Quantifying and Qualifying USGS ShakeMap Uncertainty

We describe newly-developed algorithms for quantifying and qualifying uncertainties associated with USGS ShakeMap ground motions. We calculate an uncertainty measure as a function of location on the map dependent on the underlying ground motion prediction equation. Uncertainty is high for larger magnitude earthquakes when finiteness is not yet constrained (and hence the rupture distance is also uncertain); uncertainty at each grid cell is decreased by the proximity of seismic stations. This grid-based "uncertainty map" is essential for probabilistically evaluating the losses that derive from hazard modeling based on ShakeMaps. However, many users may prefer a qualitative grade for the entire ShakeMap. This grading scale will allow them to quickly gauge the appropriate level of confidence when using rapidly produced ShakeMaps as part of the post-earthquake critical decision- making process. To this end, we describe a new uncertainty letter grading ("A" through "F") based on the uncertainty map. The letter grades are calculated from the mean uncertainty over the map area at grid cells that have intensities of VI or greater. This constraint focuses the calculation of uncertainty only on portions of the map with potentially damaging ground motions (inclusion of lower intensities would also make the average uncertainty dependent on map scaling.) A middle range ("C") grade corresponds to a ShakeMap for a moderate magnitude earthquake modeled with a point source. Lower grades "D" and "F" are assigned for larger events (M>6) where finite source dimensions are not constrained. The addition of ground motion observations (or observed macroseismic intensities) to constrain ground motions has the opposite effect, reducing uncertainties over data-constrained portions of the map. Higher grades ("A" and "B") correspond to ShakeMaps with constrained fault dimension and numerous stations, depending on the density of station/data coverage. Thus the letter grade changes with subsequent ShakeMap revisions as more data are added or when finite-faulting dimensions are established.