DOI: 10.5066/p14djfsi
title: Data for analyzing precariously balanced rocks at the Peaks of Otter, Blue Ridge Mountains of Virginia, to estimate maximum past ground motions

description: This work describes the data used to characterize boulders and their pedestals at the Peaks of Otter, southwest Virginia, which are used to calculate maximum plausible earthquake magnitudes in the surrounding region as well as scaling factors for the 2023 time-independent National Seismic Hazard Model site-specific hazard curves (Petersen et al., 2024). The work presents several new methods for analyzing precariously balanced rocks, and the scale factors represent the current best-practice for validating hazard curves using precariously balanced rocks (e.g., Rood et al., 2020). The Pratt et al. (2026) paper referenced below contains a more detailed description of the project, methods, and results.
 
Observational Data
We identified likely precariously balanced rocks (PBRs) by searching online, and then explored the surrounding area for additional PBRs. In the field we photographed the PBRs from as many directions as accessible, with an emphasis on the base of the PBR/top of the underlying pedestal(s). We produced a three-dimensional model using the open-source "Meshroom" software (https://alicevision.org/#meshroom). Ground control points provide means to orient the point cloud in a global reference frame and to scale the resulting model. We also instrumented the PBRs with oriented, portable seismometers (Lunitek Geosentinal). One 3-component geophone was placed as high as practical on the PBRs. An identical geophone was placed on bedrock 8 to 15 m away. Ambient noise was recorded for 10 to 15 minutes. The PBRs were then gently pushed in roughly orthogonal directions (precise directions were determined by accessibility). Instrument response was removed and the resulting seismometer records were used to characterize the directions, periods, and damping of the rocks’ motions.
We manually classified the points in the cloud to define the PBR itself, the pedestal on which it rests, and the geometry of the basal contact. The resulting point cloud interpretations are shown as figures in the Pratt et al. (2026) paper cited below. The essential geometric measurements were the coordinates of the principal rocking points and the centers of mass. To identify likely rocking points, we projected points into a horizontal plane and mapped the perimeter of the basal contact. We compared the model's perimeter with that measured in the field by wrapping a wire around the base. We then enclosed the perimeter points with a 2D convex hull and identified rocking points based on the seismometer recordings, photographs, and measurements made in the field. Using Meshlab (https://www.meshlab.net/), we constructed enclosed meshes from the point cloud and calculated the volume and the coordinates of the center of mass. We then calculated the angle between each rocking point and the vertical and the distance from the rocking point to the center of mass.
 
Fragility Calculations
We calculated the fragility of each precariously balanced rock (PBR) using the model of Purvance et al. (2008). Given geometric data for a PBR, this model describes the probability of toppling as a function of peak ground acceleration (PGA) and the ratio of peak ground velocity (PGV) to PGA. We use the toppling model for asymmetric PBRs. This is calculated from Equations A1 and A4 in Purvance et al. (2008) with the coefficient of Equation A1 corrected as in Rood et al. (2020).
 
Hazard curve validation
We provided a preliminary hazard curve validation at each site using the method of Baker et al. (2013) as modified by Rood et al. (2020) and used in McPhillips and Pratt (2024). We specifically validated the total National Seismic Hazard Model (NSHM) conterminous U.S. 2023 time-independent model for hard-rock site conditions (Vs30 = 1500 m/s).
Our objective was to compare the median hazard curve with the constraints derived from the PBRs at each site. In order to make the comparison, we wished to calculate the annual probability that a specific PBR will topple at a specific site, termed PannualTopple. The necessary data were the fragility model and the vector hazard. The vector hazard gives the annual occurrence rate of paired peak ground velocity (PGV) and peak ground acceleration (PGA) values. We estimated the vector hazard by using the method of Abrahamson and Bhasin (2020) to estimate the distribution of PGV over a grid of PGA values, with inputs determined by querying the USGS Earthquake Hazard Toolbox (Clayton, 2023) Disaggregation tool to find mean magnitude and mean distance for earthquake sources (U.S. Geological Survey, 2025). We calculated PannualTopple by summing the product of vector hazard and the fragility model over all pairs of PGV/PGA and PGA. We then calculated the fragility curve of Rood et al. (2020) as the cumulative contribution of PGA to PannualTopple. Finally, we calculated the scaling factor, ß, for the hazard curve given the observation that the PBR has not toppled, assuming a 5% chance of survival during its lifetime. We estimated the fragility age to be in the 20,000 to 40,000 year range.
 
Regional maximum earthquake magnitudes
We estimated the maximum earthquake magnitudes that could occur in the surrounding region with toppling any of the PBRs. To do this, at each map gridpoint in the surrounding area we computed the PGA and PGV at the PBR site by querying the USGS Earthquake Hazard Toolbox (Clayton, 2023) for typical eastern U.S. crustal earthquakes (thrust, 2 km depth to top of rupture, 45 degree dip). We increased the earthquake magnitude at each map gridpoint until the resulting PGA and PGV would topple the rock with 90% probability according to the Purvance et al. (2008) model.
 
