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[Solved] 12 Depositional Sedimentary Environments Lab

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– 2 years ago **files (2)** – ## 12labanswerpage.pdf – ## 12LabSedDepMacro.pdf **## 12labanswerpage.pdf** Lab 12 Sed. Dep. Env. Answer Pages Study the sedimentary environments in the images below and answer the questions associated with the images. Write your answers on the blanks provided at the en…

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– 2 years ago

**files (2)**

– ## 12labanswerpage.pdf

– ## 12LabSedDepMacro.pdf

**## 12labanswerpage.pdf**

Lab 12 Sed. Dep. Env. Answer Pages
Study the sedimentary environments in the images below and answer the questions associated with the
images. Write your answers on the blanks provided at the end of the lab.

Answer the questions in the blanks provided on the following pages to make it easier.

Figure A. Death Valley National Park, CA

1. What are the prominent depositional features formed at the mouths

of the canyon?

2. Describe the textural characteristics of the sediment forming the

features named above.

2. What other non-marine features could exist on the flat terrain in front

of the range?

Figure B. Navajo Sandstone in Zion NP, UT

3. What type of bedding does this represent?

4. Was this sandstone deposited in a non-marine (terrestrial)

or marine environment?

5. Was the sandstone deposited by fluvial or aeolian processes?

Figure C. Bedding surface from Capital Reef, UT

6. What type of markings are present?

7. Assuming the rock is marine in origin, what do these

markings indicate about the depth of water in which
in the sediment was deposited?

Figure D. Cracked surface in Alaska

8. What type of markings are present?

9. Assuming the rock is marine in origin, what do these

markings indicate about the depth of water in which in
the sediment was deposited?

Source: Shutterstock

Source: Shutterstock

Source: Shutterstock

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Figure E. Conglomerate in Chiang Rai, Thailand

10. What type of grain shape and particle sorting

are shown here?

11. What is a possible depositional environment?

Give reasons for your interpretation.

Figure F. Sandstone Zion NP, Utah

12. What type of bedding is present?

13. Was this sandstone deposited in a nonmarine

(terrestrial) or marine environment? Was the sandstone
deposited by fluvial or aeolian processes? If in water,
in shallow or deep water? Explain how you know.

Figure G. Breccia, Lake Mead, Nevada

14. Describe particle color, texture, and sorting?

15. What was the depositional environment

responsible for creating this rock?

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Name: ___________________________________

Lab 7: Sedimentary Environments (macro scale)
Record your answers to the questions about the images above here:

Figure A

1 __________________________________________________________

2 __________________________________________________________

3 __________________________________________________________

Figure B

4 __________________________________________________________

5 __________________________________________________________

6 __________________________________________________________

Figure C

7 __________________________________________________________

8 __________________________________________________________

Figure D

9 __________________________________________________________

10 __________________________________________________________

Figure E

11 __________________________________________________________

12 __________________________________________________________

Figure F

13 __________________________________________________________

14 __________________________________________________________

Figure G

15 __________________________________________________________

16. __________________________________________________________

General Questions

16. What general rock and rock feature would indicate a long duration of deposition in an arid
environment?
\_\_\________________________________________________________________________________

\_\_\________________________________________________________________________________

17. What type of environment would a breccia with dark grey and/or purple rock fragments likely be
from?
\_\_\________________________________________________________________________________

\_\_\________________________________________________________________________________

18. What is the probable depositional setting and source of a pure white quartz sandstone?

\_\_\________________________________________________________________________________

\_\_\________________________________________________________________________________

19. What do bidirectional ripples indicate about the depositional environment of a rock?
\_\_\________________________________________________________________________________

\_\_\________________________________________________________________________________

20. What would the sedimentary environment be for oolitic sediments?

\_\_\________________________________________________________________________________

\_\_\________________________________________________________________________________

21. How would the sediments differ from a playa lake to that of a freshwater lake?

\_\_\________________________________________________________________________________

\_\_\________________________________________________________________________________

22. List three environments that ripples can form in:

\_\_\________________________________________________________________________________

\_\_\________________________________________________________________________________

\_\_\________________________________________________________________________________

\_\_\________________________________________________________________________________

23. List two ways cross bedding can occur:

\_\_\________________________________________________________________________________

\_\_\________________________________________________________________________________

24. How does a conglomerate form? Is there more than one way? If so how?

\_\_\________________________________________________________________________________

\_\_\________________________________________________________________________________

\_\_\________________________________________________________________________________

**## 12LabSedDepMacro.pdf**

Laboratory 12: Sedimentary Depositional Environments (Macro Scale)

Objective:

To understand the large sale features that are observed in sedimentary environments and the role they
play in understanding depositional environment.

Materials Needed:
Images of various sedimentary environments provided by instructor

Paleogeography is the study of what an environment was like during a certain time in the past. Paleogeography
takes biostratigraphy one step further in reconstructing the earth's history. By examining a set of rocks in several
different locations, all representing the same age, we can begin to reconstruct the ancient environment by using
the rock type and fossil content. The rock samples can be collected over a large or small lateral area, and the
locations and shapes of landmasses and seas can be deduced by knowing which types of rocks and fossils are
expected to be found in particular environments. An environment of deposition is the sum of all physical,
geographic, climatic, ecological, and chemical parameters that affect the composition of the sediment. Many
factors must be considered when deciding on the environment of deposition, including lithology, fossil
abundance, and fossil assemblage.

I. NONMARINE (CONTINENTAL) Most non-marine environments are typically the sites of erosion or non-
deposition, although a small percentage of deposits may be preserved.

A. Aqueous-
1. Fluvial (streams and rivers)-

(a) Floodplain- Sandstone, siltstone and shale with some conglomerate and coal, moderate
sorting, moderately quartz-rich; horizontal laminations, asymmetric (current) ripple marks, animal
tracks and trails, mud cracks, raindrop impressions; plant debris and tree fossils; irregular and
thin sheet shape.
(b) Channel-Sandstone and conglomerate, moderately sorted and quartz-rich; cross-bedding,
current ripple marks, scour of channel surfaces; may contain plant debris, non-marine (aqueous
and terrestrial) fossils; irregular lenticular to sinuous shape, closely associated with floodplain
deposits.

2. Paludal (Marsh or Swamp) – fine-grained deposits (siltstone, shale, coal) with dark color and high
organic content; thin horizontal laminations or massive (no visible sedimentary structures); abundant
plant fossils; irregular lens to sheet shape.
3. Lacustrine (lake) – fine-grained shale and some limestone; varve (alternating thin, light and dark
layers) clay common; possible freshwater fossils (ex. snails); irregular lens to sheet shape

B. Terrestrial (subaerial)-
1. Desert-

(a) Aeolian dune- fine-to medium-grained sandstone with excellent rounding and sorting; large-
scale cross-bedding common; fossils rare; extensive sheet-like or “blanket” shape.
(b) Alluvial fan- poorly sorted arkosic sandstone and conglomerate, abundant feldspar and
mica; cross-bedding, massive bedding, inverse and normally graded beds; fossils rare to absent;
thick fan-or wedge-shaped deposits.

2. Glacial- poorly sorted massive sandstone and conglomerate containing angular particles striated
pebbles, large pebbles and boulders, variable mineralogy; massive or crude horizontal laminations;
fossils absent; irregular shape and patchy distribution.

II. TRANSITIONAL (MARGINAL MARINE)

A. Delta-
A complex grouping of environments including channels, floodplains, swamps, bays, etc. Deposits
range from sandstone to siltstone and shale, and generally became finer-grained outward from the
shoreline; cross-bedding, horizontal laminations, current ripple marks and animal burrows are
common in some parts; fossils generally rare but may include locally abundant plant stems and roots
and rare marine; delta complexes are generally fan or wedge shaped.

B. Barrier Island/Lagoon-

1. Barrier Island- are mostly high energy deposits consisting of well-sorted and rounded quartz rich
sandstone. Grain size decreases systematically in a seaward direction; large-scale cross-bedding;
current and symmetrical (wave) ripple marks, horizontal laminations and animal burrows common;
fragmented marine fossils may be present; sand body shape is narrow and elongate parallel to the
shoreline and a lagoon is typically present between the barrier and the mainland.
2. Lagoon- lower energy environment dominated by fine-grained sandstone, siltstone, and shale;
horizontal laminations, ripple marks, and animal burrows, tracks and trails are common; carbonate
lagoons contain abundant and diverse marine fossils; shape is characteristically elongate parallel to
shore, and a barrier island is typically present immediately offshore from the lagoon.

