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1. Dynamic Analysis of a Large Freestanding Rock Tower (Castleton Tower, Utah)

   https://doi.org/10.1785/0120190118  

   Moore, Jeffrey R. ; Geimer, Paul R. ; Finnegan, Riley ; Michel, Clotaire ( August 2019 , Bulletin of the Seismological Society of America)

   Abstract We acquired a unique ambient vibration dataset from Castleton Tower, a 120 m high bedrock monolith located near Moab, Utah, to resolve dynamic and material properties of the landform. We identified the first two resonant modes at 0.8 and 1.0 Hz, which consist of mutually perpendicular, linearly polarized horizontal ground motion at the top of the tower. Damping ratios for these modes were low at ∼1%. We successfully reproduced field data in 3D numerical eigenfrequency simulation implementing a Young’s modulus of 7 GPa, a value ∼30% lower than measured on core samples. Our analysis confirms that modal deformation at the first resonant frequencies closely resembles that of a cantilever beam. The outcome is that with basic estimates of geometry and material properties, the resonant frequencies of other freestanding rock monoliths can be estimated a priori. Such estimates are crucial to evaluate the response of rock towers to external vibration inputs. 

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2. Benchmarking Automated Rayleigh-Wave Arrival Angle Measurements for USArray Seismograms

   https://doi.org/10.1785/0220210189  

   Frazer, William D. ; Doran, Adrian K. ; Laske, Gabi ( November 2021 , Seismological Research Letters)

   Abstract Surface-wave arrival angles are an important secondary set of observables to constrain Earth’s 3D structure. These data have also been used to refine information on the alignments of horizontal seismometer components with the geographic coordinate system. In the past, particle motion has been inspected and analyzed on single three-component seismograms, one at a time. But the advent of large, dense seismic networks has made this approach tedious and impractical. Automated toolboxes are now routinely used for datasets in which station operators cannot determine the orientation of a seismometer upon deployment, such as conventional free-fall ocean bottom seismometers. In a previous paper, we demonstrated that our automated Python-based toolbox Doran–Laske-Orientation-Python compares favorably with traditional approaches to determine instrument orientations. But an open question has been whether the technique also provides individual high-quality measurements for an internally consistent dataset to be used for structural imaging. For this feasibility study, we compared long-period Rayleigh-wave arrival angles at frequencies between 10 and 25 mHz for 10 earthquakes during the first half of 2009 that were recorded at the USArray Transportable Array—a component of the EarthScope program. After vigorous data vetting, we obtained a high-quality dataset that compares favorably with an arrival angle database compiled using our traditional interactive screen approach, particularly at frequencies 20 mHz and above. On the other hand, the presence of strong Love waves may hamper the automated measurement process as currently implemented. 

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3. 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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4. Vintage factor analysis with Varimax performs statistical inference

   https://doi.org/10.1093/jrsssb/qkad029  

   Rohe, Karl ; Zeng, Muzhe ( July 2023 , Journal of the Royal Statistical Society Series B: Statistical Methodology)

   In the 1930s, Psychologists began developing Multiple-Factor Analysis to decompose multivariate data into a small number of interpretable factors without any a priori knowledge about those factors. In this form of factor analysis, the Varimax factor rotation redraws the axes through the multi-dimensional factors to make them sparse and thus make them more interpretable. Charles Spearman and many others objected to factor rotations because the factors seem to be rotationally invariant. Despite the controversy, factor rotations have remained widely popular among people analyzing data. Reversing nearly a century of statistical thinking on the topic, we show that the rotation makes the factors easier to interpret because the Varimax performs statistical inference; in particular, principal components analysis (PCA) with a Varimax rotation provides a unified spectral estimation strategy for a broad class of semi-parametric factor models, including the Stochastic Blockmodel and a natural variation of Latent Dirichlet Allocation. In addition, we show that Thurstone’s widely employed sparsity diagnostics implicitly assess a key leptokurtic condition that makes the axes statistically identifiable in these models. PCA with Varimax is fast, stable, and practical. Combined with Thurstone’s straightforward diagnostics, this vintage approach is suitable for a wide array of modern applications.

    

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5. 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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