High-frequency directivity in strong ground motion modeling methods

We are investigating two distinct strong ground motion simulation techniques as regards their high-frequency directivity: i) the composite model with a fractal subevent size distribution, based on the method of summation of empirical Green's functions, and ii) the integral model with the k-squared slip model with k-dependent rise time, based on the representation theorem. We test the simulations in a ID layered crustal model against empirical PGA attenuation relations, particularly with regard to their uncertainty, described by the standard deviation (a). We assume that any synthetic model for a particular earthquake should not provide a PGA scatter larger than the observed scatter for a large set of earthquakes. The 1999 Athens earthquake (M-w = 5.9) is studied as a test example. In the composite method, the synthetic data display a scatter of less than +/- 2 sigma around the empirical mean. The k-squared method displays a larger scatter, demonstrating strong high-frequency directivity. It is shown that the latter can be reduced by introducing a formal spectral modification.