Topographic differencing: Earthquake along the Wasatch fault
After a big earthquake happens people ask, 'Where did the earthquake occur? How big was it? What type of fault was activated?' We designed an undergraduate laboratory exercise in which students learn how geologists and geodesists use topography data acquired using airborne laser scanning (a.k.a lidar – light detection and ranging) to answer these questions for a *make-believe*, but realistic earthquake scenario along the Wasatch Fault in Salt Lake City, Utah.
During a large earthquake, tectonic plates shift past each other. Rapid slippage generates seismic waves that propagate away and cause significant damage to buildings, roads, and critical infrastructure. The movement of faults at depth permanently displaces the Earth's surface in a way that depends on the magnitude of the earthquake, the amount and sense of slip, and the fault's geometry. Immediately following an earthquake, geologists play a critical role in assessing damage, measuring the geometry of the activated fault, and estimating the likelihood of an upcoming earthquake on nearby faults.
In this assignment, students pretend that they are geologists working for the United States Geological Survey (USGS) and must respond to a recent earthquake along the Wasatch Fault. They aid in the response by mapping the surface rupture and calculating the surface displacement, coseismic slip, and earthquake magnitude from high resolution lidar topographic imagery acquired before and after the earthquake.
Lidar point cloud data are a set of (x, y, z) measurements that represent the elevation and are sometimes associated with the color of the Earth's surface. The irregular-spaced individual elevation measurements within a topography dataset are often gridded into a digital elevation model (DEM) raster where the data are represented with rows and columns of pixels each with a height value. DEM's are often visualized as topographic hillshades, which mimic how the elevation would appear from above. Topographic differencing is a technique used to estimate 3D surface displacements from high-resolution topographic imagery acquired before and after an earthquake. The exercise includes pre- earthquake imagery acquired by the state of Utah in 2013-2014. The "post-earthquake" mimics the lidar imagery that would be acquired in the days to weeks following a major earthquake.
****** The earthquake in this exercise represents a hypothetical event. The 'post' event high resolution topography was synthetically displaced, in a way that simulates a possible earthquake along the Wasatch fault given mapped fault geometry and earthquake scaling laws. An event similar to the hypothetical earthquake here is possible: Since 1847 when pioneers settled in Salt Lake City, there have been over 16 earthquakes with magnitude greater than 5.5. Geologic studies show repeated large earthquakes occurred prior to European settlement in the region. Recently (March 18, 2020), the Salt Lake Valley was shaken by the M5.7 Magna earthquake. This recent reminder further motivates our exercise.******
Keywords: Earthquakes, active tectonics, structural geology, geodesy, lidar, remote sensing
Undergraduate to master-level students. The background material is designed for students who have some geologic background, for example students who are familiar with plate tectonics and the different kinds of faults. The exercise would fit well as part of a geophysics, structural geology, geomorphology, active tectonics, or geohazards course. The exercise has been used in a GIS class where some students had little geologic background. In this case, the exercise can still be successful as long as more time is dedicated to the pre-exercise lecture.
Skills and concepts that students must have mastered
Basic knowledge of plate tectonics is ideal. For example, students should know about the different types of faults, although this material can be covered in the pre-exercise lecture. Students are not expected to have used CloudCompare software before or any other specific GIS software packages. Students are expected to do arithmetic and trigonometric calculations and to perform unit transformations.
How the activity is situated in the course
There is flexibility here and it depends on which type of course is using this activity. In a structural geology or geophysics course, this exercise would fit well within the seismic hazard and/or active faulting portion of the course. The exercise is stand-alone. The introductory lecture and introduction to CloudCompare take one hour. Three hours should be adequate for students to complete the majority of the lab. They may need to complete the write-up as a homework assignment.
Content/concepts goals for this activity
- Visualize how earthquakes permanently deform landscapes: Surface rupturing earthquakes expose fault scarps at the Earth's surface. In this exercise, students will map a fault scarp from a topographic hillshade.
- Describe the relationship between fault slip, surface displacement, and earthquake magnitude: Ideally, students will be able to visualize that earthquakes cause permanent movement of the Earth's surface and understand that the amount of fault slip at depth controls the surface displacement.
- Interpret quantitative geospatial datasets: After students have made their measurements of surface displacement, they will plot and then interpret their results. To determine which type of fault was activated students must consider the noise in their measurements.
- Learn CloudCompare skills- load data, scissors, point picker, fine point cloud alignment. Students will gain practice working with geospatial and specifically point cloud datasets.
Higher order thinking skills goals for this activity
This exercise requires students to plot geospatial data on a topographic hillshade map. To determine the type of fault activated, they must determine how noise impacts their measurements of surface displacement. Estimating the amount of fault slip requires that students can visualize and plot their measurements on both a map and a 1D profile.
Other skills goals for this activity
Team work and writing-- We found that students like to work individually to make the displacement measurements and practice using CloudCompare. This means that students get maximum practice using these tools. They benefited from discussing the results in small groups and then as a class. Students are asked to write a report where they describe and synthesize their results.
