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Rapid estimation of earthquake ground shaking and proper accounting of associated uncertainties in such estimates when conditioned on strong-motion station data or macroseismic intensity observations are crucial for downstream applications such as ground failure and loss estimation. The U.S. Geological Survey ShakeMap system is called upon to fulfill this objective in light of increased near-real-time access to strong-motion records from around the world. Although the station data provide a direct constraint on shaking estimates at specific locations, these data also heavily influence the uncertainty quantification at other locations. This investigation demonstrates methods to partition the within- (phi) and between-event (tau) uncertainty estimates under the observational constraints, especially when between-event uncertainties are heteroscedastic. The procedure allows the end users of ShakeMap to create separate between- and within-event realizations of ground-motion fields for downstream loss modeling applications in a manner that preserves the structure of the underlying random spatial processes.

We analyzed the regional dependence of ground motion to intensity conversion equations and derived a new global relationship to improve ground motion and intensity estimates for earthquake hazard applications, including those related to the ShakeMap system. For this purpose, we merged several databases collected by other authors in different geographical regions to highlight any systematic regional effects in the relationship between macroseismic intensities and both peak ground velocity and peak ground acceleration. Our database contains macroseismic intensities derived from expert assignments or from the “Did You Feel It?” database, paired with peak ground motions (PGM) from seismic stations. We constrain our intensity–ground‐motion pairs to those with a maximum 2 km separation. For each region, we derived invertible relationships between intensities and ground motion using an orthogonal regression. We also derived a global relationship to quantify the regional differences. We investigated the dependence of intensity on predictor variables such as PGM, magnitude, and hypocentral distance. Our analyses indicate that PGM is the most robust predictor variable of intensity. Within one standard deviation, our regional and global results are in agreement with the relations of Worden et al. (2012) for California, Faenza and Michelini (2010) for Italy, Tselentis and Danciu (2008) for Greece, and Atkinson and Kaka (2007) for central–eastern United States. The earthquakes in the study ranged in magnitude from 2.5 to 7.3, and the distances ranged from less than a kilometer to about 200 km from the epicenter. Online Material: Table summarizing published relationships and figures showing the relationship between peak ground acceleration and intensity.

Equations that predict intensity as a function of magnitude and distance are useful tools for hazard and risk assessment, and in interpretation of both contemporary and historical earthquake information. The intensity prediction equations of Atkinson and Wald (2007; hereafter AW07) have been remarkably successful in describing the level and intensity of motions reported under the “Did You Feel It?” (DYFI) program over the last several years. Examination of the performance of AW07 for North American earthquakes, evaluated using an extensive compiled database of DYFI observations from 2000 to 2013, suggests that there is little statistical basis for revising these equations. However, a problem with the AW07 equations is that they predict unrealistically large median intensities for large events ( M >6) at close distances. In this study, we revise AW07 to improve the intensity scaling at large magnitudes and close distances, by reconciling intensity equations with ground‐motion prediction equations.

We develop globally applicable macroseismic intensity prediction equations (IPEs) for earthquakes of moment magnitude M W 5.0–7.9 and intensities of degree II and greater for distances less than 300 km for active crustal regions. The IPEs are developed for two distance metrics: closest distance to rupture (R rup) and hypocentral distance (R hyp). The key objective for developing the model based on hypocentral distance—in addition to more rigorous and standard measure R rup—is to provide an IPE which can be used in near real-time earthquake response systems for earthquakes anywhere in the world, where information regarding the rupture dimensions of a fault may not be known in the immediate aftermath of the event. We observe that our models, particularly the model for the R rup distance metric, generally have low median residuals with magnitude and distance. In particular, we address whether the direct use of IPEs leads to a reduction in overall uncertainties when compared with methods which use a combination of ground-motion prediction equations and ground motion to intensity conversion equations. Finally, using topographic gradient as a proxy and median model predictions, we derive intensity-based site amplification factors. These factors lead to a small reduction of residuals at shallow gradients at strong shaking levels. However, the overall effect on total median residuals is relatively small. This is in part due to the observation that the median site condition for intensity observations used to develop these IPEs is approximately near the National Earthquake Hazard Reduction Program CD site-class boundary.