DeformLab (1)
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University of Massachusetts, Amherst *
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101
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Geology
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Jan 9, 2024
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14
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Chapter 7 How does the Earth deform? About this lab: How could pulling a brick with a measuring tape and rubber bands have anything to do with earthquakes? There are no rubber bands in the Earth, but all rocks (including Earth’s crust!) are elastic. The brick and sandpaper models friction and elastic rebound (release) as an example of the interaction between tectonic plates before and after an earthquake. Earthquakes can be viewed through the lens of some basic physics concepts; such as sliding and static friction, forms of energy and conversion from one form to another, and the elastic properties of materials. Learning Objectives: After this lab you will be able to: e Relate potential energy to kinetic energy; e Understand earthquakes through plotting data; e Relate experimental analogs to the real-world features they represent. 7.1 Thrust Faults and Reverse Faulting Subduction zones form when two tectonic plates of different densities converge. The force of the two plates pushing against one another results in the denser plate (usually the oceanic crust), sinking or subducting below the less dense one (usually continental crust). The boundary around the Pacific Ocean is known as the “Ring of Fire” because of the volcanic arcs associated with the subduction of the Pacific Plate underneath surrounding tectonic plates. During subduction, a wedge of sediment accumulates as the overriding plate (less dense) “scrapes” the sediments off the top of the more dense subducting plate. This wedge of sediment is called an accretionary wedge. Over time this wedge of sediment thickens and eventually forms faults to accommodate the compression and shortening of the sediments as subduction continues. Sandbox Experiment We have a classroom setup of a sand box with a moving wall. The box is filled with sand with horizontal “marker” layers of different colored sand to help observe details of the deformation. Laura Fattaruso, Michele Cooke, and Mario Del Costello designed this lab.
Geology 101/131 October 22, 2023 - R = -.‘ b k : et I e ", - e Ry I (a) The ring of fire around the Pacific Ocean. P Continental Accretionary N\ ~=77 Lithosphere N (b) An accretionary wedge above subduction zone. Figure 7.2: Geologic processes simulated by Sand Box model. The sides of the box are made of plexiglass to allow us to see the internal deformation in the sand. A rotating crank controls the moving wall. This moving wall represents the continental crust that serves as a backstop for the wedge. While in reality the oceanic plate moves and carries sediment towards the continental plate, the sandbox setup still replicates the relative motion of the bottom and the backstop wall along which sediment accumulates, providing a good approximation of accretionary wedge dynamics. Pre-Experiment Questions: 1. What type of plate boundary does this represent? (circle one) Convergent Divergent Transform 2. What type of faults do you expect to see form in the experiment? (circle one) Reverse Normal Strike-Slip 3. If you had to build a house somewhere in this sandbox, where would you put it and why?
Geology 101/131 October 22, 2023 Experiment and Data Collection As the TA turns the crank, watch to see if any faults form. At each 10-crank interval, write down the moving wall displacement, wedge thickness measurements, and fault “dip” in Table 7.2 on page 3. Turns of | Moving Max wedge | Number of | Dip of | Dip of 27d crank (#) | wall dis- | thickness faults (#) | youngest youngest placement | (c¢m) fault (°) fault (°) (cm) 10 20 30 40 50 60 70 80 Table 7.2: Data table for sand box experiment. Post-Experiment Questions 4. When you have completed the experiment, discuss where you would choose to build a house after seeing what happened. How does this differ from your original answer? What happened to the houses you set up before the experiment?
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Geology 101/131 October 22, 2023 In the above space, draw a cross-section of the fault wedge after 30 turns (use labels, colors, shading as needed; be sure to label E-W). In the space above, draw a cross-section of the wedge at 60 turns (use labels, colors, shading as needed; be sure to label E-W).
Geology 101/131 October 22, 2023 In the above space, draw a final cross-section at 80 turns (use labels, colors, shading as needed, label E-W). Figure 7.3 5. Where did new faults form in the experiment as we continued to turn the crank? What was consistent about new faults and what changed? 6. What was the most common dip direction for faults? What type of faults are these? 7. What happened to the dip of older faults after new ones formed? How did they change and 5
Geology 101/131 October 22, 2023 what do you think caused that change? 8. Sketch a simple graph showing the number of turns of the crank on the x-axis and number of faults on the y-axis. What relationship do you see? If you were to move somewhere with lots of existing faults, what does that tell you about the area?
