Structural Analysis and Synthesis Solution Manual [Part1]

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Structural Analysis and Synthesis
A Laboratory Course in Structural Geology
Third Edition
SOLUTIONS MANUAL
Stephen M. Rowland
University of Nevada, Las Vegas
Ernest M. Duebendorfer
Northern Arizona University
Ilsa M. Schiefelbein
ExxonMobil Corporation, Houston, Texas
Separate maps are available on request from artworkcd@bos.blackwellpublishing.com
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Chapter 1
Note to instructors
You may wish to accept errors of !1–28 on orthographic projection problems. Our
experience is that the careful student can always come within !18 of the attitudes
determined below.
Answers
Worked solutions are presented below.
Problem 1.1
a) N128E 0128 f) N378W 3238
b) 2988 N628E g) 2338 N538E
c) N868W 2748 h) 2708 N908W
d) N558E 0558 i) 0838 N838E
e) 1268 N548W j) N38W 3578
Problem 1.2
a) 3148, 498NW Impossible f) 3338, 158SE Impossible
b) 0868, 438W Possible g) 0898, 438N Possible
c) N158W, 878NW Impossible h) 0658, 368SW Impossible
d) 3458, 628NE Possible i) N658W, 548SE Impossible
e) 0628, 328S Possible
Attitudes a, c, f, h, and i are impossible because the strike and dip cannot be in the same
direction.
Problem 1.3
Lineation Feasible? Explanation Type of fault
a) Due north, 348 Yes Lies within fault plane; plunge less
than dip
Oblique-slip
b) 1408, 08 Yes Lies within fault plane; plunge ¼ 0 Strike-slip
c) N668W, 338 No Lineation does not lie within fault plane
d) 0508, 478 Yes Lies within fault plane; plunge ¼ dip Dip-slip
e) Due north, 758 No Plunge steeper than dip
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Problem 1.4
258NW
Problem 1.5
338SE
Problem 1.6
N248E, 33.58NW
Problem 1.7
a1 ¼ 39#S
a2 ¼ 19:5#E
Problem 1.8
25.18NW
Problem 1.9
32.58SE
Problem 1.10
Any direction between N308E and S308E
Problem 1.11
N618E, 118S
Problem 1.12
(a) 258NW
(b) 328SE
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Solutions
Problem 1.4 Problem 1.5
True dip (δ) = 2.58NW
Apparent dip (α) =338SE
Problem 1.6 Problem 1.7
Stirke = 0248, dip = 338NW α1 = 39!S
α2 = 19.5!E
E-W cross section
N
-S cross section
Problem 1.8
tan d ¼ ( tana=sinb)
a ¼ 20#
b ¼ 51#
tan d ¼ tan 20#=sin 51# ¼ 0:468
d ¼ 25:1#NW
Problem 1.9
tan d ¼ ( tana=sinb)
d ¼ 48#
b ¼ 35#
tana ¼ ( tan 48#)( sin 35#) ¼ 0:637
a ¼ 32:5#SE
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Problem 1.10
tan d ¼ ( tana= sinb)
d ¼ 2#
a ¼ 1#
sinb ¼ tan 1#= tan 2# ¼ 0:4998
b ¼ 30#
All directions between N308E and S308E
Problem 1.11
u1 ¼ 220#; a1 ¼ 4#
u2 ¼ 100#; a2 ¼ 7#
tan (angle between u1 and true dip direction) ¼ csc(u1 $ u2) [( cota1)( tana2)
$ cos (u1 $ u2)]
¼ csc 120# [(cot4#)( tan 7#)$ cos 120#]
¼ 1:155 [(14:301)(0:1228) $ ($0:5)]
tan 69# ¼ 2:606
true dip direction ¼ 220# $ 69# ¼ 151#
strike ¼ N618E
tan d ¼ ( tana=sinb)
tan d ¼ tan 4#=sin 21#
d ¼ 11#SE
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Chapter 2
Note to instructors
Problem 2.2. Note that these are elevations above sea level (not depths below
surface) to the top of the Bree conglomerate. Students should be encouraged to use
geological judgment where no data are present – specifically, structure contours in
the northwest corner of the map should be drawn to define a north-plunging
anticline by analogy with the major structure (north-plunging syncline) in the center
of the map.
You may wish to ask students to place appropriate fold symbols on the structure
contour map (see below). As a supplement, students could determine absolute strike
and the dip of surface at specified localities. These of course will vary somewhat in
dip magnitude because of slight variability in the placement of individual structure
contours from student to student.
