Utah’s red rock towers shake and shimmy to a predictable beat

The striking red rock towers and arch formations peppered throughout Southern Utah and the Colorado Plateau are known to shake and sway in response to earthquakes, high winds, thermal stresses, and other sources of vibration, such as those from helicopters, trains, passing vehicles, and blasts. Being able to assess the stability of these structures, and detect any damage from vibrations, can be challenging. That's why geologists have been measuring the natural frequencies of these towers for several years now.

Led by University of Utah geologist Jeff Moore, the group of geologists maintains an entire webpage devoted to its seismic recordings of the natural resonances (vibrations) that come out of the Utah red rock towers and arches. The geologists have now used that data set to develop a theory that can predict the frequencies at which these formations vibrate and deform, described in a recent paper published in the journal Seismological Research Letters.

Overcoming hurdles

As we've reported previously, understanding those dynamics is crucial to being able to predict how the structures will respond in the event of an earthquake or similar disruption. Yet, there haven't been many ongoing efforts to do so over the years, despite a great deal of research on manmade civil structures. One of the major challenges has been gaining the access necessary to make those vibrational measurements in the first place. Either the formations are restricted (the better to preserve them for posterity), or it's simply too difficult to place sensors in hard-to-reach spots on the formations.

So Moore and his collaborators have relied upon a team of experienced rock climbers, including expert climber Kathryn Vollinger, to climb the structures, place seismometers on the top, and then wait quietly for several hours while those instruments collected data. Co-author Riley Finnegan, a grad student at the University of Utah, and several other team members visited three of the sites Vollinger had climbed and used drones to map the structures for 3D models. "I personally could barely get to the base of one of the towers, let alone start thinking about carrying our equipment to the base and then climb up with it all in tow," he said.

Back in 2019, Moore, Finnegan, and the rest of their team made the first detailed seismic measurements of a pillar-shaped sandstone formation in Utah known as Castleton Tower. They found that the structure vibrates at two key resonant frequencies: 0.8 and 1.0 Hz, respectively. That makes the formation vulnerable to strong-magnitude earthquakes, which are fortunately quite rare in the region. Smaller quakes—or minor vibrations from traffic, construction machinery, or other environmental factors—are unlikely to trigger the natural resonances of the tower.

This time around, the team was working with a much-expanded data set, incorporating rock towers with varying heights and geometries. The researchers measured the ambient vibrations of 14 rock towers (defined as being slender in both horizontal dimensions) and fins (defined as being symmetrically long in one direction) in Utah, located on the traditional lands of the Eastern Shoshone, Hopi, Navajo, Southern Paiute, Ute, and Zuni tribes. (A student from Whitehorse High School in Montezuma Creek near Valley of the Gods, Weston Manygoat, assisted them in their field work.)

With the help of their intrepid rock climbers, the geologists were able to place seismometers directly on top of all but two of these sites: Red Narrows and Secret Spire. They were also able to source other data on the natural frequencies and geometries of rock towers, pillars, and pinnacles from previous studies and reports, including formations in Arizona, the Negev Desert of Israel, and the Vercors Massif in France, as well as formations in Utah. Then, the researchers compiled all the data collected over several years into one large data set for analysis.

Encouraging results

The results: the fundamental frequencies of the rock towers fall between 1 Hz and 15 Hz. Larger towers have lower fundamental frequencies, swaying back and forth as they vibrate in most cases. Some towers with higher fundamental frequencies, however, twist around the central axis.

The researchers had theorized that the fundamental frequency at which a beam vibrates would be proportional to its width divided by its height squared. This turned out largely to be the case. Thus, it should be possible to accurately estimate the fundamental frequency of a given formation based on measurements of its geometry alone, in addition to its material properties. (Most of the structures in the study consisted primarily of sandstone.) Their model's frequency predictions differed from the data by just 4 percent, while the predicted angle of the motion of the towers differed by about 14 degrees.

"Maybe I'm overly excited and surprised about this, but I've made enough models of rock arches in some of our other work that frustratingly didn't produce strong matches to the data, so it was refreshing to me to be able to predict tower models given the geometry" said Finnegan. He added:

This ability to make predictions about a tower's fundamental frequency using just the tower's width, height, and material properties is powerful because that means someone doesn't necessarily have to climb a 300-foot (100 m) tower with a seismometer to get this information. And knowing this information is important for any assessments related to the seismic stability of a tower or potential vibration damage.

DOI: Seismological Research Letters, 2022. 10.1785/0220210325 (About DOIs).