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1. Sparse Ambient Resonance Measurements Reveal Dynamic Properties of Freestanding Rock Arches

   https://doi.org/10.1029/2020GL087239  

   Geimer, Paul R. ; Finnegan, Riley ; Moore, Jeffrey R. ( May 2020 , Geophysical Research Letters)

   The dynamic properties of freestanding rock landforms are a function of fundamental material and mechanical parameters, facilitating noninvasive vibration‐based structural assessment. Characterization of resonant frequencies, mode shapes, and damping ratios, however, can be challenging at culturally sensitive geologic features, such as rock arches, where physical access is limited. Using sparse ambient vibration measurements, we describe three resonant modes between 1 and 40 Hz for 17 natural arches in Utah spanning a range of lengths from 3–88 m. Modal polarization data are evaluated to combine field observations with 3‐D numerical models. We find outcrop‐scale elastic moduli vary from 0.8 to 8.0 GPa, correlated with diagenetic processes and identify low damping at all sites. Correlation of dense‐array measurements from one arch validates predictions of simple bending modes and fixed boundary conditions. Our results establish use of sparse ambient resonance measurements for structural assessment and monitoring of arches and similar freestanding geologic features worldwide.

    

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2. Ground Motion Amplification at Natural Rock Arches in the Colorado Plateau

   https://doi.org/10.1785/0320220017  

   Finnegan, Riley ; Moore, Jeffrey R. ; Geimer, Paul R. ; Bessette-Kirton, Erin K. ; Dzubay, Alex ( July 2022 , The Seismic Record)

   Abstract Thousands of rock arches are situated within the central Colorado Plateau—a region experiencing small- to moderate-magnitude contemporary seismicity. Recent anthropogenic activity has substantially increased the seismicity rate in some areas, raising questions about the potential for vibration damage of natural arches, many of which have high cultural value. However, predictions of the vibration response and potential for damage at a given site are limited by a lack of data describing spectral amplification of ground motion on these landforms. We analyzed 13 sandstone arches in Utah, computing site-to-reference spectral amplitude ratios from continuous ambient seismic data, and compared these to spectral ratios during earthquakes and teleseismic activity. We found peak ground velocities on arches at their dominant natural modes (in the range of 2–20 Hz) are ∼20–180 times the velocity on adjacent bedrock, due to amplification arising from slender geometry and low modal damping (0.8%–2.7%). Ambient spectral ratios are generally 1.2–2.0 times the coseismic spectral ratios. Because arches experience highly amplified ground motion, the range of earthquakes considered potentially damaging may need to be revised to include lower-magnitude events. Our results have implications for conservation management of these and other culturally valuable landforms. 

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3. Meteorological Controls on Reversible Resonance Changes in Natural Rock Arches

   https://doi.org/10.1029/2022JF006734  

   Geimer, Paul R. ; Finnegan, Riley ; Moore, Jeffrey R. ( October 2022 , Journal of Geophysical Research: Earth Surface)

   Continuous ambient seismic monitoring is becoming common for structural health assessment of geologic features. However, the ability to detect or predict permanent mechanical change associated with damage requires detailed understanding of reversible drifts in resonance attributes associated with changing meteorological conditions. Here, we analyze the response of 17 sandstone rock arches to changing meteorological conditions during extended vibration‐based monitoring, with a focus on 1 arch in Utah which was continuously monitored for 15 months. Our results show that variations in resonance are correlated with temperature on daily and yearly time scales, but that the temperature sensitivity of frequency changes are variable at different sites and resonance modes, generally ranging from 0.5% to 6% per 10°C. Numerical modeling suggests the primary mechanism governing these frequency drifts is stress stiffening, where confined thermal dilation induces bulk stress changes in the low‐stress, nonlinear elastic regime via fracture closure. Secondary mechanisms affecting resonance attributes are driven by moisture, including formation of shallow pore ice, which can generate sharp frequency changes of up to 17% per −10°C, and moisture‐induced softening. Daily lag times of several hours between temperature and frequency extrema provide constraints on the rock volumes affected by these mechanisms, indicating modal attributes are sensitive to thermally driven changes occurring in the outermost centimeters of the structure. Through improved understanding of the reversible variations of rock mass resonance, our results aid future assessment of irreversible frequency changes associated with damage, and thus structural health monitoring of fragile geologic features.