Students should color the Bree Creek quadrangle map before Chapter 3. You may
wish to specify a uniform color scheme for map units to facilitate grading and
assisting students in the lab.
Problem 2.3. Note that values given are depths below a flat surface.
Answers and solutions
Problem 2.1
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Problem 2.2
Student maps will differ in detail from the solution provided here.
Problem 2.3
Dip ¼ tan d ¼ D elevation=map distance ¼ 6600=12500 $ 27:5#
Depth to D ¼ (map dist:)( tan d) ¼ (15600)( tan 37:5) ¼ 8110
54850 $ 8110 ¼ 46740
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Problem 2.4
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Chapter 3
Note to instructors
Problem 3.1. The strike of Thd on Gandalf’s knob can be determined easily, but the
dip cannot. However, by using information from exposures farther south within the
western fault block, it can be shown that the dip is 38NE on Gandalf’s Knob as it is
to the south. The 4000’ structure contour representing the base of Thd at Gandalf’s
Knob occurs at the correct position relative to the 4800’ and 5200’ structure
contours to the south.
Problem 3.2. We specify localities to determine thickness for sake of uniformity (and
for consistency with thicknesses that appear in subsequent cross sections (Problem
4.4)). Thicknesses could be determined from other localities on the map; however,
variable outcrop widths lead to thickness determinations that may vary by a factor
of two or more. This variation is, of course, typical of ‘‘real world’’ situations, but it
will be easier on the grader if all students measure thicknesses at the same locality.Measured thicknesses at the specified localities should vary by no more than 5–10%
between students, and can therefore be evaluated.
Problem 3.3. In some instances, it will not be possible for students to construct two
parallel strike lines at both the top and bottom of a unit. They may have to rely on
spot elevations, or in some cases, interpolate elevations between contours. Because
this exercise deals with some of the thinnest and most gently dipping units on the
map, calculated thicknesses will vary considerably.
Problem 3.4. We find that students devise all sorts of improbable solutions to these
maps. To circumvent this problem, students should be required to ‘‘defend’’ their
cross sections. Alternatively, the instructor could limit possibilities by imposing some
constraints. For example, the instructor could state that the contact in exercise (a)
dips 758 to the west. In this case, the only viable solutions are a fault or intrusive
contact – a nonconformity is virtually ruled out. As a second example, in exercise
(b), the instructor could specify that formation Y is younger than formation X and
that the contact dips west. This would restrict viable interpretations to either an
angular unconformity or normal fault.
Answers and solutions
Problem 3.1
Thd Tr Tg
Northeastern fault block
Northern exposures N628W, 58NE N168W, 118NE N168W, 118NE
Southern exposures N168W, 118NE N168W, 118NE
Central fault block
Northern area N248W, 98NE N248W, 98NE
Galadriel’s Ridge N248W, 98NE N248W, 98NE
Southwestern area N228W, 98NE N228W, 98NE
Western fault block
Gandalf’s Knob N788W, 38NE
Southern exposures N788W, 38NE
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Problem 3.2
Tmm 410’
Tm 450’
Tts 2540’
Tb 630’
Te 4430’
Problem 3.4
Problem 3.5
Stratigraphic column not provided here, but should be straightforward.
Problem 3.3
Thd Tr Tg
Gollum Ridge 120’
Gandalf’s Knob 600’
Galadriel’s Ridge >400’ 100’
Mirkwood Creek about 100’
N. of Edoras Creek >400’
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Chapter 4
Solutions
Problem 4.1
Problem 4.2
Problem 4.3
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Problem 4.4
Structure sections A–A’ and B–B’. Note that the structure sections shown on the
following pages were constructed using the Bree Creek Quadrangle map from the
second edition because the final draft of the map for the third edition was not
available to us before the publisher’s deadline for this solutions manual. Although
the map has not changed in content, it is possible that minor differences in final
production of the map for the third edition may have occurred (contacts shifted
slightly, etc.) and, therefore, there may be minor deviations between the solutions
presented below and cross sections that are constructed from the final third edition
map. We believe, however, that the solutions presented below are fundamentally
correct. Of course there will be variations from student to student due to different
interpretations regarding fold shape, etc. The critical issues are keeping bedding
thicknesses constant and maintaining consistent displacement on the faults (i.e., all
beds cut by a fault should be displaced equal amounts).
