There are many tectonically active regions on earth with little or no recorded ground motions. The Eastern United States is a typical example of regions with active faults, but with low to medium seismicity that has prevented sufficient ground motion recordings. Because of this, it is necessary to use synthetic ground motion methods in order to estimate the earthquake hazard a region might have.

Ground motion prediction equations for spectral acceleration typically have geometric attenuation proportional to the inverse of distance away from the fault. Earthquakes simulated with one-dimensional layered earth models have larger geometric attenuation than the observed ground motion recordings. We show that as incident angles of rays increase at welded boundaries between homogeneous flat layers, the transmitted rays decrease in amplitude dramatically. As the receiver distance increases away from the source, the angle of incidence of up-going rays increases, producing negligible transmitted ray amplitude, thus increasing the geometrical attenuation.

To work around this problem we propose a model in which we separate wave propagation for low and high frequencies at a crossover frequency, typically 1Hz.

The high-frequency portion of strong ground motion is computed with a homogeneous half-space and amplified with the available and more complex one- or three-dimensional crustal models using the quarter wavelength method. We also make use of seismic coda energy density observations as scattering impulse response functions. We incorporate scattering impulse response functions into our Green's functions by convolving the high-frequency homogeneous half-space Green's functions with normalized synthetic scatterograms to reproduce scattering physical effects in recorded seismograms. This method was validated against ground motion for earthquakes recorded in California and Japan, yielding results that capture the duration and spectral response of strong ground motion.