C. Littoral (between mean high and low tides)-

1. Beach – high energy environment dominated by medium- to course- grained sandstone, well-
sorted and rounded; horizontal laminations, low-angle cross-bedding, wave ripple marks are most
abundant; fossils are rare and typically broken into fragments; sand body is elongate in shape and
trends parallel to shore.
2. Tidal flat – so named due to the tide coming in and receding in this relatively flat region. It will
have inter-bedded sandstone, siltstone and shale, with grain size increasing in a seaward direction;
cross-bedding (some large-scale), wave and current ripple marks, mud cracks, scour or channel
surfaces, and animal burrows, tracks and trails are common; fossils (marine) are rare to abundant;
wedge to irregular sheet shape.

III. OPEN MARINE

A. Pelagic- These environments are within the ocean water mass; thus, they don’t have characteristic
features preserved in the geologic record. Organisms which live in these environments fall to the ocean
bottom upon death and become part of the record of one of the benthic environments listed:
1. Neritic-depth to sea-floor less than 200 meters
2. Oceanic- depth to sea-floor greater than 200 meters

B. Benthic (bottom environments)
1. Shallow marine (Shelf) – sandstone, siltstone, limestone and shale interbedded,
sandstone composed predominantly of quartz but with some marine fossil fragments; cross-
bedding (some large-scale), ripple marks, and marine burrows, tracks and trails common;
marine fossils locally abundant; widespread sheet-like or blanket shape. Water depths are
typically less than 200 m.

2. Carbonate Reef/Platform- Unbedded, very fossiliferous with large and small scale, very
course grained sediment. Abundant, often large, organisms attached to the sea-floor, high
energy environment.
3. Deep Ocean- shale, fine-grained limestone and/or sandstone; graded bedding produce by
turbidity currents; large fossils rare; microfossils may be abundant; sheet to fan-like shape.

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The following charts summarize the previous discussion

ALLUVIAL FAN FLUVIAL (river)
LACUSTRINE

(lake)
AEOLIAN DESERT

(dunes)
PALUDAL
(swamp)

ROCK TYPE breccia, conglomerate,
arkose

conglomerate, sandstone,
siltstone, shale

siltstone, shale, limestone,
evaporites

quartz arenite,
(sandstone) gypsum

peat, coal, siltstone, black
shale

composition terrigenous terrigenous
terrigenous, carbonates,

evaporites
terrigenous or evaporite terrigenous

color brown or red brown or red
black, brown, grey, green,

red
yellow, red, tan, white black, gray or brown

grain size clay to gravel
clay, silt, sand, gravel,

fining upward
clay, silt, sand (coursening

upward)
sand clay to silt

grain shape angular angular to rounded —- rounded or polished —-

sorting poor variable variable good variable

inorganic
sedimentary

structures
cross bed and graded bed

assymmetrical ripples,
crossbedding, graded

beds, tool marks

symmetrical ripples,
lamination, cross beds,

graded beds, mud cracks,
raindrops

crossbedding laminated to massive

organic or
biogenic

structures
—- tracks, trails, burrows

tracks, trails, burrows, rare
stromatolites

tracks and trails root marks, burrows

fossils —-
rare freshwater shells,

bones, plants fragments
freshwater shells, fish,
bones, plant fragmetns

—-
plant fossils, freshwater

shells, bone, fish

Continental- Sedimentary Depositional Envirnonments

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DELTA BARRIER BEACH LAGOON TIDAL FLAT

ROCK TYPE sandstone, siltstone, shale,
coal

quartz arenite, coquina
siltsone, shale, limestone,
oolitic limestone, gypsum

siltstone, shale, calcilutitie,
dolostone or gypsum

composition terrigenous, some organic terrigenous or carbonate
terrigenous, carbonate or

evaporite
terrigenous, carbonate or

evaporite

color brown, black, grey, green,
red

what to tan dark grey to black or brown grey, brown, tan

grain size clay to sand (coursening
upward)

sand clay to silt clay to silt

grain shape —- rounded to angular —- —-

sorting variable good poor variable

inorganic
sedimentary

structures

cross bedding, graded
bedding

cross bedding, symmetrical
ripples

lamination, ripples cross
bedding

lamination, mudcracks,
ripples, cross bedding

organic or
biogenic

structures
trails, burrows tracks, trails, burrows trails, burrows

stromatolites, trails, tracks,
burrows

fossils plant fragments, shells marine shells marine shells marine shells

Transitional- Sedimentary Depositional Envirnonments

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REEF
CONTINENTAL

SHELF
CONTINENTAL

SLOPE AND RISE
ABYSSAL PLAIN

ROCK TYPE fossiliferous limestone
sandstone, shale, siltstone,

fossiliferous limestone, oolitic
limestone

litharenite (grewacke),
siltstone and shale, limestone

shale, chert, micrite, chalk,
diatomite

composition carbonate terrigenous or carbonate terrigenous or carbonate terrigenous or carbonate

color grey to white grey, brown, tan, green grey, green, brown black, white, red

grain size variable frameworks, few to
no grains

clay, silt, sand, gravel clay to snad clay

grain shape —- —- —- —-

sorting —- poor to good poor good

inorganic
sedimentary

structures
—- lamination, cross bedding

graded bedding, cross
bedding, lamination, flute

marks, tool marks (turbitdites)
lamination

organic or
biogenic

structures
—- trails, burrows trails, burrows trails, burrows

fossils coral, marine shells marine shells, sharks teeth
marine shells, rare plant

fragments
marine shells (mostly

microscopic)

Marine- Sedimentary Depositional Envirnonments

**## 12LabSedDepMacro.pdf**

Laboratory 12: Sedimentary Depositional Environments (Macro Scale)

Objective:

To understand the large sale features that are observed in sedimentary environments and the role they
play in understanding depositional environment.

Materials Needed:
Images of various sedimentary environments provided by instructor

Paleogeography is the study of what an environment was like during a certain time in the past. Paleogeography
takes biostratigraphy one step further in reconstructing the earth's history. By examining a set of rocks in several
different locations, all representing the same age, we can begin to reconstruct the ancient environment by using
the rock type and fossil content. The rock samples can be collected over a large or small lateral area, and the
locations and shapes of landmasses and seas can be deduced by knowing which types of rocks and fossils are
expected to be found in particular environments. An environment of deposition is the sum of all physical,
geographic, climatic, ecological, and chemical parameters that affect the composition of the sediment. Many
factors must be considered when deciding on the environment of deposition, including lithology, fossil
abundance, and fossil assemblage.

I. NONMARINE (CONTINENTAL) Most non-marine environments are typically the sites of erosion or non-
deposition, although a small percentage of deposits may be preserved.

A. Aqueous-
1. Fluvial (streams and rivers)-

(a) Floodplain- Sandstone, siltstone and shale with some conglomerate and coal, moderate
sorting, moderately quartz-rich; horizontal laminations, asymmetric (current) ripple marks, animal
tracks and trails, mud cracks, raindrop impressions; plant debris and tree fossils; irregular and
thin sheet shape.
(b) Channel-Sandstone and conglomerate, moderately sorted and quartz-rich; cross-bedding,
current ripple marks, scour of channel surfaces; may contain plant debris, non-marine (aqueous
and terrestrial) fossils; irregular lenticular to sinuous shape, closely associated with floodplain
deposits.

2. Paludal (Marsh or Swamp) – fine-grained deposits (siltstone, shale, coal) with dark color and high
organic content; thin horizontal laminations or massive (no visible sedimentary structures); abundant
plant fossils; irregular lens to sheet shape.
3. Lacustrine (lake) – fine-grained shale and some limestone; varve (alternating thin, light and dark
layers) clay common; possible freshwater fossils (ex. snails); irregular lens to sheet shape

B. Terrestrial (subaerial)-
1. Desert-

(a) Aeolian dune- fine-to medium-grained sandstone with excellent rounding and sorting; large-
scale cross-bedding common; fossils rare; extensive sheet-like or “blanket” shape.
(b) Alluvial fan- poorly sorted arkosic sandstone and conglomerate, abundant feldspar and
mica; cross-bedding, massive bedding, inverse and normally graded beds; fossils rare to absent;
thick fan-or wedge-shaped deposits.

2. Glacial- poorly sorted massive sandstone and conglomerate containing angular particles striated
pebbles, large pebbles and boulders, variable mineralogy; massive or crude horizontal laminations;
fossils absent; irregular shape and patchy distribution.

II. TRANSITIONAL (MARGINAL MARINE)

A. Delta-
A complex grouping of environments including channels, floodplains, swamps, bays, etc. Deposits
range from sandstone to siltstone and shale, and generally became finer-grained outward from the
shoreline; cross-bedding, horizontal laminations, current ripple marks and animal burrows are
common in some parts; fossils generally rare but may include locally abundant plant stems and roots
and rare marine; delta complexes are generally fan or wedge shaped.