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Chapter 5
Note to instructors
This is a rather long chapter; you may wish to assign only selected exercises. It is our
experience that the careful student can usually obtain answers within a degree or
two from those listed below.
Answers
Problem 5.1
258NW
Problem 5.2
N658W, 308SW
Problem 5.3
(1) Plunge ¼ 138; trend ¼ S58E (1758)
(2) Pitch ¼ 148
(3) Pitch ¼ 338
Problem 5.4
Plunge ¼ 208; trend ¼ S428W (2228)
Problem 5.5
Bearings: N828E and S588W
Problem 5.6
N308E, 758SE
Problem 5.7
(1) Plunge ¼ 188; trend ¼ S758W (2558)
(2) N158W, 728E
(3) 1248
(4) N488W, 228SW
(5) Plunge ¼ 118; trend ¼ S208E (1608)
(6) Downhill
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Problem 5.8
N538W (or 1278/3078), 538SW
Problem 5.9
Plunge ¼ 708; trend ¼ N508E (0508)
Problem 5.10
228 toward 3498
Problem 5.11
Using Thd ¼ N628W, 58NE and Tr ¼ N168W, 118NE (from Problem 3.1):
Attitude ¼ N88E, 88E; direction of tilt ¼ 88 in direction of S808E (1008)
Problem 5.12
N468E, 328NW
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Solutions
Problem 5.1 Problem 5.2
Problem 5.3 Problem 5.4
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Problem 5.5 Problem 5.6
Problem 5.7 Problem 5.8
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Problem 5.11
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Problem 5.12
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Chapter 6
Answers
Problem 6.1
Fold description should contain the following descriptive elements: the block depicts
cylindrical, symmetric, open folds with interlimb angles of 90–1058 that plunge 308
northeast and whose axial surfaces strike N208E and dip 608 west.
Problem 6.2
Layer 1: class 2.
Layer 2: class 1B (possibly class 1C).
Layer 3: class 3.
See solution on p. 23 for sketch.
Problem 6.3
Class designation may vary slightly – sample size is small and it is difficult to locate
isogons precisely:
(a) Class 3 (using dark band in center of specimen).
(b) Class 2.
(c) Class 1B or 1C depending on where measured.
(d) Class 1B.
Problem 6.4
Students may have to be reminded about the rules for determining orientation of
fold axes in overturned beds. Note that, by strict definition, a noncylindrical fold has
no fold axis. Sketches are on p. 24.
(a) Trend ¼ 2508; plunge ¼ 268.
(b) Trend ¼ 1358; plunge ¼ 688.
(c) Noncylindrical folds; no fold axis (variable hinge line orientations).
(d) Trend ¼ 0008; plunge ¼ 08.
(e) Trend ¼ 1808; plunge ¼ 458.
Problem 6.5
(1) Sketches will vary – folds are high amplitude.
(2) Axial surfaces are approximately 3458, 508SW.
(3) Approximate fold axis: trend 2008 (S208W); plunge 458.
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Solutions
Problem 6.1
Instructors may wish to allow some leeway with regard to position of axial surfaces
and crest/trough lines. Because these folds are open, hinge lines (and thus trace of the
axial surface) cannot be located with great precision.
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Problem 6.4
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Chapter 7
Note to instructors
On fold profiles (Problem 7.1, question 2; and Problem 7.2, question 2) the attitudes
that students obtain for axial surfaces will vary due to imprecision inherent in
construction and choice of ‘‘best fit’’ axial surface (hinge points are not perfectly
aligned). In particular, in the case of gently plunging fold axes that trend within a
few degrees of the strike of the axial surface, slight variations in inferred strike of the
axial surface can result in large differences in estimated dip. This should be taken
into account when grading students’ lab exercises (especially axial surfaces for the
western and central blocks).
In Problem 7.2, question 2, the profile of the folds in the central block must be
drawn from southern exposures. In this region, the axial surface dips very steeply to
the west. In the northern exposures, the axial surfaces dips more moderately west-
ward (about 508). The axial surface determined by the profile technique will thus
differ from that determined by p maxima on the contour diagram (which reflects
data from both northern and southern parts of block). Students should note the
difference in orientation in their fold descriptions.
Answers
Problem 7.1
(1) Trend ¼ 2718; plunge ¼ 358 (see sketch on next page).
(2) Strike of axial plane ¼ 0168 (see sketch on next page).
(3) See sketch on next page.
(4) Folds are symmetrical and close (with interlimb angle 50–608). Axial surface
strikes 0168anddips368W.Fold axis trends2718andplunges358; a reclined fold.