    

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4. Leveraging Vibrations and Guided Waves in a Human Skull

   https://doi.org/10.1115/IMECE2021-71315  

   Kohtanen, Eetu ; Mazzotti, Matteo ; Ruzzene, Massimo ; Erturk, Alper ( November 2021 , Proceedings of the ASME 2021 International Mechanical Engineering Congress and Exposition)

   This work is centered on high-fidelity modeling, analysis, and rigorous experiments of vibrations and guided (Lamb) waves in a human skull in two connected tracks: (1) layered modeling of the cranial bone structure (with cortical tables and diploë) and its vibration-based elastic parameter identification (and validation); (2) transcranial leaky Lamb wave characterization experiments and radiation analyses using the identified elastic parameters in a layered semi analytical finite element framework, followed by time transient simulations that consider the inner porosity as is. In the first track, non-contact vibration experiments are conducted to extract the first handful of modal frequencies in the auditory frequency regime, along with the associated damping ratios and mode shapes, of dry cranial bone segments extracted from the parietal and frontal regions of a human skull. Numerical models of the bone segments are built with a novel image reconstruction scheme that employs microcomputed tomographic scans to build a layered bone geometry with separate homogenized domains for the cortical tables and the diploë. These numerical models and the experimental modal frequencies are then used in an iterative parameter identification scheme that yields the cortical and diploic isotropic elastic moduli of each domain, whereas the corresponding densities are estimated using the total experimental mass and layer mass ratios obtained from the scans. With the identified elastic parameters, the average error between experimental and numerical modal frequencies is less than 1.5% and the modal assurance criterion values for most modes are above 0.90. Furthermore, the extracted parameters are in the range of the results reported in the literature. In the second track, the focus is placed on the subject of leaky Lamb waves, which has received growing attention as a promising alternative to conventional ultrasound techniques for transcranial transmission, especially to access the brain periphery. Experiments are conducted on the same cranial bone segment set for leaky Lamb wave excitation and radiation characterization. The degassed skull bone segments are used in submersed experiments with an ultrasonic transducer and needle hydrophone setup for radiation pressure field scanning. Elastic parameters obtained from the first track are used in guided wave dispersion simulations, and the radiation angles are accurately predicted using the aforementioned layered model in the presence of fluid loading. The dominant radiation angles are shown to correspond to guided wave modes with low attenuation and a significant out-of-plane polarization. The experimental radiation spectra are finally compared against those obtained from time transient finite element simulations that leverage geometric models reconstructed from microcomputed tomographic scans. 

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5. Ambient Vibration Modal Analysis of Natural Rock Towers and Fins

   https://doi.org/10.1785/0220210325  

   Finnegan, Riley ; Moore, Jeffrey R. ; Geimer, Paul R. ; Dzubay, Alex ; Bessette-Kirton, Erin K. ; Bodtker, Jackson ; Vollinger, Kathryn ( February 2022 , Seismological Research Letters)

   Abstract The dynamic properties of freestanding rock towers are important inputs for seismic stability and vibration hazard assessments, however data describing the natural frequencies, mode shapes, and damping ratios of these landforms remain rare. We measured the ambient vibration of 14 sandstone and conglomerate rock towers and fins in Utah, United States, using broadband seismometers and nodal geophones. Fundamental frequencies vary between 0.8 and 15 Hz—inversely with tower height—and generally exhibit subhorizontal modal vectors oriented parallel to the minimum tower width. Modal damping ratios are low across all features, between 0.6% and 2.2%. We reproduced measured modal attributes in 3D numerical eigenfrequency models for 10 of the 14 landforms, showing that the fundamental mode of these features is full-height bending akin to a cantilever. Fin-like landforms commonly have a torsional second mode whereas tower-like features have a second full-height bending mode subperpendicular to the fundamental. In line with beam theory predictions, our data confirm that fundamental frequencies scale with the ratio of a tower’s width to its squared height. Compiled data from 18 other sites support our results, and taken together, provide guidance for estimating the modal properties of rock towers required for vibration risk assessment and paleoseismic shaking intensity analysis in different settings. 

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