B. Barrier Island/Lagoon-

1. Barrier Island- are mostly high energy deposits consisting of well-sorted and rounded quartz rich
sandstone. Grain size decreases systematically in a seaward direction; large-scale cross-bedding;
current and symmetrical (wave) ripple marks, horizontal laminations and animal burrows common;
fragmented marine fossils may be present; sand body shape is narrow and elongate parallel to the
shoreline and a lagoon is typically present between the barrier and the mainland.
2. Lagoon- lower energy environment dominated by fine-grained sandstone, siltstone, and shale;
horizontal laminations, ripple marks, and animal burrows, tracks and trails are common; carbonate
lagoons contain abundant and diverse marine fossils; shape is characteristically elongate parallel to
shore, and a barrier island is typically present immediately offshore from the lagoon.

C. Littoral (between mean high and low tides)-

1. Beach – high energy environment dominated by medium- to course- grained sandstone, well-
sorted and rounded; horizontal laminations, low-angle cross-bedding, wave ripple marks are most
abundant; fossils are rare and typically broken into fragments; sand body is elongate in shape and
trends parallel to shore.
2. Tidal flat – so named due to the tide coming in and receding in this relatively flat region. It will
have inter-bedded sandstone, siltstone and shale, with grain size increasing in a seaward direction;
cross-bedding (some large-scale), wave and current ripple marks, mud cracks, scour or channel
surfaces, and animal burrows, tracks and trails are common; fossils (marine) are rare to abundant;
wedge to irregular sheet shape.

III. OPEN MARINE

A. Pelagic- These environments are within the ocean water mass; thus, they don’t have characteristic
features preserved in the geologic record. Organisms which live in these environments fall to the ocean
bottom upon death and become part of the record of one of the benthic environments listed:
1. Neritic-depth to sea-floor less than 200 meters
2. Oceanic- depth to sea-floor greater than 200 meters

B. Benthic (bottom environments)
1. Shallow marine (Shelf) – sandstone, siltstone, limestone and shale interbedded,
sandstone composed predominantly of quartz but with some marine fossil fragments; cross-
bedding (some large-scale), ripple marks, and marine burrows, tracks and trails common;
marine fossils locally abundant; widespread sheet-like or blanket shape. Water depths are
typically less than 200 m.

2. Carbonate Reef/Platform- Unbedded, very fossiliferous with large and small scale, very
course grained sediment. Abundant, often large, organisms attached to the sea-floor, high
energy environment.
3. Deep Ocean- shale, fine-grained limestone and/or sandstone; graded bedding produce by
turbidity currents; large fossils rare; microfossils may be abundant; sheet to fan-like shape.

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The following charts summarize the previous discussion

ALLUVIAL FAN FLUVIAL (river)
LACUSTRINE

(lake)
AEOLIAN DESERT

(dunes)
PALUDAL
(swamp)

ROCK TYPE breccia, conglomerate,
arkose

conglomerate, sandstone,
siltstone, shale

siltstone, shale, limestone,
evaporites

quartz arenite,
(sandstone) gypsum

peat, coal, siltstone, black
shale

composition terrigenous terrigenous
terrigenous, carbonates,

evaporites
terrigenous or evaporite terrigenous

color brown or red brown or red
black, brown, grey, green,

red
yellow, red, tan, white black, gray or brown

grain size clay to gravel
clay, silt, sand, gravel,

fining upward
clay, silt, sand (coursening

upward)
sand clay to silt

grain shape angular angular to rounded —- rounded or polished —-

sorting poor variable variable good variable

inorganic
sedimentary

structures
cross bed and graded bed

assymmetrical ripples,
crossbedding, graded

beds, tool marks

symmetrical ripples,
lamination, cross beds,

graded beds, mud cracks,
raindrops

crossbedding laminated to massive

organic or
biogenic

structures
—- tracks, trails, burrows

tracks, trails, burrows, rare
stromatolites

tracks and trails root marks, burrows

fossils —-
rare freshwater shells,

bones, plants fragments
freshwater shells, fish,
bones, plant fragmetns

—-
plant fossils, freshwater

shells, bone, fish

Continental- Sedimentary Depositional Envirnonments

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DELTA BARRIER BEACH LAGOON TIDAL FLAT

ROCK TYPE sandstone, siltstone, shale,
coal

quartz arenite, coquina
siltsone, shale, limestone,
oolitic limestone, gypsum

siltstone, shale, calcilutitie,
dolostone or gypsum

composition terrigenous, some organic terrigenous or carbonate
terrigenous, carbonate or

evaporite
terrigenous, carbonate or

evaporite

color brown, black, grey, green,
red

what to tan dark grey to black or brown grey, brown, tan

grain size clay to sand (coursening
upward)

sand clay to silt clay to silt

grain shape —- rounded to angular —- —-

sorting variable good poor variable

inorganic
sedimentary

structures

cross bedding, graded
bedding

cross bedding, symmetrical
ripples

lamination, ripples cross
bedding

lamination, mudcracks,
ripples, cross bedding

organic or
biogenic

structures
trails, burrows tracks, trails, burrows trails, burrows

stromatolites, trails, tracks,
burrows

fossils plant fragments, shells marine shells marine shells marine shells

Transitional- Sedimentary Depositional Envirnonments

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REEF
CONTINENTAL

SHELF
CONTINENTAL

SLOPE AND RISE
ABYSSAL PLAIN

ROCK TYPE fossiliferous limestone
sandstone, shale, siltstone,

fossiliferous limestone, oolitic
limestone

litharenite (grewacke),
siltstone and shale, limestone

shale, chert, micrite, chalk,
diatomite

composition carbonate terrigenous or carbonate terrigenous or carbonate terrigenous or carbonate

color grey to white grey, brown, tan, green grey, green, brown black, white, red

grain size variable frameworks, few to
no grains

clay, silt, sand, gravel clay to snad clay

grain shape —- —- —- —-

sorting —- poor to good poor good

inorganic
sedimentary

structures
—- lamination, cross bedding

graded bedding, cross
bedding, lamination, flute

marks, tool marks (turbitdites)
lamination

organic or
biogenic

structures
—- trails, burrows trails, burrows trails, burrows

fossils coral, marine shells marine shells, sharks teeth
marine shells, rare plant

fragments
marine shells (mostly

microscopic)

Marine- Sedimentary Depositional Envirnonments

**## 12labanswerpage.pdf**

Lab 12 Sed. Dep. Env. Answer Pages
Study the sedimentary environments in the images below and answer the questions associated with the
images. Write your answers on the blanks provided at the end of the lab.

Answer the questions in the blanks provided on the following pages to make it easier.

Figure A. Death Valley National Park, CA

1. What are the prominent depositional features formed at the mouths

of the canyon?

2. Describe the textural characteristics of the sediment forming the

features named above.

2. What other non-marine features could exist on the flat terrain in front

of the range?

Figure B. Navajo Sandstone in Zion NP, UT

3. What type of bedding does this represent?

4. Was this sandstone deposited in a non-marine (terrestrial)

or marine environment?

5. Was the sandstone deposited by fluvial or aeolian processes?

Figure C. Bedding surface from Capital Reef, UT

6. What type of markings are present?

7. Assuming the rock is marine in origin, what do these

markings indicate about the depth of water in which
in the sediment was deposited?

Figure D. Cracked surface in Alaska

8. What type of markings are present?

9. Assuming the rock is marine in origin, what do these

markings indicate about the depth of water in which in
the sediment was deposited?

Source: Shutterstock

Source: Shutterstock

Source: Shutterstock

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Figure E. Conglomerate in Chiang Rai, Thailand

10. What type of grain shape and particle sorting

are shown here?

11. What is a possible depositional environment?

Give reasons for your interpretation.

Figure F. Sandstone Zion NP, Utah

12. What type of bedding is present?

13. Was this sandstone deposited in a nonmarine

(terrestrial) or marine environment? Was the sandstone
deposited by fluvial or aeolian processes? If in water,
in shallow or deep water? Explain how you know.

Figure G. Breccia, Lake Mead, Nevada

14. Describe particle color, texture, and sorting?

15. What was the depositional environment

responsible for creating this rock?

