Finding the Moho Under Milwaukee

Vince Cronin¹ and Keith Sverdrup²

¹Baylor University (Vince_Cronin@baylor.edu) and ²University of Wisconsin-Milwaukee (sverdrup@uwm.edu)

A version of this exercise has been used in an introductory physical geology course taught with no prerequisites to 1st-year college students, during discussions of how seismology helps us understand Earth's internal structure. This exercise could also be used in a general geophysics or introductory seismology course.

A student needs to know that seismic energy can propagate through Earth's interior, and can bounce (reflect) or bend (refract) as it interacts with Earth's internal layers. The students will also need to use some simple arithmetic, trigonometry and algebra, and will need to be able to informally estimate the uncertainty in their "picks" on the seismograms.

This is an activity that is usually completed in part of one class period, although there are many ways to expand the project to include homework or additional considerations. This exercise is typically used during the part of the course in which we investigate how seismology helps us understand Earth's subsurface structure. The worksheet can be completed in class or used as a homework problem.

The content goal is for students to estimate the thickness of the crust in a particular spot using seismic data. We also want to imprint some useful information, that the thickness of the continental crust in the middle of North America is in the ballpark of ~40 ± 5 km. (It is up to 50 km thick in parts of the Rockies and in northern parts of Minnesota and UP Michigan, and is as thin as 30 km thick along the Gulf Coast and in places west of the Colorado Plateau.) After working with the data in this project, students should have a better grasp of crustal-thickness maps (e.g., Braile, 1989, GSA Memoir 172, p. 310, Fig. 23B).

This project involves some simple math skills (trigonometry, simple algebra, arithmetic), interpretation of a graphic depiction of a time series (the seismograms), conceptualization of seismic waves propagating from a source and bouncing (reflecting) off the Moho. Students also work with seismic velocities that vary with direction (The near-surface direct wave has a lower velocity than the wave that travels down through the crust to reflect off the top of the mantle and return to the surface.) This exercise involves 2 spatial dimensions and time.

A second goal is to introduce students to the interpretation of phase data on a set of seismograms.

A few PowerPoint or Keynote slides are used to set the historical context of the project and to introduce the general problem (see "Presentation Files" and "Instructors Notes" below). Bouncing a rubber ball in class from differing heights above the floor, and letting students see and hear the effects of differing travel times, helps students understand that longer travel time in a reflection experiment indicates a deeper reflector. The relevant parts of YouTube videos are shown (see links under "Other Materials" below). Have the students measure the time interval between the explosion and the impact a few times while showing the videos. One of the correspondents talks about (and attempts to show) how the bridge vibrated after the explosion.

Pass out the worksheet and the raw seismograms related to the Hoan demolition experiment. Then, with a copy of the seismograms projected onto the screen, hold an initial discussion of how to interpret the graphics: note the time scale, discuss what the different wave amplitudes mean, and so on. Then cluster into groups of 2-4 students and have each group try to "pick" the first arrivals of [1] the explosion-induced direct wave, [2] the impact-induced direct wave, and [3] the corresponding reflected waves. Depending on the type of students involved (intro non-geologists, intro geology/geophysics, geophysics), the teacher can provide more or less assistance in picking the arrivals of the direct and reflected waves.

Work through the quantitative material on the worksheet. Questions about how to handle uncertainty always occur, and if the students do not admit to having questions about this the teacher should ask them how they handle uncertainties. In a nutshell, the resultant uncertainty associated with the sum or difference in two numbers are the sum of the two uncertainties. For example, (23 ± 2) + (14 ± 1) = 37 ± 3. The resultant uncertainty associated with the product of two numbers can be estimated with the sum of the fractional (or percentage) uncertainties. For example, the percentage uncertainty of 23 ± 2 is (2/23) or 8.7% and the percentage uncertainty of 14 ± 1 is (1/14) or 7.1 %, so (23 ± 2) x (14 ± 1) = 322 ± 51 because (8.7% + 7.1%) = 15.8% and 15.8% of 322 is ~51. For a nice summary of simple uncertainty calculations, refer to http://spiff.rit.edu/classes/phys273/uncert/uncert.html or http://webpages.ursinus.edu/lriley/ref/unc/unc.html, or the statistics resources on the SERC website.

When the worksheets are completed, recap the experiment and compare the results with a map of crustal thicknesses for North America (e.g., Braile, 1989, Fig. 23B). Finally, it is nice to have the students evaluate the experience as homework.

Successful completion of the worksheet resulting in a credible estimate of crustal thickness is an initial indication that the student has grasped the material. The immediate goal of having students gain an experience in measuring the thickness of the continental crust should give them a more intimate understanding of contour maps of crustal thickness.

Beyond the immediate goals, one hopes that students might be at the beginning of an understanding of other related ideas. Can students participate in a meaningful discussion of other similar experiments such as the subsurface studies that utilized the implosion of the Seattle Kingdome stadium in 2000 (e.g., http://geopubs.wr.usgs.gov/open-file/of02-123/ and http://earthquake.usgs.gov/research/groundmotion/movies/KingDome_movie.php). Can they grasp why geophysicists use reflection seismology to image the subsurface in their search for oil and gas? Can they extend the analogy to understand other forms of geo-sensing that use reflections, such as radar, sonar, lidar, laser rangefinding?

Having students write a brief retrospective assessment of the experience for homework is another way to gauge how successful the exercise has been.

Braile, L.W., 1989, Crustal structure of the continental interior, in Pakiser, L.C., and Mooney, W.D., Geophysical framework of the continental United States: Boulder, Colorado, Geological Society of America Memoir 172, p. 285-315.

Christensen, N.I., and Mooney, W.D., 1995, Seismic velocity structure and composition of the continental crust -- A global review: Journal of Geophysical Research, v. 100, no. B7, p. 9761-9788.

Dix, C.H., 1955, Seismic velocities from surface measurements: Geophysics, v. 20, p. 68-86.

Herak, M., Web resource describing Andrija Mohorovicic's work in discovering the seismic discontinuity at the base of the crust: http://www.gfz.hr/sobe-en/discontinuity.htm accessed 23 March 2010

Herak, D., and Herak, M., 2007, Andrija Mohorovicic (1857-1936) --On the occasion of the 150th anniversary of his birth: Seismological Research Letters, v. 78, no. 6, p. 671-674.

Herak, D., and Herak, M., 2010, The Kupa Valley (Croatia) Earthquake of 8 October 1909 -- 100 Years Later: Seismological Research Letters, v. 81, no. 1, p. 30-36.

Lichtenstein Consulting Engineers archives on Hoan Bridge: http://web.archive.org/web/20070311050511/www.lce.us/Hoan/

Shah, P.M., and Levin, F. K., 1973, Gross properties of time-distance curves: Geophysics, v. 38, p. 643-656.

Wisconsin Highways description of Hoan Bridge: http://www.wisconsinhighways.org/indepth/hoan_bridge.html