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Geology 101/131 October 22, 2023 7.2 Earthquakes and Elastic Rebound Theory Vocabulary Fault A break or fracture in Earth’s crust along which movement has taken place. Friction Mechanical resistance to motion of two objects or bodies in contact. Stick-slip movement A jerky, sliding movement along a fault surface. It occurs when the friction between the two sides of a fault keeps them from sliding smoothly. Stress is built up over time and then suddenly released as an earthquake. Elastic rebound theory Rocks can rupture, or break, in a sudden movement that releases accu- mulated energy, and then snap back almost to their original shape. Variable In a scientific experiment, the one element that is altered to test the effect on the rest of the system. Background The cause of ground shaking during an earthquake is slip (movement) along faults. Until 1891 most scholars believed that shaking during earthquakes caused the ground to crack and form faults. In that year a large earthquake in Japan formed a scarp, or steep slope, up to 6 m high and 70 to 80 km long, offsetting, or separating, many physical features as much as 5.5 m in both horizontal and vertical directions. Japanese geologist Bunjiro Koto claimed that offset (amount of movement) along the fault had caused the earthquake, not the other way round. His hypothesis was a reversal of the common thinking at the time. Following the 1906 San Francisco earthquake (Figure 7.5), Harry Fielding Reid proposed a radical new theory for what causes earthquakes. Reid’s Elastic Rebound theory suggests that stress (force/area) is constantly building up in the region where an earthquake is going to occur. When that stress reaches the frictional strength of the fault, the fault slips, causing an earthquake and relieving the stress. The stress slowly builds up again until another earthquake occurs. The process repeats over and over, as part of an earthquake cycle. During strain accumulation, the slow, steady motion of rocks on each side of a fault deforms the crust in an elastic manner, similar to the elastic deformation of a stretched rubber band or a squeezed rubber ball. Analyzing the amount of time between earthquakes (recurrence), we find that reality is a bit more complicated than this. Earthquakes occur on fault segments, so only a portion of a fault will slip in a given earthquake. Based on material from Jefl Barker, Binghamton University and Dorothy Merritts, Franklin & Marshall College, Dorothy.merrittsfandm.edu.
Geology 101/131 October 22, 2023 Earthquakes and Elastic Rebound The apparatus shown in Figure 7.4 is designed to illustrate some of these physical principles. The force is applied by pulling on the rubber band attached to the brick. We can assume that the force applied is proportional to the length of the rubber band. Stress is force divided by the area of the fault (or brick in this case). Since the brick’s bottom surface area is constant, the length of the rubber band is also proportional to the stress applied to the fault. The basic earthquake machine (Figure 7.4) consists of a heavy object that is dragged steadily with a rubber band, simulating elasticity. We can simulate the earthquake cycle with a physical model that consists of some tape measures, a rubber band, a bricks attached to the rubber band, and a board covered with sand paper. Pulling the rubber band is analogous to the steady motion of moving plates at Earth’s surface. The rubber band is an analog for elastic crust that can stretch before breaking. The bricks against the sandpaper are analogs for the blocks of crust on each side of a fault plane, or plate boundary. As you slowly and steadily pull the band, the elastic tightens, increasing the stored elastic strain energy in the rubber band. Eventually, the brick will slip, sometimes in a sudden large jump, but other times in small steps. These “jumps and slips” are analogous to large and small earthquakes. The next slip occurs after sufficient strain has once again accumulated to overcome the frictional resistance between the brick and sandpaper board. The frictional strength of the fault depends on the roughness of the sandpaper, on the area of the brick, and on the force pushing the brick against the board. In this case, force is simply the weight of the brick. Note that there are two types of friction in this experiment; static friction and dynamic friction. When at rest, the strength of the fault is determined by the static friction. However, as soon as the brick starts moving, the fault strength (or the stress that stops the motion) is determined by the dynamic friction. Static friction is always greater than dynamic friction; the static friction is higher when the brick is at rest than when it is moving. Finally, the displacement of the fault is simply the position of the brick measured on the tape measure along side the board. The slip during a particular “earthquake” is simply the difference in displacement before and after the earthquake. Hypothesis testing We can explore several hypotheses about how earthquakes behave with the model. Think about these hypotheses as you perform and observe earthquake machine experiment. Hypothesis 1 Earthquakes are periodic (in other words, all of the same amount of slip, and all separated by the same amount of time). There is some evidence for this, particularly among very small earthquakes on creeping faults. Hypothesis 2 Earthquakes are “time-predictable” (this means that the larger the slip in the last earthquake, the longer the wait until the next one.) This idea was formulated in the 1980s by Shimazaki and Nakata in Japan and has been widely used. Hypothesis 3 Earthquakes occur randomly in time and and have randomly varying size. (This “Poisson” hypothesis is also widely used, particularly when little information about a fault and its past earthquakes is available).