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Name: ___________________________________

Lab 7: Sedimentary Environments (macro scale)
Record your answers to the questions about the images above here:

Figure A

1 __________________________________________________________

2 __________________________________________________________

3 __________________________________________________________

Figure B

4 __________________________________________________________

5 __________________________________________________________

6 __________________________________________________________

Figure C

7 __________________________________________________________

8 __________________________________________________________

Figure D

9 __________________________________________________________

10 __________________________________________________________

Figure E

11 __________________________________________________________

12 __________________________________________________________

Figure F

13 __________________________________________________________

14 __________________________________________________________

Figure G

15 __________________________________________________________

16. __________________________________________________________

General Questions

16. What general rock and rock feature would indicate a long duration of deposition in an arid
environment?
\_\_\________________________________________________________________________________

\_\_\________________________________________________________________________________

17. What type of environment would a breccia with dark grey and/or purple rock fragments likely be
from?
\_\_\________________________________________________________________________________

\_\_\________________________________________________________________________________

18. What is the probable depositional setting and source of a pure white quartz sandstone?

\_\_\________________________________________________________________________________

\_\_\________________________________________________________________________________

19. What do bidirectional ripples indicate about the depositional environment of a rock?
\_\_\________________________________________________________________________________

\_\_\________________________________________________________________________________

20. What would the sedimentary environment be for oolitic sediments?

\_\_\________________________________________________________________________________

\_\_\________________________________________________________________________________

21. How would the sediments differ from a playa lake to that of a freshwater lake?

\_\_\________________________________________________________________________________

\_\_\________________________________________________________________________________

22. List three environments that ripples can form in:

\_\_\________________________________________________________________________________

\_\_\________________________________________________________________________________

\_\_\________________________________________________________________________________

\_\_\________________________________________________________________________________

23. List two ways cross bedding can occur:

\_\_\________________________________________________________________________________

\_\_\________________________________________________________________________________

24. How does a conglomerate form? Is there more than one way? If so how?

\_\_\________________________________________________________________________________

\_\_\________________________________________________________________________________

\_\_\________________________________________________________________________________

**## 12LabSedDepMacro.pdf**

Laboratory 12: Sedimentary Depositional Environments (Macro Scale)

Objective:

To understand the large sale features that are observed in sedimentary environments and the role they
play in understanding depositional environment.

Materials Needed:
Images of various sedimentary environments provided by instructor

Paleogeography is the study of what an environment was like during a certain time in the past. Paleogeography
takes biostratigraphy one step further in reconstructing the earth's history. By examining a set of rocks in several
different locations, all representing the same age, we can begin to reconstruct the ancient environment by using
the rock type and fossil content. The rock samples can be collected over a large or small lateral area, and the
locations and shapes of landmasses and seas can be deduced by knowing which types of rocks and fossils are
expected to be found in particular environments. An environment of deposition is the sum of all physical,
geographic, climatic, ecological, and chemical parameters that affect the composition of the sediment. Many
factors must be considered when deciding on the environment of deposition, including lithology, fossil
abundance, and fossil assemblage.

I. NONMARINE (CONTINENTAL) Most non-marine environments are typically the sites of erosion or non-
deposition, although a small percentage of deposits may be preserved.

A. Aqueous-
1. Fluvial (streams and rivers)-

(a) Floodplain- Sandstone, siltstone and shale with some conglomerate and coal, moderate
sorting, moderately quartz-rich; horizontal laminations, asymmetric (current) ripple marks, animal
tracks and trails, mud cracks, raindrop impressions; plant debris and tree fossils; irregular and
thin sheet shape.
(b) Channel-Sandstone and conglomerate, moderately sorted and quartz-rich; cross-bedding,
current ripple marks, scour of channel surfaces; may contain plant debris, non-marine (aqueous
and terrestrial) fossils; irregular lenticular to sinuous shape, closely associated with floodplain
deposits.

2. Paludal (Marsh or Swamp) – fine-grained deposits (siltstone, shale, coal) with dark color and high
organic content; thin horizontal laminations or massive (no visible sedimentary structures); abundant
plant fossils; irregular lens to sheet shape.
3. Lacustrine (lake) – fine-grained shale and some limestone; varve (alternating thin, light and dark
layers) clay common; possible freshwater fossils (ex. snails); irregular lens to sheet shape

B. Terrestrial (subaerial)-
1. Desert-

(a) Aeolian dune- fine-to medium-grained sandstone with excellent rounding and sorting; large-
scale cross-bedding common; fossils rare; extensive sheet-like or “blanket” shape.
(b) Alluvial fan- poorly sorted arkosic sandstone and conglomerate, abundant feldspar and
mica; cross-bedding, massive bedding, inverse and normally graded beds; fossils rare to absent;
thick fan-or wedge-shaped deposits.

2. Glacial- poorly sorted massive sandstone and conglomerate containing angular particles striated
pebbles, large pebbles and boulders, variable mineralogy; massive or crude horizontal laminations;
fossils absent; irregular shape and patchy distribution.

II. TRANSITIONAL (MARGINAL MARINE)

A. Delta-
A complex grouping of environments including channels, floodplains, swamps, bays, etc. Deposits
range from sandstone to siltstone and shale, and generally became finer-grained outward from the
shoreline; cross-bedding, horizontal laminations, current ripple marks and animal burrows are
common in some parts; fossils generally rare but may include locally abundant plant stems and roots
and rare marine; delta complexes are generally fan or wedge shaped.

B. Barrier Island/Lagoon-

1. Barrier Island- are mostly high energy deposits consisting of well-sorted and rounded quartz rich
sandstone. Grain size decreases systematically in a seaward direction; large-scale cross-bedding;
current and symmetrical (wave) ripple marks, horizontal laminations and animal burrows common;
fragmented marine fossils may be present; sand body shape is narrow and elongate parallel to the
shoreline and a lagoon is typically present between the barrier and the mainland.
2. Lagoon- lower energy environment dominated by fine-grained sandstone, siltstone, and shale;
horizontal laminations, ripple marks, and animal burrows, tracks and trails are common; carbonate
lagoons contain abundant and diverse marine fossils; shape is characteristically elongate parallel to
shore, and a barrier island is typically present immediately offshore from the lagoon.

C. Littoral (between mean high and low tides)-

1. Beach – high energy environment dominated by medium- to course- grained sandstone, well-
sorted and rounded; horizontal laminations, low-angle cross-bedding, wave ripple marks are most
abundant; fossils are rare and typically broken into fragments; sand body is elongate in shape and
trends parallel to shore.
2. Tidal flat – so named due to the tide coming in and receding in this relatively flat region. It will
have inter-bedded sandstone, siltstone and shale, with grain size increasing in a seaward direction;
cross-bedding (some large-scale), wave and current ripple marks, mud cracks, scour or channel
surfaces, and animal burrows, tracks and trails are common; fossils (marine) are rare to abundant;
wedge to irregular sheet shape.

III. OPEN MARINE

A. Pelagic- These environments are within the ocean water mass; thus, they don’t have characteristic
features preserved in the geologic record. Organisms which live in these environments fall to the ocean
bottom upon death and become part of the record of one of the benthic environments listed:
1. Neritic-depth to sea-floor less than 200 meters
2. Oceanic- depth to sea-floor greater than 200 meters

B. Benthic (bottom environments)
1. Shallow marine (Shelf) – sandstone, siltstone, limestone and shale interbedded,
sandstone composed predominantly of quartz but with some marine fossil fragments; cross-
bedding (some large-scale), ripple marks, and marine burrows, tracks and trails common;
marine fossils locally abundant; widespread sheet-like or blanket shape. Water depths are
typically less than 200 m.

2. Carbonate Reef/Platform- Unbedded, very fossiliferous with large and small scale, very
course grained sediment. Abundant, often large, organisms attached to the sea-floor, high
energy environment.
3. Deep Ocean- shale, fine-grained limestone and/or sandstone; graded bedding produce by
turbidity currents; large fossils rare; microfossils may be abundant; sheet to fan-like shape.

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The following charts summarize the previous discussion

ALLUVIAL FAN FLUVIAL (river)
LACUSTRINE

(lake)
AEOLIAN DESERT

(dunes)
PALUDAL
(swamp)

ROCK TYPE breccia, conglomerate,
arkose

conglomerate, sandstone,
siltstone, shale

siltstone, shale, limestone,
evaporites

quartz arenite,
(sandstone) gypsum

peat, coal, siltstone, black
shale

composition terrigenous terrigenous
terrigenous, carbonates,

evaporites
terrigenous or evaporite terrigenous

color brown or red brown or red
black, brown, grey, green,

red
yellow, red, tan, white black, gray or brown

grain size clay to gravel
clay, silt, sand, gravel,

fining upward
clay, silt, sand (coursening

upward)
sand clay to silt

grain shape angular angular to rounded —- rounded or polished —-

sorting poor variable variable good variable

inorganic
sedimentary

structures
cross bed and graded bed

assymmetrical ripples,
crossbedding, graded

beds, tool marks

symmetrical ripples,
lamination, cross beds,

graded beds, mud cracks,
raindrops

crossbedding laminated to massive

organic or
biogenic

structures
—- tracks, trails, burrows

tracks, trails, burrows, rare
stromatolites

tracks and trails root marks, burrows

fossils —-
rare freshwater shells,

bones, plants fragments
freshwater shells, fish,
bones, plant fragmetns

—-
plant fossils, freshwater

shells, bone, fish

Continental- Sedimentary Depositional Envirnonments

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DELTA BARRIER BEACH LAGOON TIDAL FLAT

