DOI: 10.5066/p13sxgwx
title: Data for analyzing Precariously Balanced Rocks (PBRs) in the northeastern U.S. to estimate maximum post-glacial ground motions

description: This work describes the data used to characterize boulders and their pedestals in the northeastern U.S. (Maine, New Hampshire, Massachusetts), 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 represents the current best-practice for validating hazard curves using precariously balanced rocks (e.g., Rood et al., 2020; McPhillips and Pratt, 2024). These data support the paper by Stirling and Pratt (2026) referenced below. A detailed description of the methodology is contained in the Pratt et al. (2026) paper referenced below.

Observational Data
We identified likely precariously balanced rocks (PBRs) primarily using a series of books by hobbyists (Butler and Butler, 2018; Butler and Dunn, 2016). 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 practicable on the PBRs. An identical geophone was placed on bedrock 8 to 15 m away for some rocks (but ommitted for other rocks). 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 in a figures in the Stirling and Pratt (2026) paper cited below. The essential geometric measurements were the coordinates of the principal rocking points and the center 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, "water-tight" 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. 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 took the lifetime to be equivalent to the age of the final retreat of the Laurentide Ice Sheet from the study area (Barth et al., 2019).
 
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. The resulting map is shown in Stirling and Pratt (2026).
 
 
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. The Lynn Woods directory does not contain seismic records because the instrument did not function properly when testing that rock, so there are no records available.

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 included in the Meshlab directory is a map of the point cloud from a few tens of cm above to a few tens of cm below the base of the PBR, with the distance dependent on the slope and shape of the contact surface. This “contact surface plot” can be used to measure the width of the base of the PBR, which is the key parameter for determining fragility, and the calculations for determining this are shown in a spreadsheet in the directory. Also in the directory is a GNU Octave script used to compute the contact surface plot; 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 output are the figures contained in Stirling and Pratt (2026). The details of this analysis are described in Pratt et al. (2026). 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 has a “miniseed” subdirectory containing the 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. These push tests can be used as input responses to calibrate computer models of the rock subjected to ground motions.
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 Stirling and Pratt (2026), 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
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