This article presents a quantitative case study on the site amplification effect observed at Heathcote Valley, New Zealand, during the 2010-2011 Canterbury earthquake sequence for 10 events that produced notable ground acceleration amplitudes up to 1.4g and 2.2g in the horizontal and vertical directions, respectively. We performed finite element analyses of the dynamic response of the valley, accounting for the realistic basin geometry and the soil non-linear response. The site-specific simulations performed significantly better than both empirical ground motion models and physics based regional-scale ground motion simulations (which empirically accounts for the site effects), reducing the spectral acceleration prediction bias by a factor of two in short vibration periods. However, our validation exercise demonstrated that it was necessary to quantify the level of uncertainty in the estimated bedrock motion using multiple recorded events, to understand how much the simplistic model can over- or under-estimate the ground motion intensities. Inferences from the analyses suggest that the Rayleigh waves generated near the basin edge contributed significantly to the observed high frequency (f>3Hz) amplification, in addition to the amplification caused by the strong soil-rock impedance contrast at the site fundamental frequency. Models with and without considering soil non-linear response illustrate, as expected, that the linear elastic assumption severely overestimates ground motions in high frequencies for strong earthquakes, especially when the contribution of basin edge-generated Rayleigh waves becomes significant. Our analyses also demonstrate that the effect of pressure-dependent soil velocities on the high frequency ground motions is as significant as the amplification caused by the basin edge-generated Rayleigh waves.
Damage distribution maps from strong earthquakes and recorded data from field experiments have repeatedly shown that the ground surface topography and subsurface stratigraphy play a decisive role in shaping the ground motion characteristics at a site. Published theoretical studies qualitatively agree with observations from past seismic events and experiments; quantitatively, however, they systematically underestimate the absolute level of topographic amplification up to an order of magnitude or more in some cases. We have hypothesized in previous work that this discrepancy stems from idealizations of the geometry, material properties, and incident motion characteristics that most theoretical studies make. In this study, we perform numerical simulations of seismic wave propagation in heterogeneous media with arbitrary ground surface geometry, and compare results with high quality field recordings from a site with strong surface topography. Our goal is to explore whether high-fidelity simulations and realistic numerical models can – contrary to theoretical models – capture quantitatively the frequency and amplitude characteristics of topographic effects. For validation, we use field data from a linear array of nine portable seismometers that we deployed on Mount Pleasant and Heathcote Valley, Christchurch, New Zealand, and we compute empirical standard spectral ratios (SSR) and single-station horizontal-to-vertical spectral ratios (HVSR). The instruments recorded ambient vibrations and remote earthquakes for a period of two months (March-April 2017). We next perform two-dimensional wave propagation simulations using the explicit finite difference code FLAC. We construct our numerical model using a high-resolution (8m) Digital Elevation Map (DEM) available for the site, an estimated subsurface stratigraphy consistent with the geomorphology of the site, and soil properties estimated from in-situ and non-destructive tests. We subject the model to in-plane and out-of-plane incident motions that span a broadband frequency range (0.1-20Hz). Numerical and empirical spectral ratios from our blind prediction are found in very good quantitative agreement for stations on the slope of Mount Pleasant and on the surface of Heathcote Valley, across a wide range of frequencies that reveal the role of topography, soil amplification and basin edge focusing on the distribution of ground surface motion.