ROCK TYPE sandstone, siltstone, shale,
coal

quartz arenite, coquina
siltsone, shale, limestone,
oolitic limestone, gypsum

siltstone, shale, calcilutitie,
dolostone or gypsum

composition terrigenous, some organic terrigenous or carbonate
terrigenous, carbonate or

evaporite
terrigenous, carbonate or

evaporite

color brown, black, grey, green,
red

what to tan dark grey to black or brown grey, brown, tan

grain size clay to sand (coursening
upward)

sand clay to silt clay to silt

grain shape —- rounded to angular —- —-

sorting variable good poor variable

inorganic
sedimentary

structures

cross bedding, graded
bedding

cross bedding, symmetrical
ripples

lamination, ripples cross
bedding

lamination, mudcracks,
ripples, cross bedding

organic or
biogenic

structures
trails, burrows tracks, trails, burrows trails, burrows

stromatolites, trails, tracks,
burrows

fossils plant fragments, shells marine shells marine shells marine shells

Transitional- Sedimentary Depositional Envirnonments

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REEF
CONTINENTAL

SHELF
CONTINENTAL

SLOPE AND RISE
ABYSSAL PLAIN

ROCK TYPE fossiliferous limestone
sandstone, shale, siltstone,

fossiliferous limestone, oolitic
limestone

litharenite (grewacke),
siltstone and shale, limestone

shale, chert, micrite, chalk,
diatomite

composition carbonate terrigenous or carbonate terrigenous or carbonate terrigenous or carbonate

color grey to white grey, brown, tan, green grey, green, brown black, white, red

grain size variable frameworks, few to
no grains

clay, silt, sand, gravel clay to snad clay

grain shape —- —- —- —-

sorting —- poor to good poor good

inorganic
sedimentary

structures
—- lamination, cross bedding

graded bedding, cross
bedding, lamination, flute

marks, tool marks (turbitdites)
lamination

organic or
biogenic

structures
—- trails, burrows trails, burrows trails, burrows

fossils coral, marine shells marine shells, sharks teeth
marine shells, rare plant

fragments
marine shells (mostly

microscopic)

Marine- Sedimentary Depositional Envirnonments

**## 12labanswerpage.pdf**

Lab 12 Sed. Dep. Env. Answer Pages
Study the sedimentary environments in the images below and answer the questions associated with the
images. Write your answers on the blanks provided at the end of the lab.

Answer the questions in the blanks provided on the following pages to make it easier.

Figure A. Death Valley National Park, CA

1. What are the prominent depositional features formed at the mouths

of the canyon?

2. Describe the textural characteristics of the sediment forming the

features named above.

2. What other non-marine features could exist on the flat terrain in front

of the range?

Figure B. Navajo Sandstone in Zion NP, UT

3. What type of bedding does this represent?

4. Was this sandstone deposited in a non-marine (terrestrial)

or marine environment?

5. Was the sandstone deposited by fluvial or aeolian processes?

Figure C. Bedding surface from Capital Reef, UT

6. What type of markings are present?

7. Assuming the rock is marine in origin, what do these

markings indicate about the depth of water in which
in the sediment was deposited?

Figure D. Cracked surface in Alaska

8. What type of markings are present?

9. Assuming the rock is marine in origin, what do these

markings indicate about the depth of water in which in
the sediment was deposited?

Source: Shutterstock

Source: Shutterstock

Source: Shutterstock

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Figure E. Conglomerate in Chiang Rai, Thailand

10. What type of grain shape and particle sorting

are shown here?

11. What is a possible depositional environment?

Give reasons for your interpretation.

Figure F. Sandstone Zion NP, Utah

12. What type of bedding is present?

13. Was this sandstone deposited in a nonmarine

(terrestrial) or marine environment? Was the sandstone
deposited by fluvial or aeolian processes? If in water,
in shallow or deep water? Explain how you know.

Figure G. Breccia, Lake Mead, Nevada

14. Describe particle color, texture, and sorting?

15. What was the depositional environment

responsible for creating this rock?

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Name: ___________________________________

Lab 7: Sedimentary Environments (macro scale)
Record your answers to the questions about the images above here:

Figure A

1 __________________________________________________________

2 __________________________________________________________

3 __________________________________________________________

Figure B

4 __________________________________________________________

5 __________________________________________________________

6 __________________________________________________________

Figure C

7 __________________________________________________________

8 __________________________________________________________

Figure D

9 __________________________________________________________

10 __________________________________________________________

Figure E

11 __________________________________________________________

12 __________________________________________________________

Figure F

13 __________________________________________________________

14 __________________________________________________________

Figure G

15 __________________________________________________________

16. __________________________________________________________

General Questions

16. What general rock and rock feature would indicate a long duration of deposition in an arid
environment?
\_\_\________________________________________________________________________________

\_\_\________________________________________________________________________________

17. What type of environment would a breccia with dark grey and/or purple rock fragments likely be
from?
\_\_\________________________________________________________________________________

\_\_\________________________________________________________________________________

18. What is the probable depositional setting and source of a pure white quartz sandstone?

\_\_\________________________________________________________________________________

\_\_\________________________________________________________________________________

19. What do bidirectional ripples indicate about the depositional environment of a rock?
\_\_\________________________________________________________________________________

\_\_\________________________________________________________________________________

20. What would the sedimentary environment be for oolitic sediments?

\_\_\________________________________________________________________________________

\_\_\________________________________________________________________________________

21. How would the sediments differ from a playa lake to that of a freshwater lake?

\_\_\________________________________________________________________________________

\_\_\________________________________________________________________________________

22. List three environments that ripples can form in:

\_\_\________________________________________________________________________________

\_\_\________________________________________________________________________________

\_\_\________________________________________________________________________________

\_\_\________________________________________________________________________________

23. List two ways cross bedding can occur:

\_\_\________________________________________________________________________________

\_\_\________________________________________________________________________________

24. How does a conglomerate form? Is there more than one way? If so how?

\_\_\________________________________________________________________________________

\_\_\________________________________________________________________________________

\_\_\________________________________________________________________________________

**## 12LabSedDepMacro.pdf**

Laboratory 12: Sedimentary Depositional Environments (Macro Scale)

Objective:

To understand the large sale features that are observed in sedimentary environments and the role they
play in understanding depositional environment.

Materials Needed:
Images of various sedimentary environments provided by instructor

Paleogeography is the study of what an environment was like during a certain time in the past. Paleogeography
takes biostratigraphy one step further in reconstructing the earth's history. By examining a set of rocks in several
different locations, all representing the same age, we can begin to reconstruct the ancient environment by using
the rock type and fossil content. The rock samples can be collected over a large or small lateral area, and the
locations and shapes of landmasses and seas can be deduced by knowing which types of rocks and fossils are
expected to be found in particular environments. An environment of deposition is the sum of all physical,
geographic, climatic, ecological, and chemical parameters that affect the composition of the sediment. Many
factors must be considered when deciding on the environment of deposition, including lithology, fossil
abundance, and fossil assemblage.

I. NONMARINE (CONTINENTAL) Most non-marine environments are typically the sites of erosion or non-
deposition, although a small percentage of deposits may be preserved.

A. Aqueous-
1. Fluvial (streams and rivers)-

(a) Floodplain- Sandstone, siltstone and shale with some conglomerate and coal, moderate
sorting, moderately quartz-rich; horizontal laminations, asymmetric (current) ripple marks, animal
tracks and trails, mud cracks, raindrop impressions; plant debris and tree fossils; irregular and
thin sheet shape.
(b) Channel-Sandstone and conglomerate, moderately sorted and quartz-rich; cross-bedding,
current ripple marks, scour of channel surfaces; may contain plant debris, non-marine (aqueous
and terrestrial) fossils; irregular lenticular to sinuous shape, closely associated with floodplain
deposits.

2. Paludal (Marsh or Swamp) – fine-grained deposits (siltstone, shale, coal) with dark color and high
organic content; thin horizontal laminations or massive (no visible sedimentary structures); abundant
plant fossils; irregular lens to sheet shape.
3. Lacustrine (lake) – fine-grained shale and some limestone; varve (alternating thin, light and dark
layers) clay common; possible freshwater fossils (ex. snails); irregular lens to sheet shape

B. Terrestrial (subaerial)-
1. Desert-

(a) Aeolian dune- fine-to medium-grained sandstone with excellent rounding and sorting; large-
scale cross-bedding common; fossils rare; extensive sheet-like or “blanket” shape.
(b) Alluvial fan- poorly sorted arkosic sandstone and conglomerate, abundant feldspar and
mica; cross-bedding, massive bedding, inverse and normally graded beds; fossils rare to absent;
thick fan-or wedge-shaped deposits.

2. Glacial- poorly sorted massive sandstone and conglomerate containing angular particles striated
pebbles, large pebbles and boulders, variable mineralogy; massive or crude horizontal laminations;
fossils absent; irregular shape and patchy distribution.

