Modeling Geometrical Spreading and the Relative Amplitudes of Vertical and Horizontal High-Frequency Ground Motions in Eastern North America

Horizontally layered velocity models were used with point-source and finite-fault sources to investigate geometrical spreading and the relative amplitudes of vertical and horizontal ground acceleration within 120 km of the source. Full-wave-field simulations were done for a range of focal depths and for strike-slip and reverse focal mechanisms. The attenuation of the geometric mean of randomly oriented horizontal-component maximum acceleration amplitudes, averaged over all azimuths, significantly exceeds the theoretical geometrical spreading for far-field body waves in a homogeneous whole space for hypocentral distances less than approximately 60 km. The behavior of the vertical component is different from the horizontal: vertical attenuation near the epicenter is greater and is more dependent on source mechanism and depth. Because of the rapid near-source decay of the direct S wave, reflections from the mid-lower crust and Moho control the maximum amplitude of the vertical-component acceleration in the 60-120-km hypocenter distance range, resulting in a flattening of the vertical amplitude-distance relation. Near-source vertical maximum amplitudes averaged over all source-receiver azimuths tend to be less than the geometric mean horizontal amplitude for strike-slip focal mechanisms, but, near the source for reverse faults, the azimuthally averaged vertical-component amplitude exceeds that of the geometric mean horizontal. The modeling indicates that similar vertical- and horizontal-component geometrical spreading and approximately constant horizontal/vertical amplitude ratios observed in connection with the Lg phase at distances greater than approximately 100 km in eastern North America may not hold at smaller distances. Ground-motion prediction models for the vertical component near the source may need to incorporate strong geometrical spreading and dependence on radiation pattern.