the two slip lineations on each fault.
Orient your hand to represent fault 1. Then use a pencil to represent the slip lineation on it,
using the pitch. Put your other hand on the pencil (orient the pointed part of the pencil down
for normal, up for reverse, and horizontal for strike slip fault), and move your upper hand along
the pencil (don’t roll the pencil), making sure to do it the right way, i.e., if it is normal, move
your upper hand down along the pencil. Then see if the motion is right lateral or left lateral.
Repeat for the other fault.
Procedure when only a single fault is given in addition to a slip lineation
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Plot the fault as great circle and its pi (pole) with the  symbol
Plot the slip lineation on the fault. Mark the lineation with the SL symbol.
Plot the great circle of the 13 or Movement or ‘M’ plane by connecting the pole to the fault
() and the slip lineation (SL).
The intermediate principal stress (2) lies along the pole to the M-Plane.
Mark it with a 2 symbol
Locate 1 on the M-Plane, at an acute angle of about 30 (i.e., assume the angle  ~30o).
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Find the 3 perpendicular to the 1 on the M-Plane
Read the pitch of the slip lineation on the fault
Use your hand and a pencil, as described above, to determine the sense of slip.
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