II. TRANSITIONAL (MARGINAL MARINE)

A. Delta-
A complex grouping of environments including channels, floodplains, swamps, bays, etc. Deposits
range from sandstone to siltstone and shale, and generally became finer-grained outward from the
shoreline; cross-bedding, horizontal laminations, current ripple marks and animal burrows are
common in some parts; fossils generally rare but may include locally abundant plant stems and roots
and rare marine; delta complexes are generally fan or wedge shaped.

B. Barrier Island/Lagoon-

1. Barrier Island- are mostly high energy deposits consisting of well-sorted and rounded quartz rich
sandstone. Grain size decreases systematically in a seaward direction; large-scale cross-bedding;
current and symmetrical (wave) ripple marks, horizontal laminations and animal burrows common;
fragmented marine fossils may be present; sand body shape is narrow and elongate parallel to the
shoreline and a lagoon is typically present between the barrier and the mainland.
2. Lagoon- lower energy environment dominated by fine-grained sandstone, siltstone, and shale;
horizontal laminations, ripple marks, and animal burrows, tracks and trails are common; carbonate
lagoons contain abundant and diverse marine fossils; shape is characteristically elongate parallel to
shore, and a barrier island is typically present immediately offshore from the lagoon.

C. Littoral (between mean high and low tides)-

1. Beach – high energy environment dominated by medium- to course- grained sandstone, well-
sorted and rounded; horizontal laminations, low-angle cross-bedding, wave ripple marks are most
abundant; fossils are rare and typically broken into fragments; sand body is elongate in shape and
trends parallel to shore.
2. Tidal flat – so named due to the tide coming in and receding in this relatively flat region. It will
have inter-bedded sandstone, siltstone and shale, with grain size increasing in a seaward direction;
cross-bedding (some large-scale), wave and current ripple marks, mud cracks, scour or channel
surfaces, and animal burrows, tracks and trails are common; fossils (marine) are rare to abundant;
wedge to irregular sheet shape.

III. OPEN MARINE

A. Pelagic- These environments are within the ocean water mass; thus, they don’t have characteristic
features preserved in the geologic record. Organisms which live in these environments fall to the ocean
bottom upon death and become part of the record of one of the benthic environments listed:
1. Neritic-depth to sea-floor less than 200 meters
2. Oceanic- depth to sea-floor greater than 200 meters

B. Benthic (bottom environments)
1. Shallow marine (Shelf) – sandstone, siltstone, limestone and shale interbedded,
sandstone composed predominantly of quartz but with some marine fossil fragments; cross-
bedding (some large-scale), ripple marks, and marine burrows, tracks and trails common;
marine fossils locally abundant; widespread sheet-like or blanket shape. Water depths are
typically less than 200 m.

2. Carbonate Reef/Platform- Unbedded, very fossiliferous with large and small scale, very
course grained sediment. Abundant, often large, organisms attached to the sea-floor, high
energy environment.
3. Deep Ocean- shale, fine-grained limestone and/or sandstone; graded bedding produce by
turbidity currents; large fossils rare; microfossils may be abundant; sheet to fan-like shape.

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The following charts summarize the previous discussion

ALLUVIAL FAN FLUVIAL (river)
LACUSTRINE

(lake)
AEOLIAN DESERT

(dunes)
PALUDAL
(swamp)

ROCK TYPE breccia, conglomerate,
arkose

conglomerate, sandstone,
siltstone, shale

siltstone, shale, limestone,
evaporites

quartz arenite,
(sandstone) gypsum

peat, coal, siltstone, black
shale

composition terrigenous terrigenous
terrigenous, carbonates,

evaporites
terrigenous or evaporite terrigenous

color brown or red brown or red
black, brown, grey, green,

red
yellow, red, tan, white black, gray or brown

grain size clay to gravel
clay, silt, sand, gravel,

fining upward
clay, silt, sand (coursening

upward)
sand clay to silt

grain shape angular angular to rounded —- rounded or polished —-

sorting poor variable variable good variable

inorganic
sedimentary

structures
cross bed and graded bed

assymmetrical ripples,
crossbedding, graded

beds, tool marks

symmetrical ripples,
lamination, cross beds,

graded beds, mud cracks,
raindrops

crossbedding laminated to massive

organic or
biogenic

structures
—- tracks, trails, burrows

tracks, trails, burrows, rare
stromatolites

tracks and trails root marks, burrows

fossils —-
rare freshwater shells,

bones, plants fragments
freshwater shells, fish,
bones, plant fragmetns

—-
plant fossils, freshwater

shells, bone, fish

Continental- Sedimentary Depositional Envirnonments

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DELTA BARRIER BEACH LAGOON TIDAL FLAT

ROCK TYPE sandstone, siltstone, shale,
coal

quartz arenite, coquina
siltsone, shale, limestone,
oolitic limestone, gypsum

siltstone, shale, calcilutitie,
dolostone or gypsum

composition terrigenous, some organic terrigenous or carbonate
terrigenous, carbonate or

evaporite
terrigenous, carbonate or

evaporite

color brown, black, grey, green,
red

what to tan dark grey to black or brown grey, brown, tan

grain size clay to sand (coursening
upward)

sand clay to silt clay to silt

grain shape —- rounded to angular —- —-

sorting variable good poor variable

inorganic
sedimentary

structures

cross bedding, graded
bedding

cross bedding, symmetrical
ripples

lamination, ripples cross
bedding

lamination, mudcracks,
ripples, cross bedding

organic or
biogenic

structures
trails, burrows tracks, trails, burrows trails, burrows

stromatolites, trails, tracks,
burrows

fossils plant fragments, shells marine shells marine shells marine shells

Transitional- Sedimentary Depositional Envirnonments

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REEF
CONTINENTAL

SHELF
CONTINENTAL

SLOPE AND RISE
ABYSSAL PLAIN

ROCK TYPE fossiliferous limestone
sandstone, shale, siltstone,

fossiliferous limestone, oolitic
limestone

litharenite (grewacke),
siltstone and shale, limestone

shale, chert, micrite, chalk,
diatomite

composition carbonate terrigenous or carbonate terrigenous or carbonate terrigenous or carbonate

color grey to white grey, brown, tan, green grey, green, brown black, white, red

grain size variable frameworks, few to
no grains

clay, silt, sand, gravel clay to snad clay

grain shape —- —- —- —-

sorting —- poor to good poor good

inorganic
sedimentary

structures
—- lamination, cross bedding

graded bedding, cross
bedding, lamination, flute

marks, tool marks (turbitdites)
lamination

organic or
biogenic

structures
—- trails, burrows trails, burrows trails, burrows

fossils coral, marine shells marine shells, sharks teeth
marine shells, rare plant

fragments
marine shells (mostly

microscopic)

Marine- Sedimentary Depositional Envirnonments

November 5, 2026
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– 2 years ago **files (1)** – ## exam-2024-fall.pdf **## exam-2024-fall.pdf** Selected Algorithms in Linear Algebra Home Exam Sivan Toledo February 2025 General Instructions 1. Submission of a solution to this exam constitutes a statement that you followed these instructions. If you failed to follo…

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**files (1)**

– ## exam-2024-fall.pdf

**## exam-2024-fall.pdf**

Selected Algorithms in Linear Algebra
Home Exam

Sivan Toledo

February 2025

General Instructions
1. Submission of a solution to this exam constitutes a statement that you followed these instructions.

If you failed to follow some of the instructions for whatever reason, explain at the top of the exams
which instructions you failed to follow, how you solved the relevant parts of the exam, and why.

2. The exam is individual. You may not discuss the exam, your solutions or other solutions, or anything
having to do with the algorithms and computations that the exam focuses on with any person except
Sivan Toledo. You must follow this rule before, during, and after you solve the exam (including in the
periods before you start the exam and after you submit your solution, since different students may
solve it at different times).

3. You may only discuss this exam with persons other than Sivan Toledo after the grades are published.

4. You may use any publicly-accessible non-human resource to solve the exam, but you must cite every
resource that you use. For books, articles, web sites, and so on, cite the title, author, and URL, and
explain how you used the resource. For AI tools and other responsive resources, give the name of the
tool (and URL if not well known) and the prompts. If the interaction was complex, just summarize
the interaction. In both cases, explain how you used the results.

5. Include all the code that you used, and mark clearly code that you wrote, code from other sources
(static or responsive/AI). If you fixed or corrected existing or generated code, indicate your changes
or fixes clearly.

6. All code must be clearly documented using comments.

7. Use diagrams and graphs where appropriate to clarify and/or enhance your answers.

1 Efficient and Stable Factorization of Anti-Symmetric Matrices
(40 points)

We can solve a linear system of equation with an <-by-< symmetric positive-definite matrix � using the
Cholesky factorization using 1

3<
3 + =(<3) arithmetic operations. The algorithm is backward stable and it is

about twice as efficient as an !* factorization with partial pivoting, which is also usually backward stable,
but does not exploit symmetry. In some vague way it makes sense that Cholesky would be twice as efficient,

1

ראינו בשיעור 2

because due to the symmetry of the matrix, we can represent it using its upper and lower half, so we do not
need to update the entire trailing submatrix after every elimination step.

