Variability of shallow soil amplification from surface-wave inversion using the Markov-chain Monte Carlo method

We conduct numerical experiments to estimate the variability of 1D linear and nonlinear soil amplifications due to the uncertainty in shallow S-wave velocity profiles derived from surface-wave phase velocity inversions using the Markov-chain Monte Carlo method. We first generate synthetic, observed phase velocities of Rayleigh waves for two- and three-layer models of shallow soil. Our final models from sampling can explain well the true S-wave velocity profiles and the phase velocities. We also estimate the uncertainties of each model parameter. A synthetic strong motion is applied to the engineering bedrock of the sampled models to obtain the surface motion assuming linear and nonlinear amplifications. It is found that the nonlinear amplification shows less variability and also has a flatter spectral shape than the linear amplification, particularly at high frequencies. The distributions of ground motion proxies generally have less uncertainty for the nonlinear amplification as well. We also find that the observational errors of the phase velocities have less influence on the variability of the nonlinear amplification than the linear case. This result is caused by the high damping factor applied in the nonlinear soil response.