Numerically Efficient Methodology for Developing Non-Ergodic Ground-Motion Models Using Large Datasets

Session: Forthcoming Updates of the USGS NSHMs: Hawaii, Conterminous U.S. and Alaska [Poster]
Type: Poster
Date: 4/28/2020
Time: 08:00 AM
Room: Ballroom
Description: 

The field of Probabilistic Seismic Hazard Analysis (PSHA) is currently moving from the ergodic assumption, which assumes that the ground-motion model applies to all sites in a broad region, to the non-ergodic assumption, in which the coefficients in the ground-motion models are allowed to vary with spatial locations called Varying-Coefficient Models (VCM). The VCM approach uses the available dataset to include source, site and path conditions that are specific to each spatial location. To have enough local data, the recorded ground-motion data sets are expanded to include data from small magnitude earthquakes. As the small magnitude data is included for a region, the dataset can become very large (e.g. up to 100,000 recordings in California), or even larger if numerical simulations are used (e.g. up to 1,000,000 simulated ground motions). Efficient numerical methods are required to compute the hyperparameters of the VCM model and to compute the median ground motion and its epistemic uncertainty for each site/source pair. For a dataset of 100,000 ground motions, the covariance matrix involved in the predictions is of size 10^5 x 10^5, which requires about 100 GB of memory storage with double precision and large amounts of computational power to obtain its inverse and use it in forward predictions, which does not make the method practical. To avoid such large memory and computational requirements, we use Scalable Kernel Interpolation for Products (SKIP) to obtain a low-rank decomposition of the large covariance matrix by interpolation of the covariance between some reference (inducing) points and by exploiting product kernel structure. Such a low-rank representation of the covariance matrix removes the large memory requirement and brings down the computational cost of ground-motion predictions by several orders of magnitude. This numerical method makes the development of non-ergodic ground-motion models practical using a regular laptop computer.

Presenting Author: Maxime Lacour

Authors