Estimating an upper limit probability distribution for peak ground acceleration using the randomly clipped normal distribution

The randomly clipped normal distribution is introduced to model peak ground acceleration (PGA) saturation for increasing magnitude in the near field. Attenuation and clipping parameters are simultaneously estimated through regression for a data set comprising 243 worldwide PGA observations for surface-wave magnitudes (M-S) between 5 and 7.8 and Joyner-Boore distances r(JB) between 0 and 15 km. Attenuation in the near field is modeled by combining the attenuation law (for PGA expressed in m/sec(2)) log(10) (PGA) = -2.09 + 0.47M(S) - 0.039r(JB), sigma = 0.3 with clipping at a normally distributed random threshold with mean 0.7 (corresponding to 5.01 m/sec(2)) and standard deviation 0.22. The model succeeds in predicting decreasing attenuation and decreasing scattering of PGA for increasing magnitude. The probability distribution of the clipping threshold constitutes the limit probability distribution for the logarithm of PGA for increasing magnitude and decreasing distance.