In this problem we want to factor in a backward-stable a real matrix that is not symmetric, but satis-
fies the constraint �) = −�. In other words, its elements satisfy �7 8 = −�87. We will call such matrices
anti symmetric. Such matrices are fully defined by about <2/2 real values, not <2, so we hope to achieve
computational savings similar to the savings in Cholesky.

The main building block in our new algorithm will be to zero most of the first column by subtracting
a multiple of the second row of � from rows 3 : <. We will then zero most of the first row by subtracting
the same multiples of the second column from columns 3 : <. We continue with the trailing submatrix in the
same way, until we reduce � to a tridiagonal matrix) , in only sub- and super-diagonal elements)7+7,7,)7,7+1
are nonzero, and which is also anti symmetric.

1. Implement this algorithm and test it on random matrices with Gaussian elements. The algorithm
should return twomatrices, a lower triangularmatrix !with 1s on the diagonal and an anti symmetric
matrix ) , such that � satisfies � = !)!) (but a weaker condition in floating point). For simplicity,
operate on all the elements of � and the trailing submatrices, not only on one triangle. Try to make
the code as efficient as possible (while operating on both triangles). Test that it works correctly and
explain how you performed the tests. Hint: As in !* with Gaussian elimination, if you eliminate
column 8 with using a matrix !8 with ones on the diagonal and the negation of the multipliers below
the diagonal in one column (which one?), thematrix ! should have themultipliers in the same position,
but not negated.

2. Roughly how many arithmetic operation does your code perform? The answer should be given as an
explicit multiple of <3; you can ignore low order terms. Please relate your answer to the number of
operations that the !* factorization performs. Explain the result.

3. If you were to modify the algorithm and the code from Part 1 so that it would only operate on one
triangle, say the lower one, howmany operations would the improved algorithm perform? How does
this relate to the number of operations performed by the !* factorization?

4. The main motivation for this algorithm is that we can incorporate into it partial pivoting. Show that
the algorithm, as presented up to now, can fail, and explain why it might be unstable even in cases
where it does not fail.

5. We can avoid these problems by exchanging before we eliminate column 8 and row 8 two rows and the
same two columns so that the element in position 8+1, 8 in the trailing submatrix has the largest mag-
nitude among elements 8 + 1 : <, 8. We can express the overall factorization as %�%) = !)!) ,where
% is a permutation matrix. Explain how these exchanges affect the matrix !. How do you think we
can characterize the trailing submatrices and) if we perform these exchanges, both in the worst case
and in practice? You only need to provide a reasonable characterization and to justify it from what
we know about !* with partial pivoting; you do not need to provide a formal analysis.

6. We can make this algorithm even more efficient by noticing that the matrix � = )!) is upper Hes-
senberg (elements �7 8 with 7 > 8 + 1 are zeros). Prove that this is indeed the case and explain how
elements of ) relate to elements of � (so that we can construct ) from �).

7. Modify your code from Part 1 so that it computes ! and � . You can again update the entire trailing
submatrix.

2

8. Explain how this modification reduces the number of arithmetic operations and give an estimate for
the number of operations that the algorithm performs if it exploits the anti-symmetry (the leading
term only).

9. To solve a system �F = %)!)!)%F = 1, we need to solve linear systems with a anti-symmetric tridi-
agonal matrix) . Explain howwe can do that in a backward-stable way in$(<) arithmetic operations
and storage.

2 Benchmarking Linear Solvers (30 Points)
The aim of this problem is to benchmark a number of exiting solvers of linear equations. The focus is on
producing valid and robust results and on presenting them well. For this problem, it is important that the
solvers be efficient. Matlab is considered the gold standard for this problem. All its solvers are good enough
(if used correctly); you can use some other programming environment (e.g., Python), but if one or more of
its solvers is inefficient, you may lose points.

1. Implement a function lap2d that creates the Laplacian of an <-by-< two dimensional grid. Theweight
of all edges should be 1, and the row-sums of all rows other than the first should be 0. The sum of
the elements in the first row should be 1. The row/column ordering of the matrix should be a row-
by-row ordering of the grid vertices (the so-called natural order). Thematrixmust be represented
efficiently as a sparsematrix (inmatlab, the form S=sparse(i,j,a) is a goodway to construct the
matrix from a set of nonzero values 07 8) Plot the nonzero structure of the matrix (spy) for a 10-by-10
grid.

2. Implement a similar function lap3d for 3-dimensional grids. Plot it for some convenient size for
which the structure of the matrix is clear from the plot.

3. Write a code that measures the performance of several linear solvers for �F = 1, where � is a Lapla-
cian from Part 1 and 1 is a random vector. You The solvers that you need to implement are:

(a) A dense Cholesky factorization. In Matlab, A=full(S) creates a dense representation of a
sparse matrix.

(b) A sparse Cholesky factorization, with a row/column permutation to enhance sparsity in the
factor. In Matlab, help chol (or the more detailed doc chol) will tell you how to invoke the
Cholesky factorization so that it can permute the rows and columns of a sparse matrix.

(c) Conjugate gradients without a preconditioner (pcg in Matlab).

(d) Conjugate gradients with an incomplete-Cholesky factorization with no fill (ichol in Matlab).

4. Demonstrate that each of the solvers is correct. For the iterative solvers, explain their accuracy of the
solution that they return and compare to the solution of the direct (Cholesky factorization) solvers.
For the sparse solver, show the nonzero structure of the factor, to demonstrate that it is indeed sparse.

5. Compare the performance of the 4 solvers by finding out the size of the largest grid they can handle
(in both 2D and 3D) in 10s (only the linear solver should take 10s; exclude the time to construct the
test problem). You will need to write code that finds these problem sizes. You are free to also present
the performance of the 4 solvers in other ways. Make sure your results are statistically robust; the

3

actual running times are not deterministic even if the algorithm is. You need not perform a statistical
analysis, but you need to account for the running-times variability and to explain how do you did it.
In this part of the problem, do your best to ensure that the solver is using only 1 CPU core (in Matlab,
maxNumCompThreads(1) should work); explain how you restricted the solvers to 1 core and how
you checked that they are indeed using only one.

6. Repeat Part 5, but with at as many cores as you can. Try to the speedups.

3 Efficient Multiplication of Sparse Matrices (20 Points)
This problem investigates the efficient multiplication of sparse matrices represented using a compressed
sparse column (CSC) representations. In this representation, the nonzero values of elements each column
are stored consecutively in an array, and the row indices of these elements are stored in the same order in
an integer array. These arrays need not be sorted in increasing row order. A third array points to the two
arrays representing each column; this array represents the columns in increasing index order.

1. Given the CSC representation of two sparse matrices � ∈ R;×< and � ∈ R<×9, show how to create
the CSC representation of the product �� in $(; + 9 + >) operations, where > is the number of
arithmetic operations on nonzeros required to multiply the two matrices. Make sure you explain
how to determine the size of each column in the product (that is, the size of the arrays that represent
that column).

2. Given the CSC representation a sparse matrix � ∈ R;×<, show how to create the CSC representation
of the product �) �. Try tomake this as efficient as possible and analyze the total number of operations
that the multiplication requires in terms of ;, <, and >.

3. Suggest a mechanism to improve the efficiency of the solution of Part 1 in cases in which ; � >.
That is, try to find a way to remove the dependence on ; from the running time.

4 A Tradeoff in the LLL Basis Reduction Algorithm (10 points)
The !!! algorithm ensures that in the output matrix ' satisfies��'7,8�� ≤ 1

2
��'7,7��

'27,7 ≥ H'27−1,7−1 − '27−1,7 .

for some 1/4 < H < 1. That is, the client code that calls LLL sets H to some value in this range. Explain the
tradeoff: what happens when we set H just above 1/4? What happens when we set H just below 1?

4

**## exam-2024-fall.pdf**

Selected Algorithms in Linear Algebra
Home Exam

Sivan Toledo

February 2025

General Instructions
1. Submission of a solution to this exam constitutes a statement that you followed these instructions.

If you failed to follow some of the instructions for whatever reason, explain at the top of the exams
which instructions you failed to follow, how you solved the relevant parts of the exam, and why.

2. The exam is individual. You may not discuss the exam, your solutions or other solutions, or anything
having to do with the algorithms and computations that the exam focuses on with any person except
Sivan Toledo. You must follow this rule before, during, and after you solve the exam (including in the
periods before you start the exam and after you submit your solution, since different students may
solve it at different times).

3. You may only discuss this exam with persons other than Sivan Toledo after the grades are published.

4. You may use any publicly-accessible non-human resource to solve the exam, but you must cite every
resource that you use. For books, articles, web sites, and so on, cite the title, author, and URL, and
explain how you used the resource. For AI tools and other responsive resources, give the name of the
tool (and URL if not well known) and the prompts. If the interaction was complex, just summarize
the interaction. In both cases, explain how you used the results.