Problem 7.2
(1) See sketches on p. 27.
(2) See sketches on p. 28.
West block: hinge trend¼ 148, plunge¼ 128. Axial surface strike¼N128E, dip 838E.
Central block: hinge trend ¼ 128, plunge ¼ 108. Axial surface strike ¼ N138E,
dip ¼ 858E.
Northeast block: hinge trend ¼ 158, plunge ¼ 248. Axial surface strike ¼ N128E,
dip ¼ 848E.
(3) West block: class 1B.
Central block: class 2.
Northeast block: class 3 (slightly convergent; some students may get class 2).
(4) West block: these are class 1B, symmetrical, open folds (interlimb angle
of 1208). Axial surfaces strike N128E, dip 838E, and p axis trends N148E and
plunges 128. Crosscutting relationships indicate that these folds formed between
the Eocene and Miocene.
Central block: these are class 2, symmetrical, close folds (interlimb angle of 458).
Axial surfaces strike N138E, dip 58E, and p axis trends N128E and plunges 108.
Crosscutting relationships indicate that these folds formed between the Eocene and
Miocene.
Northeast block: these are class 3, symmetrical, open folds (interlimb angle of
90–1008). Axial surfaces strike N128E, dip 848E, and p axis trends N158E and
plunges 248. Crosscutting relationships indicate that these folds formed between the
Eocene and Miocene.
(5) See plots for Problem 7.2, question 1 (p. 27).
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Solutions
Problem 7.1
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Problem 7.2
7.2 (1) Solutions will vary depending upon contour interval used. Overall patterns
should be similar to those shown.
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Chapter 8
Note to instructors
For Problems 8.1 and 8.3, the strike and dip of bedding shown on the maps do not
correspond to a single bed but rather to random bedding attitudes measured in the
field. This is a common situation in strongly cleaved rocks where specific marker
beds cannot be identified. Students should merely use form lines to define the shapes
of folds. Students will have a difficult time completing this exercise if they treat each
attitude as if it were measured on a single bedding surface.
Solutions
Problem 8.1
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Problem 8.2
Problem 8.3
Actual positions of axial surfaces will vary with student; there is some leeway. The
number and sequence of folds must be as shown.
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Problem 8.5
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Chapter 9
Answers
Problem 9.1
Slip ¼ 320 m (see solution on p. 38).
Problem 9.2
Slip ¼ 260 m (see solution on p. 38).
Problem 9.3
(1) Yes, attitude 3338, 678NE could be the result of rotation (see solution on p. 39).
(2) 358 rotation.
Problem 9.4
Post-Rohan Tuff/pre-Helm’s
Deep Sandstone tilting
Post-Helm’s Deep Sandstone
tilting
Northeastern fault block 88 toward 1048 58 toward 238
Central fault block 78 toward 628 38 toward 128
Western fault block 38 toward 128
ROWLAND / Structural Analysis and Synthesis xxxxxxxxxx_4_01-09 Final Proof page 35 9.1.2007 3:13pm Compositor Name: SJoearun
Problem 9.5
(1) Fault A: normal fault; post-Lower Miocene, pre-Middle Miocene.
Fault B: left-slip tear fault; post-Triassic, pre-Middle Miocene (by inference
that tear fault is related to the thrust fault, Fault C).
Fault C: thrust fault; post-Triassic, pre-Middle Miocene.
Fault D: left-slip fault; post-Middle Miocene, pre-Miocene (upper, Tm).
Fault E: thrust fault; post-Silurian (may wishto accept post-Triassic if the two
thrusts are considered related), pre-Jurassic.
(2) Contact ‘‘a’’: nonconformity.
Contact ‘‘b’’: intrusive.
Contact ‘‘c’’: angular unconformity.
Contact ‘‘d’’: disconformity.
Structure at ‘‘e’’: trough of northeast-plunging syncline.
Structure at ‘‘f’’: fenster.
Structure at ‘‘g’’: klippe.
Structure at ‘‘h’’: axial region of northeast-trending overturned anticline.
(3) Overturned dips: the 778W dip in the Ordovician just west of fault E; the 478W
dip in the Silurian just east of fault E; the 728W dip in the Pennsylvanian-
Permian just east of fault C.
(4) Tm must be younger than other Miocene units because it overlaps fault D that
cuts the middle Miocene unit
(5) 20 km based on presence of klippe.
