Structural Geology (3443) Lab 1

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Structural Geology (3443)Lab 1 Attitude of
Lines and Planes
Department of Geology University of Texas at
Arlington
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Lab 1 - Assigned Exercises
Problems 1.1, 1.2 and 1.3 on pg. 3 Problem 1.4 on
pg. 6 using orthographic methods Problems 1.4,
1.5 and 1.10 using the trigonometric
equations. Problem 1.6 using orthographic
methods Problem 1.6 and 1.7 using trigonometric
methods
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Lab 1 Attitude Location
Terms Attitude (Spatial orientation of a line or
Plane) Bearing Horizontal angle between a line
and North. Strike Bearing of a horizontal line
lying on a plane
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Lab 1 Attitude Location
Dip The vertical angle measured in an imaginary
plane perpendicular to the strike of a plane of
interest. Dip Direction Two planes can have the
same numerical value of strike and dip, so the
dip direction (bearing) must always be specified.
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There are two ways of measuring bearing The
Quadrant method records the angle (from 0 to 90)
either clockwise or counterclockwise from North
or South and specifies the quadrant (NE NW SE
SW left). The Azimuth method records only the
clockwise angle from North (0 to 360), and
doesnt need to specify the quadrant (right).
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A line doesnt have sense i.e. one end of the
line is no different that the other end. A
vector, however, does have sense it points in
one particular direction. The strike of a plane
is usually considered a line, so the bearing
could be referred to either end (N45E S45W 135
315)
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Lab 1 Attitude Location
However, we will convert the strike to a vector
using a convention the right hand or
clockwise rule (left). All geologists will
agree that the dip lies clockwise to the strike,
so that end of the strike is its direction. Also,
if you look in the direction of its strike, the
plane will dip off to your right.
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Lab 1 Attitude Location
Exercise Estimate strike dip of the map
symbols below using the Clockwise Convention.
Give your estimates using first the Quadrant
Method and then the Azimuth Method
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The strike describes a special horizontal line
that lies in a plane. However, there are many
types of geological features that can be
described as lines - fault grooves
(slickenlines) current directions glacial
striations ripple marks intersections between
two planes, etc. These lines are called
lineations
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Lab 1 Attitude Location
Lineations are measured like strikes except that
the bearing is the horizontal angle to the
vertical plane that passes through the line. That
bearing is called the trend (instead of strike).
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Lab 1 Attitude Location
The direction of the lineation is the direction
of the geological process that caused it (glacial
or fault movement or a current). Exercise if
North is at the top of the picture, what is the
trend of the lineation caused by wind? What is
its plunge?
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Lineations caused by the intersection of two
planes do not have a geological direction
associated with them. In that case, geologists
assign the trend in the direction the line
plunges (like the dip direction) The plunge is
the vertical angle measured in the vertical plane
passing through the lineation (like dip).
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In the photo, assume you are looking due North,
and that the flat area is bedding (layering)
dipping toward you. The dark lines crossing the
bedding surface are the intersection of fractures
with the bedding plane. There are two directions
of intersection lineations. Estimate their trends
and plunges.
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Attitudes of Lines Rake (or Pitch) Lines
commonly lie in planes so their orientation can
be described by their Rake the acute angle
between the line and the strike of the plane
measured in the plane. Exercise the plane is
defined by ruled lines. The lineation goes
diagonally from left to right. What letters
describe the strike and dip of the plane? Which
letters describe the trend, plunge and rake of
the lineation?
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Exercise Assume that horizontal is perpendicular
to the photo, and that North is in the direction
you are looking. Estimate the strike and dip of
the surface that contains the pencil. Estimate
the trend, plunge and rake of the lineation that
parallels the pencil.
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Lab 1 Attitude Location
The Compass Used to measure the bearing of a line
or the strike of a plane. Used to measure
vertical angles and rakes.
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Lab 1 Attitude Location
The Compass needle tries to line up with lines of
force of the Earths magnetic field, and those
lines of force point to Magnetic North (MN), and
only by chance do they ever point to the
rotational pole, or true North (TN).
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Lab 1 Attitude Location
The lines of force are nearly horizontal at the
equator but plunge steeper until they plunge 90
degrees at the magnetic poles. Compasses are
useless near the magnetic poles because the
needle is constrained to the horizontal plane.
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The angular difference between the magnetic line
of force and true north is called the
DECLINATION, and varies from place to
place. Because the magnetic pole moves around,
maps showing declination must be updated every
year or so.
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Lab 1 Attitude Location
Declination can be set on the compass so it reads
the angle to true North instead to magnetic
North.
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Lab 1 Attitude Location
Using the Compass We will wait until the field
trip to learn how to measure strike Dip
Bearing and Plunge. Do problems 1.1, 1.2 and 1.3
on pg. 3 of the lab manual
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Projections
Geology is 3-D, so depiction of geological
features requires a projection of the 3-D image
onto a 2-D surface. All maps are projections.
There are a number of ways to project (Fig
3.1) We will be using the orthographic projection
(b)
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Projections
To see different aspects of the 3-D body, it is
projected in different directions and a folding
line is used to rotate the projections onto a
flat plane.
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Projections
Several folding lines are possible to get picture
of the 3-D body from different directions.
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Projections
In this lab, we are finding the attitude (strike
and dip) of planes. This makes use of the fact
that the intersection of two planes makes a line.
The strike line is the intersection of what two
planes? The dip and dip direction is the
intersection of what two planes?
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True Apparent Dip
True dip is always measured perpendicular to
strike. Apparent dip is the angle measured on
any other vertical plane and is always less than
the true dip.
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True Apparent Dip