5. Include all the code that you used, and mark clearly code that you wrote, code from other sources
(static or responsive/AI). If you fixed or corrected existing or generated code, indicate your changes
or fixes clearly.

6. All code must be clearly documented using comments.

7. Use diagrams and graphs where appropriate to clarify and/or enhance your answers.

1 Efficient and Stable Factorization of Anti-Symmetric Matrices
(40 points)

We can solve a linear system of equation with an <-by-< symmetric positive-definite matrix � using the
Cholesky factorization using 1

3<
3 + =(<3) arithmetic operations. The algorithm is backward stable and it is

about twice as efficient as an !* factorization with partial pivoting, which is also usually backward stable,
but does not exploit symmetry. In some vague way it makes sense that Cholesky would be twice as efficient,

1

ראינו בשיעור 2

because due to the symmetry of the matrix, we can represent it using its upper and lower half, so we do not
need to update the entire trailing submatrix after every elimination step.

In this problem we want to factor in a backward-stable a real matrix that is not symmetric, but satis-
fies the constraint �) = −�. In other words, its elements satisfy �7 8 = −�87. We will call such matrices
anti symmetric. Such matrices are fully defined by about <2/2 real values, not <2, so we hope to achieve
computational savings similar to the savings in Cholesky.

The main building block in our new algorithm will be to zero most of the first column by subtracting
a multiple of the second row of � from rows 3 : <. We will then zero most of the first row by subtracting
the same multiples of the second column from columns 3 : <. We continue with the trailing submatrix in the
same way, until we reduce � to a tridiagonal matrix) , in only sub- and super-diagonal elements)7+7,7,)7,7+1
are nonzero, and which is also anti symmetric.

1. Implement this algorithm and test it on random matrices with Gaussian elements. The algorithm
should return twomatrices, a lower triangularmatrix !with 1s on the diagonal and an anti symmetric
matrix ) , such that � satisfies � = !)!) (but a weaker condition in floating point). For simplicity,
operate on all the elements of � and the trailing submatrices, not only on one triangle. Try to make
the code as efficient as possible (while operating on both triangles). Test that it works correctly and
explain how you performed the tests. Hint: As in !* with Gaussian elimination, if you eliminate
column 8 with using a matrix !8 with ones on the diagonal and the negation of the multipliers below
the diagonal in one column (which one?), thematrix ! should have themultipliers in the same position,
but not negated.

2. Roughly how many arithmetic operation does your code perform? The answer should be given as an
explicit multiple of <3; you can ignore low order terms. Please relate your answer to the number of
operations that the !* factorization performs. Explain the result.

3. If you were to modify the algorithm and the code from Part 1 so that it would only operate on one
triangle, say the lower one, howmany operations would the improved algorithm perform? How does
this relate to the number of operations performed by the !* factorization?

4. The main motivation for this algorithm is that we can incorporate into it partial pivoting. Show that
the algorithm, as presented up to now, can fail, and explain why it might be unstable even in cases
where it does not fail.

5. We can avoid these problems by exchanging before we eliminate column 8 and row 8 two rows and the
same two columns so that the element in position 8+1, 8 in the trailing submatrix has the largest mag-
nitude among elements 8 + 1 : <, 8. We can express the overall factorization as %�%) = !)!) ,where
% is a permutation matrix. Explain how these exchanges affect the matrix !. How do you think we
can characterize the trailing submatrices and) if we perform these exchanges, both in the worst case
and in practice? You only need to provide a reasonable characterization and to justify it from what
we know about !* with partial pivoting; you do not need to provide a formal analysis.

6. We can make this algorithm even more efficient by noticing that the matrix � = )!) is upper Hes-
senberg (elements �7 8 with 7 > 8 + 1 are zeros). Prove that this is indeed the case and explain how
elements of ) relate to elements of � (so that we can construct ) from �).

7. Modify your code from Part 1 so that it computes ! and � . You can again update the entire trailing
submatrix.

2

8. Explain how this modification reduces the number of arithmetic operations and give an estimate for
the number of operations that the algorithm performs if it exploits the anti-symmetry (the leading
term only).

9. To solve a system �F = %)!)!)%F = 1, we need to solve linear systems with a anti-symmetric tridi-
agonal matrix) . Explain howwe can do that in a backward-stable way in$(<) arithmetic operations
and storage.

2 Benchmarking Linear Solvers (30 Points)
The aim of this problem is to benchmark a number of exiting solvers of linear equations. The focus is on
producing valid and robust results and on presenting them well. For this problem, it is important that the
solvers be efficient. Matlab is considered the gold standard for this problem. All its solvers are good enough
(if used correctly); you can use some other programming environment (e.g., Python), but if one or more of
its solvers is inefficient, you may lose points.

1. Implement a function lap2d that creates the Laplacian of an <-by-< two dimensional grid. Theweight
of all edges should be 1, and the row-sums of all rows other than the first should be 0. The sum of
the elements in the first row should be 1. The row/column ordering of the matrix should be a row-
by-row ordering of the grid vertices (the so-called natural order). Thematrixmust be represented
efficiently as a sparsematrix (inmatlab, the form S=sparse(i,j,a) is a goodway to construct the
matrix from a set of nonzero values 07 8) Plot the nonzero structure of the matrix (spy) for a 10-by-10
grid.

2. Implement a similar function lap3d for 3-dimensional grids. Plot it for some convenient size for
which the structure of the matrix is clear from the plot.

3. Write a code that measures the performance of several linear solvers for �F = 1, where � is a Lapla-
cian from Part 1 and 1 is a random vector. You The solvers that you need to implement are:

(a) A dense Cholesky factorization. In Matlab, A=full(S) creates a dense representation of a
sparse matrix.

(b) A sparse Cholesky factorization, with a row/column permutation to enhance sparsity in the
factor. In Matlab, help chol (or the more detailed doc chol) will tell you how to invoke the
Cholesky factorization so that it can permute the rows and columns of a sparse matrix.

(c) Conjugate gradients without a preconditioner (pcg in Matlab).

(d) Conjugate gradients with an incomplete-Cholesky factorization with no fill (ichol in Matlab).

4. Demonstrate that each of the solvers is correct. For the iterative solvers, explain their accuracy of the
solution that they return and compare to the solution of the direct (Cholesky factorization) solvers.
For the sparse solver, show the nonzero structure of the factor, to demonstrate that it is indeed sparse.

5. Compare the performance of the 4 solvers by finding out the size of the largest grid they can handle
(in both 2D and 3D) in 10s (only the linear solver should take 10s; exclude the time to construct the
test problem). You will need to write code that finds these problem sizes. You are free to also present
the performance of the 4 solvers in other ways. Make sure your results are statistically robust; the

3

actual running times are not deterministic even if the algorithm is. You need not perform a statistical
analysis, but you need to account for the running-times variability and to explain how do you did it.
In this part of the problem, do your best to ensure that the solver is using only 1 CPU core (in Matlab,
maxNumCompThreads(1) should work); explain how you restricted the solvers to 1 core and how
you checked that they are indeed using only one.

6. Repeat Part 5, but with at as many cores as you can. Try to the speedups.

3 Efficient Multiplication of Sparse Matrices (20 Points)
This problem investigates the efficient multiplication of sparse matrices represented using a compressed
sparse column (CSC) representations. In this representation, the nonzero values of elements each column
are stored consecutively in an array, and the row indices of these elements are stored in the same order in
an integer array. These arrays need not be sorted in increasing row order. A third array points to the two
arrays representing each column; this array represents the columns in increasing index order.

1. Given the CSC representation of two sparse matrices � ∈ R;×< and � ∈ R<×9, show how to create
the CSC representation of the product �� in $(; + 9 + >) operations, where > is the number of
arithmetic operations on nonzeros required to multiply the two matrices. Make sure you explain
how to determine the size of each column in the product (that is, the size of the arrays that represent
that column).

2. Given the CSC representation a sparse matrix � ∈ R;×<, show how to create the CSC representation
of the product �) �. Try tomake this as efficient as possible and analyze the total number of operations
that the multiplication requires in terms of ;, <, and >.

3. Suggest a mechanism to improve the efficiency of the solution of Part 1 in cases in which ; � >.
That is, try to find a way to remove the dependence on ; from the running time.

4 A Tradeoff in the LLL Basis Reduction Algorithm (10 points)
The !!! algorithm ensures that in the output matrix ' satisfies��'7,8�� ≤ 1

2
��'7,7��

'27,7 ≥ H'27−1,7−1 − '27−1,7 .

for some 1/4 < H < 1. That is, the client code that calls LLL sets H to some value in this range. Explain the
tradeoff: what happens when we set H just above 1/4? What happens when we set H just below 1?

4

November 5, 2026

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