STRUCTURAL GEOLOGY LAB 1: GEOMETRIC and KINEMATIC ANALYSIS in a SANDBOX

Author: Kimberly Hannula, Fort Lewis College, hannula_k@fortlewis.edu

Goals:

Use sketches and structural map symbols to make a geometric description of structures.

Observe and record kinematic analysis of an analog model. Use density, thickness, and strength measurements to determine the real-world

scale of an analog structure model. Separate descriptions from interpretations in a lab write-up.

Sandbox lab introduction

Geometric analysis

Structural geology involves imagining and describing the 3-dimensional shapes of things like bedding, faults, and joints, and describing the differences between the deformed rocks that we see today and their original, undeformed state. These descriptions of shapes are usually different from the shape of the topography, but they are important for very practical reasons: they let us figure out where things are underground. Maybe we want to know about fractures that allow groundwater to flow. Maybe we want to know the location of a bed that we want to quarry for building stone. Maybe we want to know whether oil or gas will be trapped, or know where our “horizontal” well should run in order to follow a hydrocarbon-rich bed. Maybe we want to figure out where gold, or copper, or rare-earth elements have been concentrated, and we need to know where fluids could have traveled easily. Maybe we want to know whether a particular fault is likely to be reactivated in an earthquake. All of these problems require knowing the shapes of beds and fractures and faults underground.

Geometric analysis is important for other reasons, too. Our observations of geometry allow us to test our ideas about how tectonics has shaped mountains and sedimentary basins – we can’t do kinematic or dynamic analysis without also describing structures geometrically.

There are many tools that we use for geometric analysis. Sometimes we can see cuts through structures in an outcrop, and can sketch part of a shape. Measuring the strike and dip of beds, foliations, joints, and faults gives local information about their shapes. The full three-dimensional shapes require imagining how strike and dip information connects between many different outcrops. Geologic maps show the intersection between topography and the structure of rock layers and fractures underground. At a much smaller scale, thin sections can be used to show what’s inside a rock on the scale of individual minerals. Cross-sections drawn from geologic maps show a two-dimensional cut through the structure; they are one way to communicate your interpretation of the subsurface geology to other people. We can also use descriptions of rocks from wells or boreholes to constrain what’s present below the surface. Geophysical information can provide other constraints. In particular, seismic reflection is used, especially in the oil and gas industry, to identify the shapes of beds in the subsurface. Other geophysical data, such as measurements of gravity, earthquake locations, magnetic anomalies, etc. should also be consistent with the geometry that we predict underground.

Through the semester, you will learn many different tools for geometric description and analysis, both qualitative and quantitative. This week, you will use geologic map symbols to describe (qualitatively, in this case) the shape of a surface that you make using the sandbox.

Kinematic analysis

Kinematic analysis involves thinking about how structures form – thinking about changes through time. Those may involve changing the shape of a feature (such as folding a bed, or stretching a pebble), moving objects (such as beds sliding along faults or plates moving over the asthenosphere), or rotating objects (like tilting a bed). It also includes thinking about the process that formed the structures – the “deformation path.” Sometimes kinematic models are conceptual – sketches that show the processes that you imagine in your mind. Kinematic conceptual models often include arrows showing how objects move through time, or several frames showing the changes that occur through time.

Kinematic models can also be quantitative. Models of progressive strain explain how the changes of shape occur through time. High-precision GPS makes it possible to observe kinematics that are happening today at a plate scale, in the form of velocity vectors showing how fast each point is currently moving.

Fig. 1. Map of the velocity of Earth’s surface in eastern Asia, derived from repeated high-precision GPS measurements. Each arrow represents a measured velocity in one place. The star is the location of a past earthquake. Map source: Tectonics Observatory at Caltech, http://www.tectonics.caltech.edu/outreach/highlights/seasonal_eq/velocity.html

Dynamic analysis

Dynamic analysis involves thinking about the forces that cause structures to form – why, rather than how. Ultimately, we’re talking about physics here. Gravity is always important when you’re dealing with structures on Earth. Other forces might involve horizontal forces associated with plate tectonics, or forces caused by the shrinking of a cooling lava flow, or forces associated with increasing water pressure in cracks.

We’ll actually be talking about “stresses” rather than forces in this class. Stresses are related to forces, but work as three-dimensional fields (pushing harder in one direction than another). We’ll talk more about stresses (and the math behind them) during the second week of class (and throughout the semester). For this lab, I would like you to think about which direction your model is being pushed or pulled; we won’t get quantitative about stress this week.

