Class of efficient algorithms for stochastic seismic ground motions, A

Abstract

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 picture of ground motion intensities. The USGS computer model, ShakeMap, utilizes a deterministic approach to simulate median ground motions based on observed seismic data. ShakeMap based simulations are used to estimate fatalities and economic losses after a seismic event. Incorporating the spatial correlation of ground motion residuals has been shown to improve seismic loss estimation. The method of Park et al. (2007) has been investigated for computing spatially correlated random fields of residuals. However, for large scale ShakeMap models, computational requirements of the method by Park et al. (2007) are prohibitive. In this thesis, for our application-specific seismic ground motion problem, we develop and implement three new computationally efficient methods to model spatially correlated random field of residuals, in conjunction with ShakeMap. First, we develop a memory efficient algorithm to improve the approach proposed by Park et al. (2007). This new, multilevel parallel algorithm is based on decay properties of an associated ground motion correlation function. The first approach is dependent on input grids and the stochastic dimension is induced by the grid size. In the second method, we seek to reduce the dimensionality associated with the computation through global Karhunen Loeve (KL) expansions for random fields on the sphere. In the third method, we use a localized version of the KL representation using needlet approximations. We demonstrate the three approaches using extensive simulations.