• Sometimes we can only measure apparent dips, so
  true dip must be calculated from apparent dips.
• The following types of problems are solved using
  orthographic and trigonometric methods
• True dip from a strike an apparent dip.
• True dip from 2 apparent dips
• Apparent dip from true dip.

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Ex 1.1 True Dip from strike Apparent Dip
Example 1.1 Strike of quartzite layer 205
(S25W) (Fig a) Vertical quarry wall faces North.
The apparent dip of the quartzite layer in the
quarry wall is 40 toward the West. (What is trend
and plunge (a) of the intersection lineation
formed by the quarry wall and the quartzite
layer?) (Fig b)
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Ex 1.1 True Dip from strike Apparent Dip
Take the block and flip up the vertical quarry
wall to the horizontal plane (Fig e). Now draw a
diagram with North pointing to the top of the
page showing the exact angular relationships on
the horizontal plane of the strike, apparent dip
(a), and the true dip direction (Fig f).
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Ex 1.1 True Dip from strike Apparent Dip
Now draw the depth (d) from the surface to the
quartzite layer (Fig e f). The depth d is
arbitrary just make it long enough to measure
angles with the protractor.
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Ex 1.1 True Dip from strike Apparent Dip
Now imagine that the vertical plane containing
the true dip is flipped up (Fig g). Because the
quarry wall and the true dip plane intersect at
d, the depth d is the same in both planes.
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Ex 1.1 True Dip from strike Apparent Dip
Depth d is perpendicular to the horizontal plane
so you can now construct d on the true dip plane
that has been folded up (Fig h). Using a
protractor, measure the true dip (d).
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Ex 1.1 True Dip from strike Apparent Dip
Now solve Problem 1.4
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Ex 1.1 True Dip from strike Apparent Dip
Trigonometric solutions Find d (true dip) if
(a) apparent dip (b) angle from strike to
apparent dip direction Tan(a) d/FL1 Tan(d)
d/FL2 Sin(b) FL2/FL1 Tan(d) d/(FL1 Sin(b))
d/d(Sin(b)/Tan(a)) Tan(a)/Sin(b) d
Tan-1(Tan(a)/Sin(b))
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Ex 1.1 True Dip from strike Apparent Dip

• Tan-1(Tan(a)/Sin(b))
• Solve problems 1.4, 1.5 and 1.10 using the
  trigonometric equation.

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Ex 1.2 Strike True Dip from two Apparent Dips
Example 1.2 A fault is cut by two vertical cliff
faces. The trend and plunge of the intersections
of the fault and cliff faces are 15, S50E and
28, N45E respectively. Convert the trend and
plunge to azimuth and find the strike and true
dip of the fault.
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Ex 1.2 Strike True Dip from two Apparent Dips
Example 1.2 The apparent dip directions are shown
in Fig c (N45E 045 S50E 130) Next, flip up
the vertical cliffs to horizontal and draw the
apparent dips of the fault plane (Fig c)
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Next, pick any convenient depth d to the fault
plane and perpendicular to the horizontal plane .
Draw that length so it just fits between the
horizontal plane and the fault plane intersection
(Fig e). Make sure it is perpendicular to the
apparent dip direction.
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Now, points X and Z are at the same elevation on
the fault plane, and points A and C are also at
the same elevation directly above. The line
between X Z (not shown) as well as A C is
horizontal and lies on the fault plane so it is
the strike of the fault.
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Ex 1.2 Strike True Dip from two Apparent Dips
The horizontal line between A C on the surface
is also parallel to the strike. (Fig f).
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In the block diagram (Fig b) d is constant so
both XZ and AC define the strike line. Now
construct OB perpendicular to the strike line AC
on the horizontal plane that is the true dip
direction.
Now flip up the true dip vertical plane along OB,
measure depth d from B to Y, draw OY and measure
true dip d.
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Strike True Dip from two Apparent Dips
Do Problem 1.6
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True Dip from two Apparent DipsTrigonometric
solution
Example 1.2 Trig Solution Using the law of
cosines on triangle OAC, an equation can be
derived for the true dip in terms of the apparent
dip. d true dip OC and OA are apparent dip
directions AOC is angle between apparent dip
directions a1 apparent dip OCZ a2 apparent
dip OAX The spreadsheet on next page can be used
to calculate true dip
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True Dip from two Apparent DipsTrigonometric
solution
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True Dip from two Apparent DipsTrigonometric
solution
Do Problem 1.6 and 1.7 using trigonometric methods