Rheology: relation between dynamic and kinematic analysis

Different materials respond to stresses in different ways. Corn syrup flows. Glass breaks. Sand collapses along steep faces. The technical term for the way that a material responds to stress is “rheology.” Some materials have a brittle rheology – they respond to stresses by breaking. Other materials have a viscous rheology – they flow. During the third week of class, we’ll talk about some other ways that materials can behave – elastic rheology (things that bounce back) and plastic rheology (things that stay the same shape up to a certain stress, and then suddenly start to change shape after that).

When making models of geologic processes, it’s important to choose a modeling material that has an appropriate rheology for your process. If you’re going to model the mantle, corn syrup might work well, but you’ll need something different if you’re interested in studying the upper crust.

One important concept related to rheology is failure. “Failure” refers to the amount of stress that a material can take before it starts to permanently change shape. (The term comes from engineering – when your bridge changes shape, that is a bad thing. In geology, it just means that the rocks get more interesting.)

Another import concept is strength. The “strength” of a material is the largest amount of stress it can withstand before it fails. During lab, you will measure one kind of strength (of granular materials, like sand or sugar or flour): the cohesion.

Analog modeling

Geologic processes are slow. (Except when they’re not. If you’ve been in an earthquake or seen a landslide, you know what I mean.) The Earth is also big – it doesn’t fit in a lab. That means that we mostly work with rocks that record past processes, and imagine the processes that could have created them, and come up with (often indirect) tests to see if our imagined causes are likely to be right. Those tests might involve field work, looking at your rocks at a different scale (such as in thin section), measuring something that you

can’t see (like finding out the U-Pb age of a zircon), or many other clever tests. We usually come up with lots of working hypotheses, and design tests to tell them apart.

Analog modeling makes different kinds of tests possible. We start with a possible cause for a feature – for example, could folded rocks in the Appalachians be a result of horizontally compressing layers? Then we build some kind of apparatus that applies the forces that we think caused our feature, and see if the result resembles features in the real world.

It’s more complicated than that. We need to think about ways in which our model matches the process that we’re modeling, and the ways in which it is different. Is the rheology of our modeling material appropriate? Does it respond to stresses in a similar way that the real material on Earth does? Does it matter how fast we run the model? How big does the model need to be in order to model the structure that we’re interested in? If we’re making a model in a box, how does friction on the sides of the box affect the model? If the model doesn’t have sides, how does the piled up sand or clay on the edges affect the behavior of the model?

Scaling analog models

If you make a scale model of Earth, you don’t just change its size. You also change the density of the material, the strength of the material (garnet sand, rather than solid rock), and how fast things move (cm/second, rather than km/million years). If you want to make something that has similar shapes to geologic structures on Earth (e.g. geometrically similar), and that moves in the same way (kinematically similar), the models also have to be dynamically similar. That means that the laws of physics (like force = mass * acceleration) also scale, and you can use the laws of physics to figure out whether you’ve created anything that’s similar to what’s found in the real world.

Most scale models involve some kind of simplification of the physics. In the case of your sandbox models, you’ve moved them slowly enough that you don’t have to think about acceleration. That means that you can just think about scaling the stress that the rocks experience.

In order to figure out what real-world features are analogous to the sandbox models that you made, you’ll need to do the math in the section below:

Imagine the stress at the bottom of a column of rock.

Stress (, the Greek letter sigma) = force/area

Or

σ= Flength∗width

The force at the bottom of the column is the force due to the acceleration of gravity:

Force=mass∗gravity

Geologists tend to think about mass as a function of density (mass/volume) (the Greek letter ), rather than as a total quantity.

Mass= ρ∗length∗width∗height

So geologists would write

Force=ρ∗length∗width∗height∗gravity

And stress at the bottom of the column would be

σ= ρ∗length∗width∗height∗glength∗width

or simplified,

σ=ρ∗height∗g

We’ll use z for height for the rest of these equations. We’ll also use subscripts to keep track of what’s the model (m), and what’s the real world (prototype, or p).

The assumption in scaling calculations is that the ratio of stresses in the model and the real world should be the same. So:

σm

σ p=

ρm∗zm∗gρp∗zp∗g

The cohesion that you just measured is the stress that your material can withstand without collapsing: it is one measure of the strength of the sand.

The ratio of cohesions between your model and real rocks should allow you to figure out how large of an area you modeled!

