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 dis- tribution, 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 1D layered crustal model against em- pirical PGA attenuation relations, particularly with regard to their uncertainty, described by the standard deviation ( ). We assume that any synthetic model for a particular earth- quake should not provide a PGA scatter larger than the observed scatter for a large set of earthquakes. The 1999 Athens earthquake (Mw=5.9) is studied as a test example. In the composite method, the synthetic data display a scatter of less than ±2 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. 1 Introduction Low-frequency directivity effects are well known. For example, there is a number of seismic recordings of recent earthquakes (e.g., 1992 Landers, 1994 Northridge, 1995 Kobe, 1999 Chi-Chi), which show long-period velocity pulses caused by rupture propagation towards a station. This effect can be successfully explained by the apparent source time function varying with azimuth (Haskell, 1964).