(6)
1. Deposition of Cambrian through Devonian rocks; unconformity; deposition of
Pennsylvanian through Triassic rocks.
2. Folding and associated thrusting of these rocks along faults C and E; tear fault
B forms during this time.
3. Intrusion of Jurassic plutons.
4. Uplift and erosion.
5. Deposition of Eocene through lower Miocene rocks.
6. Normal faulting (fault A) and associated tilting of Eocene–lower Miocene
rocks.
7. Post-faulting erosion.
8. Deposition of middle Miocene rocks.
9. Southwest tilting of middle Miocene rocks.
10. Left-slip faulting along fault D.
11. Erosion (probable).
12. Deposition of Tm unit.
13. Erosion to present.
ROWLAND / Structural Analysis and Synthesis xxxxxxxxxx_4_01-09 Final Proof page 36 9.1.2007 3:13pm Compositor Name: SJoearun
36 --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- Structural Analysis and Synthesis -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
Pr
ob
le
m
9.
6
M
irk
w
oo
d
fa
ul
t
Br
ee
C
re
ek
fa
ul
t
G
ol
lu
m
Ri
dg
e
fa
ul
t
N
or
th
Br
ee
C
re
ek
fa
ul
t
1.
Ty
pe
N
or
th
:
no
rm
al
So
ut
h:
re
ve
rs
e
(p
ro
ba
bl
y
re
ve
rs
e
fa
ul
t
w
ith
m
in
or
no
rm
al
re
ac
tiv
at
io
n
po
st
-T
r)
N
or
m
al
se
pa
ra
tio
n;
pr
ob
ab
ly
no
rm
al
sl
ip
.
Pr
es
er
va
tio
n
of
Te
rt
ia
ry
st
ra
ta
in
ha
ng
in
g
w
al
l
su
gg
es
ts
at
le
as
t
a
si
gn
ifi
ca
nt
co
m
po
ne
nt
of
no
rm
al
sl
ip
N
or
m
al
se
pa
ra
tio
n;
pr
ob
ab
ly
tr
ue
no
rm
al
sl
ip
be
ca
us
e
ha
ng
in
g
w
al
lr
oc
ks
ar
e
co
ns
is
te
nt
ly
yo
un
ge
r
N
or
m
al
se
pa
ra
tio
n;
pr
ob
ab
ly
tr
ue
no
rm
al
sl
ip
be
ca
us
e
en
tir
e
Te
rt
ia
ry
se
ct
io
n
pr
es
er
ve
d
in
ha
ng
in
g
w
al
lr
oc
ks
2.
A
tt
itu
de
N
-S
to
N
20
8E
;
35
8W
N
58
W
to
N
58
E;
75
8W
N
58
W
to
N
58
E;
75
8W
N
21
8E
to
N
45
8E
;
80
8N
W
3.
St
rik
e
se
pa
ra
tio
n
D
ip
se
pa
ra
tio
n
(c
he
ck
fo
r
co
ns
is
te
nc
y
w
ith
st
ud
en
t
cr
os
s
se
ct
io
ns
)
In
de
te
rm
in
at
e
Po
or
ly
co
ns
tr
ai
ne
d
41
00
m
m
ea
su
re
d
fro
m
Tt
s-
Tb
co
nt
ac
t
(p
ro
je
ct
ed
to
fa
ul
t)
M
in
im
um
58
00
m
ba
se
d
on
se
pa
ra
tio
n
of
K
dt
un
it
4.
A
ge
Po
st
-M
io
ce
ne
,
pr
e-
Pl
io
ce
ne
Po
st
-C
re
ta
ce
ou
s
is
on
ly
co
ns
tr
ai
nt
Po
st
-M
io
ce
ne
Po
st
-M
io
ce
ne
ROWLAND / Structural Analysis and Synthesis xxxxxxxxxx_4_01-09 Final Proof page 37 9.1.2007 3:13pm Compositor Name: SJoearun
Solutions
Problems 9.1 and 9.2
ROWLAND / Structural Analysis and Synthesis xxxxxxxxxx_4_01-09 Final Proof page 38 9.1.2007 3:13pm Compositor Name: SJoearun
38 --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- Structural Analysis and Synthesis -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------Problem 9.3
ROWLAND / Structural Analysis and Synthesis xxxxxxxxxx_4_01-09 Final Proof page 39 9.1.2007 3:13pm Compositor Name: SJoearun
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- Structural Analysis and Synthesis -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- 39