σm

σ p=

ρm∗zm∗gρp∗zp∗g

Or

z p

zm=

ρm

ρp∗σ p

σm

Plug into the equation:

m : Density of your sand (from your measurement)

p : Density of typical crustal rock (2.7 g/cm3 – this is a reasonable density for granite, sandstone, shale, and limestone, and is the number that is most often used to represent continental crust in density problems)

m : the cohesion that you measured for the sand

p : Use 50,000,000 Pa (= 50 MPa) (Cohesion of real rocks varies from 15 to 110 MPa, Schellart, 2000; 50 MPa is close to the cohesion of Tennessee sandstone, Weber sandstone, and Blair dolomite)

Your final ratio tells you how many times larger the real-world equivalent should be. If your model is 10 cm thick, you would multiply 10 cm by the final ratio to know what depth in the crust you will have modeled.

For today’s lab, assume that the scaling is the same for vertical distances as for horizontal distances. (But you should think more about whether this is reasonable, especially when you discuss differences between your model and your classmates’ models.)

STRUCTURAL GEOLOGY LAB 1: GEOMETRIC and KINEMATIC ANALYSIS in a SANDBOX (instructions during lab)

Goals:

Use sketches and structural map symbols to make a geometric description of structures.

Observe and record kinematic analysis of an analog model. Use density, thickness, and strength measurements to determine the real-world

scale of an analog structure model. Separate descriptions from interpretations in a lab write-up.

To turn in (at beginning of your lab next week):

Table summarizing the set-up of your model. Table with the measurements needed for the scaling problem. Scaling calculation (showing enough steps that I can follow it while grading) Map- and cross-section-view sketches of your model after deformation. Structure map of your final model (with at least 5 qualitative strike & dip

symbols, and with fold and fault symbols as appropriate) Image from Google Earth, showing the scale of a real-world analog to what you

created during lab. Write-up (bullets ok), with separate description and discussion/interpretation

sections

Do during lab:

1) Select fault type and material (sand or flour).

Record information about conditions. Sketch your set-up. Include:

o Shape of baseo Arrows showing movement of every part that moveso Concept sketch annotations, explaining the parts of the set-up

2) Run your model at least 3 times. Watch for things that are similar in each run, and things that are different each time. Sketch notes for yourself to help you remember your observations.

3) After your third run, make three sketches to show the geometry of the surface that resulted from your experiment.

a) Sketch the shape of the surface in map view. After you have made your sketch, compare your sketch with those of other students in your group. Discuss what features you drew in common, and what features are different. Then make a second drawing, showing the features that you think would be most important for

communicating the deformation that you observed. Be prepared to show your second drawing to students in the other groups.

b) Sketch a cross-section view of your model. (In your group, discuss which side of your model to draw.)

c) Make a structure map showing the key structural features that resulted from your experiment. (See Appendix for a list of symbols to use.) Your map should include:

At least 5 qualitative (no numbers) strike and dip symbols, showing the approximate strike and the direction in which the surface is tilted. You don’t need to measure the exact orientation of the surface, but use the same kind of symbols from a geologic map to show the shape of the surface.

Fold hinge symbols, showing the location of anticline and syncline hinges. Fault symbols, showing the location of thrust faults, normal faults, and/or

strike-slip faults that cut the surface.

4) Use the GoPro to record one final experiment. You will use this last experiment for the rest of the interpretation for your lab, so you can do the recording over if it doesn’t behave in the way that your other experiments did.

5) Measure the properties of your sand.

In order to relate an analog model to examples of structures found in the real world, you need to measure the properties of your material and then do scaling calculations. (See the introduction handout for more details.) Make the measurements in the field lab; we will return to the classroom to do the calculations.

Density (mass/volume)

Weigh the container (the plastic weigh boat) before putting sand in it. Measure 100 mL of sand. (100 mL = 100 cm3) Pour the 100 mL of sand into the weigh boat. Measure the mass in grams of 100 cm3 of sand + the weigh boat. Subtract the weight of the weigh boat from the total measured weight to give the

weight of the sand alone. Calculate density = mass/volume (= grams/100 cm3).

Thickness

Use a ruler to measure the thickness of your sand pile in centimeters.