Description and Teaching Materials
The material includes a pre-exercise lecture about Basin and Range tectonics, seismic hazard, and relevant material for completing the assignment. We include PowerPoint slides that guide students through the steps of making 3D displacement measurements using CloudCompare. This material is also available in this YouTube Video. Each tile below contains the pre and 'post' earthquake topography in .laz files for a different portion of the fault. Students will want to use at least one of the tiles to make their measurements. The student handout contains a topographic hillshade where students map the Wasatch Fault, a table to record displacement measurements, and the background material required to estimate the earthquake magnitude. The assignment asks students to answer eight questions about aspects of the laboratory assignment and seismic hazard in Salt Lake City.
(1) Activity Lecture (PowerPoint 2007 (.pptx) 30.2MB Apr22 20)
(2) Student Handout for Differencing Exercise (Microsoft Word 2007 (.docx) 1.4MB Apr22 20)
(3) Teaching Notes (Microsoft Word 2007 (.docx) 378kB Apr22 20)
(4) High resolution topography for the exercise: Download any of the tiles. Use the 'small tile' for slower internet connections.
Teaching Notes and Tips
Computer Software Prep:
CloudCompare software is required. The software is open source and works on Mac, Windows, and Linux OS. We recommend downloading the most recent stable version of the software (i.e., not beta) available for your operating system. For Mac, open the dmg file and then click the Cloud Compare icon. A warning message saying that the application was downloaded from the internet may open. It is okay to open Cloud Compare. If you still cannot open CloudCompare, you may have to go to System Preferences-> Security and Privacy-> Allow apps downloaded from: App store and identified developers. These instructions may change for future Mac OS. In this case, the solution is likely easily searchable on Google. For Windows, the downloaded and run the exe file. The rest of the exercise is best done with paper and pencil. Students need to make a few arithmetic calculations (adding, multiplication, trigonometry). These calculations can be performed with a calculator, cell-phone, internet, etc.
Places where students often have difficulty:
- Drawing boxes on CloudCompare: ICP displacement measurements are typically better for larger box sizes. As long as the boxes do not cross the fault, there is really no limit to the box size. It is very important that the reference window has a buffer on all sides relative to the compare window.
- Color for CloudCompare measurements: The pre- earthquake dataset has RGB color, and the post-earthquake dataset does not. This can make it easier to distinguish between the two datasets when looking over a student's shoulder.
- If a CloudCompare measurement does not look good or generates an error, it is best if the student ignores that individual measurement and makes a new measurement elsewhere.
- In CloudCompare, there is no 'back' or 'undo' button. If you are looking for these buttons, it can be easier to restart CloudCompare and reload the data.
- For many students, the most challenging part of the exercise is determining the type of fault activated in the earthquake (e.g., normal, reverse, strike-slip). Overall, the measurements that the students make should be consistent with a single fault type, but in detail each measurement has noise. Typically, the vertical displacements have less noise than the horizontal displacements. Some students struggle with the fact that their data contain noise, and asking them to think about the sources of noise can shift their perspective about how to interpret the measurements. Also, a suggestion to emphasize the vertical displacements helps many students get the correct answer and then they ponder why there is more noise in the horizontal displacements.
- We asked students to plot their measurements on the board. This helped to increase the sample size in the case that a student has a particularly noisy set of measurements. This also facilitated conversation between students as they decided how to collectively plot their measurements.
- Often, the vertical motion of dip-slip faults is emphasized. But dip-slip faults also produce significant horizontal motion in the direction perpendicular to the fault strike. So the students should expect some horizontal motion in dip-slip faults when considering which type of fault was activated.
- Due to the logarithmic scale of earthquake magnitude, students should get approximately the correct magnitude even with some minor errors in the estimated fault geometry and the amount of slip. However, their estimated magnitude will be very wrong if they do unit conversions incorrectly (i.e., confuse meters with kilometers).
The exercise contains eight questions that the students should answer as they complete the activity. The questions ask students to map the active fault from the topographic hillshade, record their displacement measurements, estimate the amount of fault slip based on the displacement measurements, calculate the earthquake magnitude, state error sources, and reflect on earthquake hazard and preparation. Students can also be assessed based on discussion with individual students, student groups, or the entire class.
References and Resources
Calculating 3D displacements from the Iterative Closest Point Algorithm:
Nissen, E., Krishnan, A.K., Arrowsmith, J.R., and Saripalli, S., 2012, Three-dimensional surface displacements and rotations from differencing pre- and post-earthquake LiDAR point clouds: Geophysical Research Letters, v. 39, doi:10.1029/2012GL052460.
Scott, C.P., Arrowsmith, J.R., Nissen, E., Lajoie, L., Maruyama, T., and Chiba, T., 2018, The M 7 2016 Kumamoto, Japan, Earthquake: 3-D Deformation Along the Fault and Within the Damage Zone Constrained From Differential Lidar Topography: Journal of Geophysical Research: Solid Earth, doi:10.1029/2018JB015581.