Computing spatial correlation of ground motion intensities for ShakeMap

Modeling the spatial correlation of ground motion residuals, caused by
coherent contributions from source, path, and site, can provide valuable loss
and hazard information, as well as a more realistic depiction of ground motion
intensities. The U.S. Geological Survey (USGS) software package, ShakeMap,
utilizes a deterministic empirical approach to estimate median ground shaking
in conjunction with observed seismic data. ShakeMap-based shaking estimates
are used in concert with loss estimation algorithms to estimate fatalities and
economic losses after significant seismic events around the globe. Incorporating
the spatial correlation of ground motion residuals has been shown to improve
seismic loss estimates. In particular, Park, Bazzuro, and Baker (Applications of
Statistics and Probability in Civil Engineering, 2007) investigated computing
spatially correlated random fields of residuals. However, for large scale
ShakeMap grids, computational requirements of the method are prohibitive.
In this work, a memory efficient algorithm is developed to compute the random
fields and implemented using the ShakeMap framework. This new, iterative
parallel algorithm is based on decay properties of an associated ground motion
correlation function and is shown to significantly reduce computational
requirements associated with adding spatial variability to the ShakeMap g
round motion estimates. Further, we demonstrate and quantify the impact of
adding peak ground motion spatial variability on resulting earthquake loss
estimates.