Directories
In the database, there is a zipped directory for each of the PBRs. Within each of these directories are three folders: (1) “Meshlab”; (2) “fragility plots”; and (3) “Seismic records”. These directories are described below.
Meshlab: This directory contains the three-dimensional (3D) model of the PBR. There is a “textured mesh” which is the rock model, there is a “point cloud” which are the individual x-y-z points forming the model (the point cloud), and there is a “Poisson surface”, which is an enclosed, “water-tight” surface fitted to the PBR (i.e. only the balanced rock, not the underlying bedrock). The Poisson surface is used to compute the location of the center of mass and the volume, both of which require an enclosed surface. The three components of the models can be imported into standard 3D modeling software such as “Meshlab”, “Cloud Compare”, “Agisoft”, etc. We used “Meshlab” (a free, open-source program) to compute these. Also in the directory is a GNU Octave script used to compute the contact surface plot shown in Pratt et al. (2026); GNU Octave is an open-source, free equivalent of Matlab, but the script can likely be run with Matlab with only minor modification because most of the commands are the same.
 
fragility_plots: This directory contains the information to compute the fragility matrix for the PBR, and to compare it with the USGS National Seismic Hazard Model (NSHM) hazard curve at the PBR site. The spreadsheets in these directories contain the PGA data at the PBR site, the NSHM “disaggregation” file for the PBR site, and the total probability density function of smoothed, gridded seismicity in the eastern U.S. (Petersen et al., 2024; Llenos et al., 2024). These spreadsheet data are used to compute the probability that a given event in the disaggregation file will topple the PBR. Also in this directory are the GNU Octave scripts to produce the fragility plots, with “make_PGA_fragility_curve_{rock name}_v6” being the main script that calls the other scripts (functions). The plots from this script are shown as figures in Pratt et al. (2026) and its electronic supplement. The methodology follows that of Rood et al. (2020).
Note that the scripts in this directory are closely integrated with the USGS NSHM software, in that the scripts make extensive use of the online “query” function available at the NSHM website. To run the scripts, therefore, the computer must be connected to the internet. The scripts sometimes abort if the internet connection is interrupted, so if an internet error occurs with the “query” command it can often be fixed by simply re-running the script.
 
Seismic records: This directory contains the seismic recordings of the ambient noise and the push tests. It has a “miniseed” subdirectory containing the raw seismic records we collected by placing a seismometer on top of the rock. These were 6-channel seismometers with 3-component geophones (HNE, HNN, HNZ records) and 3-component accelerometers (BNE, BNN, BNZ records). The records are in both miniseed format from the instrument, and converted to the standard “Seismic Analysis Code” (sac) format. Also included in the miniseed directory are the response files for the geophone records, and a “convert_to_disp” script for converting the geophone velocity records to displacements using the “Seismic Analysis Code” (sac) software package. The displacement records made from the geophone records have “DISP” in their names; we did not use the accelerometer records in our analyses, so they are not converted.
 
In the main directory are GNU Octave scripts for plotting the records from our “push tests” in which we pushed the rock from perpendicular directions to see its response to input perturbations; the resulting plots are shwon in Pratt et al. (2026).
The above directories contain all of the data and scripts for analyzing the PBRs using the methods described in Pratt et al. (2026), which largely follows the procedures in Baker et al. (2013) and Rood et al. (2020). The rocks are described, with locations listed, in a table in the Pratt et al. (2026) paper, which also contains photos of the PBRs.

Any use of trade, firm, or product names is for descriptive purposes only and does not imply endorsement by the U.S. Government.
 
References
Abrahamson, N. A., and S. Bhasin (2020). Conditional groundmotion model for peak ground velocity for active crustal regions, Pacific Earthquake Engineering Research Center Rept. 2020-05, 11–15, doi: 10.55461/AORD2776.
 
Baker, J. W., Abrahamson, N. A., Whitney, J. W., Board, M. P., & Hanks, T. C. (2013). Use of fragile geologic structures as indicators of unexceeded ground motions and direct constraints on probabilistic seismic hazard analysis. Bulletin of the Seismological Society of America, 103(3), 1898–1911. https://doi.org/10.1785/0120120202.


Clayton, B. S. (2023). USGS Earthquake Hazard Toolbox: nshmp-apps, U.S. Geological Survey software release, doi: 10.5066/P9UAIISF, Available at https://earthquake.usgs.gov/nshmp (last accessed February 2026).
 
Llenos, A. L., A. J. Michael, A. M. Shumway, J. L. Rubinstein, K. L. Haynie, M. P. Moschetti, J. M. Altekruse, and K. R. Milner (2024). Forecasting the Long-Term Spatial Distribution of Earthquakes for the 2023 U.S. National Seismic Hazard Model Using Gridded Seismicity, Bull. Seismol. Soc. Am. 114, 2028–2053, doi: 10.1785/0120230220.
 
McPhillips, D. and T.L. Pratt (2024). Precariously balanced rocks in northern New York and Vermont, U.S.A.: Ground-motion constraints and implications for fault sources, Bull. Seismol. Soc. Am. 114, 3171-3182, doi: 10.1785/0120240069.
 
Petersen, M.D., Shumway, A.M., Powers, P.M., Field, E.H., Moschetti, M.P., Jaiswal, K.S., Milner, K.R., Rezaeian, S., Frankel, A.D., Llenos, A.L. and Michael, A.J. (2024). The 2023 US 50-State National Seismic Hazard Model: Overview and implications. Earthquake Spectra, 40(1), 5-88, doi:10.1177/87552930231215428.
 
Pratt, T.L., Stirling, M.W., McPhillips, D., and Figueiredo, P.M. (2026; in press). Characterizing precariously balanced rocks in the eastern U.S. for estimating maximum earthquake ground motions, Bulletin of the Seismological Society of America.
 
Purvance, M.D., Anooshehpoor, A. and Brune, J.N. (2008). Freestanding block overturning fragilities: Numerical simulation and experimental validation. Earthquake Engineering & Structural Dynamics, 37(5), pp.791-808, doi:10.1002/eqe.789.
 
Rood, A. H., Rood, D. H., Stirling, M.W., Madugo, C. M., Abrahamson, N. A.,Wilcken, K. M., et al. (2020). Earthquake hazard uncertainties improved using precariously balanced rocks. AGU Advances, 1,e2020AV000182, doi:10.1029/2020AV000182.