Estimating two-dimensional static stabilities and geomorphic settings of precariously balanced rocks from unconstrained digital photographs

The need to accurately document the spatiotemporal distribution of earthquakegenerated strong ground motions is essential for evaluating the seismic vulnerability of sites of critical infrastructure. Understanding the threshold for maximum earthquakeinduced ground motions at such sites provides valuable information to seismologists, earthquake engineers, local agencies, and policymakers when determining ground motion hazards of seismically sensitive infrastructures. In this context, fragile geologic features such as precariously balanced rocks (PBRs) serve as negative evidence for earthquake-induced ground motions and provide important physical constraints on the upper limits of ground motions. The three-dimensional (3D) shape of a PBR is a critical factor in determining its static stability and thus susceptibility to toppling during strong ground shaking events. Furthermore, the geomorphic settings of PBRs provide important controls on PBR exhumation histories that are interpreted from surface exposure dating methods. In this paper, we present PBRslenderness, a MATLAB-based program that evaluates the two-dimensional (2D) static stabilities of PBRs from unconstrained digital photographs. The program's graphical user interface allows users to interactively digitize a PBR and calculates the 2D geometric parameters that defi ne its static stability. A reproducibility study showed that our 2D calculations compare well against their counterparts that were computed in 3D (R²=0.77-0.98 for 22 samples). A sensitivity study for single-user and multiuser digitization routines further confi rmed the reproducibility of PBRslenderness estimates (coeffi cients of variation c_v=4.3%-6.5% for 100 runs; R²=0.87-0.99 for 20 PBRs). We used PBRslenderness to analyze 261 PBRs in a low-seismicity setting to investigate the local geomorphic controls on PBR stability and preservation. PBRslenderness showed that a PBR's shape strongly controls its static stability and that there is no relationship between a PBR's stability and its geomorphic location in a drainage basin. However, the geomorphic settings of PBRs control their preservation potential by restricting their formation to hillslope gradients <40^o and the upper reaches of drainage basins. Such examples of our program's utility have led to its use in archival efforts of PBRs in southern California and Nevada, USA.