Geology 101/131 October 22, 2023 Strain high 0 X EQ Slip E’_ Y EQ— Stress Drop Y Figure 7.4: Demonstration of the “earthquake machine” and plotting the movement with respect to time. Scientists often say “distance is a function of time”. Experimental Procedure During each experiment, you will note the amount of displacement each time the brick moves. You will be creating a plot showing the displacement versus “time” for each experiment. Here are the steps you will be following to acquire, analyze, and interpret the data you gather. e Measure displacement, calculate differences, and record this information in table 7.3 on page 11. e Plot a graph of the tape measure difference along the x-axis and the brick difference along the y-axis. We are using the tape measure difference as the “time” between events. One of my favorite equations is distance = rate X time. We measure the distance the tape measure moves between “earthquakes”. Since we are pulling at a near-constant rate, the distance is directly proportional to the time. Another example is driving on a highway at a constant rate of 60 mph. Driving 20 miles will take you 20 minutes. So, you can relate distance to time in this case. This is similar to what we are doing with the earthquake machine and the brick. e Draw conclusions about the strength of the fault and the cycles of earthquake recurrence.
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Geology 101/131 October 22, 2023 = :flzflzflfi After earthquake Before earthquake T A A /‘\ This picture, taken near Bolinas in Marin County by G.K. Gilbert, shows a fence that was offset about 8.5 feet along the trace of the fault (from Steinbrugge Collection of the UC Berkeley Earthquake Engineering Research Center Pacific Plate North American Plate San Andreas fault Figure 7.5: Cartoon of elastic rebound on the right and, on the left, a photo taken near Bolinas in Marin County by G. K. Gilbert, shows a fence that was offset about 8.5 feet along the trace of the fault (from Steinbrugge Collection of the UC Berkeley Earthquake Engineering Research Center). Start at the bottom of the right figure. A straight fence is built across a fault, such as the San Andreas fault. As the Pacific plate moves northwest, it gradually distorts the fence. Just before an earthquake, the fence has an “S” shape. When the earthquake occurs the distortion is released and the two parts of the fence are again straight; but now there is an offset. This diagram greatly exaggerates the distortion. Actually, the distortion is spread over many miles and can only be seen with precise instrumentation. 10
Geology 101/131 October 22, 2023 Name: TA: Earthquake Model Experiment Table 7.3: Data table for the Earthquake Machine experiment collect data here Brick Start (cm) | Brick End (cm) | Tape Start (cm) | Tape End (cm) = i) Z o Ol | O TY =] W DN — Allow approximately 20 “earthquakes” to occur, so that you are sure you are not observing an anomalous event. If you run out of room on the sandpaper board, reset your brick and continue. 1. How would you describe the movement of the brick? How does this relate to stick-slip behavior? 2. On average, how much does the brick slip per “earthquake” event? 3. Is all of the force in the rubber band relieved? 4. Does the brick move the same amount in each cycle of slip? 11
Geology 101/131 October 22, 2023 5. In this model, what does the brick represent? 6. What does the rubber band represent? 7. What does the sandpaper represent? 8. What does the movement of the brick represent? 9. What kind of energy does the rubber band have? 10. What kind of energy does the brick have before the “fault” ruptures? 11. Describe the cycle of energy changes that occur in the model. 12. What parts of the model have balanced forces? 12
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Geology 101/131 October 22, 2023 Data Analysis and Plotting 13. Using a program such as Microsoft Excel or LibreOffice Calc, input the data you collected in Table 7.3 into a new sheet. In two new columns, calculate how far the brick moved during each event and how far the tape was pulled to cause the event. 14. In this model, we use the how far the tape moved as a proxy for time. Therefore, we can get the fault slip rate using our favorite equation: distance = rate x time. Calculate the short-term average slip rate for each seismic cycle (a.k.a. earthquake event). 15. Next, create a line plot showing the movement of the brick over time. 16. In Excel or LibreOffice Calc, calculate the long-term average slip rate for the full set of earthquakes in the experiment. Do you think this average slip rate is representative of all the “earthquakes” you saw during the experiment? Why or why not? (2 to 3 sentences) 13
Geology 101/131 October 22, 2023 Connecting The Experiments The brick model portion of this lab displayed stick-slip behavior along a discrete fault. The sandbox model showed both local, discrete faulting as well as folding. Over long time scales, fault motion can be approximated as continuous, even though most of the surface displacement we see is achieved by discrete earthquake events. 17. Which model corresponds to long time scales? Which model corresponds to discrete events? 18. Compare the deformation behavior between the two models. Where might you expect in the sandbox model to see the stick-slip behavior that was displayed in the brick experiment? Explain below and then draw/label on Figure 7.3. 19. How would you link the two different parts of the lab into one synthesis of earthquakes and fault dynamics? In other words, what parts of the two models are analogous with each other and which are not? 14