GEOL 4334
Lab 01: Lines and Planes
Lab 01:
v. 2015
Orientation of Lines & Planes in Rocks
Objectives
Ø These exercises will develop the skills of 3D visualization and description of geologic structures
using correct terminology.
Ø Enable students to communicate the 3D orientation of geologic structures to other co-workers,
collaborators using precise terminology and symbols
Ø Enable students to evaluate the geometry of geologic structures
Ø After completion, can you i) visualize the orientation of a structure described in a report or an oral
presentation, and ii) articulate the orientation of a given geologic structure to your colleagues?
Materials:
pencil, colored pencils, trig-calculator, tracing paper, paper, ruler, protractor
I. Vocabulary
Many of the structures that we can observe in seismic lines, cores, or in outcrops can be approximated by
lines and planes. In this lab you will learn the rudiments of structural orientation, including strike, dip,
apparent dip, trend, plunge, and rake. You will then examine and use two different techniques to solve planar
and linear geometric problems that you would typically encounter working in industry or conducting geologic
field research. MEMORIZE the following terms and learn to visualize these features in 3-D.
Attitude: the orientation in space of a structural element; e.g., bed, fault, lineation, etc. The attitude of a
planar structure is expressed by its strike and dip; the attitude of a line is expressed as trend and plunge.
Bearing (azimuth): The horizontal angle between a line and a specified coordinate direction, e.g., north, etc.,
or in degrees from 0-360.
Quadrant: Four quarters of the cardinal directions; e.g., NE, SE, SW, NW. Compasses in the U.S.
predominantly use quadrants in which each quarter is divided into 90° increments beginning with 0° at
both N and S and 90° at both E and W.
Strike: The bearing of a horizontal line contained within an inclined plane. The strike is a line produced by the
intersection of a horizontal and inclined plane. Measured relative to north in quadrant space.
Dip (δ): The vertical angle between an inclined plane and a horizontal line that is perpendicular to the strike
line.
(Trend of) Dip direction: The bearing of a line that is perpendicular to the strike line that points to the dip
direction.
Trend: The bearing of a line. Non-horizontal lines trend in the down-plunge direction.
Plunge: The vertical angle between a line and horizontal.
Pitch or rake: The angle measured within an inclined plane between a horizontal line (the strike line) and the
line in question. (Measured with a protractor.)
Apparent Dip (α): The vertical angle between an inclined plane and a horizontal line that is NOT
perpendicular to the strike of the plane. For an inclined plane, the apparent dip is ALWAYS LESS THAN
THE TRUE DIP. Apparent dip, therefore, really defines the inclination of a line and may be expressed
with a trend and plunge or by its pitch (or rake).
Horizontal Line
Horizontal STRIKE
Line
Dip direction
Line 2
Line 1
GEOL 4334
Lab 01: Lines and Planes
v. 2015
II. Conventions for expressing strike & dip of a PLANE
Strike and dip can be expressed in a number of different ways and it is advantageous to be able to
conceptualize these conventions.
In the U.S., strike is measured using
the quadrant method in which the
compass is divided into four
quadrants (NE, SE, SW, NW). A fault
plane that strikes north-west/southeast and dips 42° southwest would
be expressed as N45W/42SW;
meaning that the line produced by
the intersection of an imaginary
horizontal plane and the inclined fault
plane trends 45° west of north. The
dip of this plane, measured
perpendicular to the strike, is 42° in
the southwest direction. Quadrant data should always be recorded and displayed relative to north in the
following way: e.g., NxW/ySW, where x is the measured strike and y is the measured dip.
The other convention is the azimuthal method, in which the compass is divided into 360° (0°/360° at the top,
counting in a clockwise direction). Using the azimuthal method, the fault plane noted above would have a
strike of either 315° or 135°. You would then have to specify the dip direction: 315/42SW.
Dip direction may be specified in two ways:
1) The ‘right-hand rule’: looking in the direction of the strike the plane should dip to your right.
Therefore, in the above case, the strike would be 135° and the dip would be 42°. The convention for
displaying ‘right-hand rule’ data is strike first, then dip; e.g., 135°/42°.
2) Alternatively, you could specify the dip direction; e.g., 315° 42W. In this case, you do not have to look
down the strike line and worry about the ‘right-hand rule’ because the dip direction, “W”, is noted.
III. Conventions for expressing plunge & trend of a LINE
The convention for noting the trend of a line is that it should always be measured in the ‘down-plunge’ view,
and the plunge is always recorded first. For example, 36°/S54W means that a line plunges 36 degrees in a
direction 54 degrees west of due south. When measuring a line in quadrant notation, you may use all
quadrants, not just the north half.
IV. Map symbols and notation conventions
PLANES
The symbols to the left represent strike and dip symbols for planes of
the various orientations noted. The long line represents the strike
direction; the shorter tick points toward the dip direction. The bold
italics notation is in quadrant form; the regular font is in azimuth with
“right hand rule”.
GEOL 4334
Lab 01: Lines and Planes
v. 2015
LINES
The symbols to the left represent plunge and trend symbols for lines of
the various orientations noted. The bold italics notation is in quadrant
form; the regular font is in azimuth. Note that the direction of trend for a
given line is always measured toward the plunge direction. For
example, the measurement of 30°/S45°E defines a line that plunges
30° from horizontal toward the direction of S45°E.
V. True vs. Apparent Dip
The block diagram below (A) displays the difference between apparent
dip and true dip. Apparent dip, α, is the vertical angle measured from
horizontal down to an inclined plane in a
vertical plane that is NOT perpendicular to
ion
the strike line. The horizontal angle
rect
i
d
ke
between the apparent dip direction and the
stri
strike line is β.
