Structural Geology (3443)Lab 1 Attitude of

Lines and Planes

Department of Geology University of Texas at

Arlington

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 orthog

raphic methods Problem 1.6 and 1.7 using trigonom

etric methods

Lab 1 Attitude Location

Terms Attitude (Spatial orientation of a line or

Plane) Bearing Horizontal angle between a line a

nd North. Strike Bearing of a horizontal line ly

ing on a plane

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.

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 onl

y the clockwise angle from North (0 to 360), and

doesnt need to specify the quadrant (right).

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 i

s usually considered a line, so the bearing could

be referred to either end (N45E S45W 135

315)

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 agre

e 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.

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

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 lineati

ons

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).

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?

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).

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.

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 def

ined 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?

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.

Lab 1 Attitude Location

The Compass Used to measure the bearing of a line

or the strike of a plane. Used to measure vertic

al angles and rakes.

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).

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.

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.

Lab 1 Attitude Location

Declination can be set on the compass so it reads

the angle to true North instead to magnetic

North.

Lab 1 Attitude Location

Using the Compass We will wait until the field t

rip 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

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)

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.

Projections

Several folding lines are possible to get picture

of the 3-D body from different directions.

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 intersec

tion of what two planes?

True Apparent Dip

True dip is always measured perpendicular to

strike. Apparent dip is the angle measured on an

y other vertical plane and is always less than

the true dip.

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 t

rue dip.

Ex 1.1 True Dip from strike Apparent Dip

Example 1.1 Strike of quartzite layer 205 (S25

W) (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)

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).

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.

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.

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).

Ex 1.1 True Dip from strike Apparent Dip

Now solve Problem 1.4

Ex 1.1 True Dip from strike Apparent Dip

Trigonometric solutions Find d (true dip) if

(a) apparent dip (b) angle from strike to app

arent 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))

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.

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.

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)

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.

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.

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).

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.

Strike True Dip from two Apparent Dips

Do Problem 1.6

True Dip from two Apparent DipsTrigonometric

solution

Example 1.2 Trig Solution Using the law of cosin

es 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 directi

ons 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

True Dip from two Apparent DipsTrigonometric

solution

True Dip from two Apparent DipsTrigonometric

solution

Do Problem 1.6 and 1.7 using trigonometric methods