Effects of Fault Dip and Slip Rake Angles on Near-Source Ground Motions: Why Rupture Directivity Was Minimal in the 1999 Chi-Chi, Taiwan, Earthquake

We study how the fault dip and slip rake angles affect near-source ground velocities and displacements as faulting transitions from strike-slip motion on a vertical fault to thrust motion on a shallow-dipping fault. Ground motions are computed for five fault geometries with different combinations of fault dip and rake angles and common values for the fault area and the average slip. The nature of the shear-wave directivity is the key factor in determining the size and distribution of the peak velocities and displacements. Strong shear-wave directivity requires that (1) the observer is located in the direction of rupture propagation and (2) the rupture propagates parallel to the direction of the fault slip vector. We show that predominantly along-strike rupture of a thrust fault (geometry similar in the Chi-Chi earthquake) minimizes the area subjected to large-amplitude velocity pulses associated with rupture directivity, because the rupture propagates perpendicular to the slip vector; that is, the rupture propagates in the direction of a node in the shear-wave radiation pattern. In our simulations with a shallow hypocenter, the maximum peak-to-peak horizontal velocities exceed 1.5 m/sec over an area of only 200 km^2 for the 30°-dipping fault (geometry similar to the Chi-Chi earthquake), whereas for the 60°- and 75°-dipping faults this velocity is exceeded over an area of 2700 km^2. These simulations indicate that the area subjected to large-amplitude long-period ground motions would be larger for events of the same size as Chi-Chi that have different styles of faulting or a deeper hypocenter.