Angle of repose:

Pour sand through a funnel to make a conical hill. Measure the slope of the hill with a protractor (Check with a different measurement: measure the height of the hill and the width

of the hill; use trig to calculate angle)

Coefficient of friction: height/half width, or tan of angle

Cohesion

Cut a small vertical slope in your sand hill. Gradually cut larger and larger vertical slopes, until your sand pile just begins to

collapse. Measure the height (HC) of the vertical cliff in cm. After the cliff collapses, measure the slope angle () (in degrees, using a

protractor) of the sand pile that develops from the collapsed cliff. Calculate the friction angle B using the following equation:

(1) φB=2∗(κ−45 °)

Calculate cohesion using the following equation:

(2) CB=

HC∗ρ∗g40

∗(1−sin φB )

cosφB

CB = bulk cohesion (Pascals)

HC = height of vertical cliff (cm)

= slope angle of the collapsed cliff (degrees)

B = friction angle (degrees)

= density (g/cm3)

g = acceleration of gravity (980 cm/sec2)

6) Jigsaw tour: show your observations to members of other groups.

7) Return to the lab classroom to complete the calculations.

Do the scaling calculation (see instructions below, and additional math in the “Introduction” handout) and find an image on Google Earth that is the correct size to correspond to your model.

Scaling instructions:

What did you just make?

a) Use the following equation to calculate the scaling ratio (z p

zm¿ of your model.

z p

zm=

ρm

ρp∗σ p

σm

Use the following values:

m : Density of your sand (from your measurement)

p : Density of typical crustal rock (2.7 g/cm3 – this is a reasonable density for granite, sandstone, shale, and limestone, and is the number that is most often used to represent continental crust in density problems)

m : the cohesion (CB ) that you measured for the sand

p : 50,000,000 Pa (= 50 MPa) (Cohesion of real rocks varies from 15 to 110 MPa, Schellart, 2000; 50 MPa is close to the cohesion of Tennessee sandstone, Weber sandstone, and Blair dolomite)

b) Multiply your scaling ratio by the length of your model to figure out how big your model would be in the real world. (Don’t forget to convert cm to km.)

c) Use Google Earth to find an image with a scale that makes sense for your model. (Some starting points are in the attached .kmz files, but you will need to zoom in or out in order to get your feature to the correct scale.)

Save a picture of the image at the correct scale, and turn that in on the course management system.

8) Examine the recordings and complete the write-up. The write-up should include:

Observations (could be a bulleted list for this lab; in the future, this will be a paper, written in well-organized and grammatically correct sentences and paragraphs)

o Geometric description of the final surface of the sandbox Refer to sketches and structure map

o Kinematic description of the development of the surface while you observed it

Refer to sketches with arrows that show the movement of various parts of the model

Discussion/interpretationso How did the final shape of the surface develop? (Relate the kinematic

observations to the geometric observations.)o What stresses seemed to cause the kinematic development of the model?

(Sketches could help your explanation.)o What scale of feature did you model? (Refer to your scaling calculations

to back up this interpretation.)o How did the edges of the model behave? Why did the edges behave in that

way? How far into the model would you need to look to get away from the edge effects?

Sandbox lab data sheet

Model conditions:Options Your conditionsType of fault (strike-slip, bend in strike-slip, thrust):Modeling material (e.g. sand or flour):Thickness of material at start of model:Length at start of model:Width at start of model:

Density data:

Variable DataMass of empty weigh boat (g):Volume of material (mL, same as cm3):Total mass of material (material + weigh boat) (g):Mass of material (g) (= total mass – empty weigh boat): = Density of sand (g/cm3) (= mass/volume)

Rheology data (follow instructions in lab handout):Variable DataAngle of repose (degrees):HC (Maximum height of vertical cliff, cm) (slope of collapsed cliff, degrees)B (friction angle, degrees)

φB=2∗(κ−45 °)CB (bulk cohesion, Pascals)

CB=

HC∗ρ∗g40

∗(1−sin φB )

cosφB

Scaling calculation:

Sketch of base of model:

Map-view sketch of model after deformation (after discussing most important characteristics with your group):

Sketched structure map (with appropriate symbols) of model after deformation:

Cross-section view sketch of model:

Common geologic map symbols

Description Map SymbolContact (identity and existence certain, location accurate)

Contact (identity and existence certain, location approximate)

Contact (identity and existence certain, location concealed)

BeddingHorizontal bedding

Vertical beddingOverturned beddingFoliation

Vertical foliationJoint

Vertical jointLineationAnticline

Syncline

Overturned anticline

Overturned syncline

Normal faultThrust faultStrike-slip faultFault with dip amount

Steep fault (where difficult to tell if normal vs reverse, but relative offset can be observed) D

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