A
α
The true dip, δ, is equal to the maximum
dip of the plane and is therefore always
greater than α.
δ
VI. Putting it all together
B
Notice how the profile
plane in Fig. B containing
the apparent dip (α = 56°)
is not perpendicular to
strike.
a
C
N
ike
β angle: 60° (acute
angle)
Map View
str
Example based on oblique block diagram
and associated map view.
Strike & Dip
Quadrant: N30°W/60°SW
Azimuthal: 330°/60°SW; 150/60SW
Oblique Perspective
Azimuthal, r.h.r.:
150°/60°
Dip Direction:
Quadrant: S60°W
Azimuthal: 240°
n
io
Apparent Dip Direction:
ct
re
di
p
Quadrant: N90°W;
di
ue
r
t
n
S90°W; or due W
ctio
dire
dip
t
n
Azimuthal: 270°
re
ppa
n
ctio
ire
d
ip
ed
tru
apparent dip direction
VII. Website Resources:
http://earthsci.org/education/fieldsk/compass/compass.html
http://www.geo.utexas.edu/courses/420k/PDF_files/Brunton_Compass_09.pdf This shows some examples of
how geologists measure strike and dip.
http://www.fault-analysis-group.ucd.ie/structurecontours/contours/strike.html
GEOL 4334 • Lab 01: Lines & Planes
Name:
R#:
TA:
PROBLEMS • PART I
1. Translate from the azimuthal convention to the quadrant convention, or vice-versa, as is necessary (6 pts.).
a. N43°E _______
d. 087°
_______
g. S62°W _______
j. 241°
_______
b. N43°W _______
e. S20°E _______
h. N62°E _______
k. 270°
_______
c. N90°W _______
f. 355°
i. 127°
l. due S
_______
_______
_______
2. Circle those attitudes in the list below that are impossible (i.e., a bed with the indicated strike cannot possibly dip in the direction that
is indicated) (3 pts).
a. N23W/57SE
c. N45W/78NW
e. N34W/14N
g. 089°, 3N
b. N46W/56NE
d. 089°, 43SW
f. 089°, 43E
h. 341°, 84NE
3. Translate the following attitudes into the azimuthal convention according to the right-hand rule. (3 pts.)
a. N30W/34NE __________
c. 078, 76SE __________
e. 234, 43NW __________
b. N48E/56SE __________
d. 067, 74NW __________
f. 117, 21NE
__________
4. Translate the following strike and dip measurements into equivalent dip and dip direction measurements. The trend of the dip
direction may be written either in quadrant or azimuthal convention. (3 pts.)
a. N34W/38NE ____________
c. N48°E/57°SE ____________
b. 087, 21NW ____________
d. 245°, 41°NW ____________
e. 117°, 33°NE ____________
PART II – Apparent Dip Problems
With the following problems you will learn how to visualize and draw diagrams that help to illustrate & calculate the 3-D orientation of
structures. The following equation will provide the true dip, if you know the apparent dip, apparent dip direction, and strike of a planar
structure. You can rearrange the equation to solve for apparent dip, apparent dip direction and/or strike.
tan δ = tan α/sin β,
or, the tangent of the plunge of true dip (δ) = the tangent of the plunge of the apparent dip (α) divided by the sine of the angle (β)
between the strike of a plane and the bearing of an apparent dip.
True Dip from two apparent dips
Tan of φ = (csc angle between θ1 and θ 2)((cotα1)(tanα2)-(cos angle between θ 1 and θ 2)),
where:
φ = horizontal angle between true dip direction & apparent dip direction;
θ1 and θ 2 = apparent dip direction 1 and 2, respectively;
α1 and α2 = apparent dip angle 1 and 2, respectively.
This equation will give you the true dip and dip direction from two apparent dips. (If you know the true dip and dip direction, then you
also know the strike. Right? Right. Now explain it to your neighbor!)
Complete each of the following problems on separate pages of engineering paper. Be sure to properly label your answers. Be sure to
include all steps.
5. Along a road cut, a bed of coal has an apparent dip of 20° in a direction of N62W. The bed strikes N67E.
a. Draw and label a 3-D block diagram that illustrates this problem. (3 pts.)
b. Calculate the true dip. (3 pts.)
6. A fault has an attitude of N80E/48SE.
a. Determine the apparent dip of this fault in a vertical cross-section that strikes N65W. (4 pts.)
b. Draw and label a 3-D block diagram that illustrates this problem. (4 pts.)
7. A coal seam dips 2° due east. Dingbat Mining Co. wants its mining adits (mining tunnels) to slope at least 1° so that water will drain
out of the toxic pit and pollute the local trout stream.
a. In what directions can adits (tunnels) be driven without plunging less than 1°? (5 pts.)
b. Draw and label a 3-D block diagram that illustrates this problem. (6 pts.
GEOL 4334 • Lab 01: Lines & Planes
Name:
R#:
TA:
cut out along bold black line prior to lab!!!!!
True versus apparent
dip model. Cut out
along bold perimeter
line.
Redrafted from the
Fault Analysis Group,
University College
Dublin.
stirike/dip
symbol
B
ap
pa
re
nt
dip
β
A
line parallel to strike
line normal to
strike
ke
true dip
45°
A
tr i
α
Cut-out model to display strike/dip, plunge/trend
and apparent dip. Cut out along perimeter line.
Redrafted from the Fault Analysis Group, University
College Dublin.
bli
qu
et
os
B
eo
trend
lin
γ
GEOL 4334 • Lab 01: Lines & Planes
Name:
cut out along border line PRIOR to LAB
R#:
plunge/trend
symbol
29°
TA: