A Revised Ground-Motion and Intensity Interpolation Scheme for ShakeMap

Wedescribe aweighted-average approach for incorporating varioustypes of data (observed peak ground motions and intensities and estimates from ground- motion prediction equations) into theShakeMap ground motion and intensity mapping framework.ThisapproachrepresentsafundamentalrevisionofourexistingShakeMap methodology. In addition, the increased availability of near-real-time macroseismic intensitydata,thedevelopmentofnewrelationshipsbetweenintensityandpeakground motions, and new relationships to directly predict intensity from earthquake source information have facilitated the inclusion of intensity measurements directly into ShakeMap computations. Our approach allows for the combination of (1) direct observations (ground-motion measurements or reported intensities), (2) observations converted from intensity to ground motion (or vice versa), and (3) estimated ground motionsandintensities frompredictionequationsornumerical models.Critically,each oftheaforementioneddatatypesmustincludeanestimateofitsuncertainties,including those caused by scaling the influence of observations to surrounding grid points and those associated with estimates given an unknown fault geometry. The ShakeMap ground-motion and intensity estimates are an uncertainty-weighted combination of these various data and estimates. A natural by-product of this interpolation process is an estimate of total uncertainty at each point on the map, which can be vital for comprehensive inventory loss calculations. We perform a number of tests to validate this new methodology and find that it produces a substantial improvement in the accuracy of ground-motion predictions over empirical prediction equations alone.