Abstract

The site response during the 1998 Miyagiken–Nanbu earthquake was investigated using nine close downhole arrays in Sendai City, Japan. The site amplification function was calculated as a shear-wave spectral ratio of the surface record to that of the borehole record. The observed amplification functions reveal different peak frequencies and amplification values compared to theoretical predictions using 1D soil models with S-logging data at the sites investigated. There are two peak frequencies with low amplifications that are split around the predicted 1D peak frequencies. The 2D effect of a small-scale basin in Sendai (tens of meters) was numerically examined using the 2D finite-element FLIP computer program to find a possible explanation for the observed amplification functions. The results of the numerical analysis indicate that the site amplification characteristics in the high-frequency range (>1 Hz) could be influenced by the 2D effect of a small-scale basin, which is a consequence of the coupling between two shear waves propagating with different velocities in close proximity to the basin edge. Therefore, a new analytical wave equation including shear-wave coupling was introduced and solved for layered media using wave propagation theory. The method was applied to obtain the observed amplification functions in two horizontal directions by optimizing the model parameters (coupling coefficients) at the array sites. A successful estimation of the observed amplification functions by the method proved the validity of the shear-wave coupling hypothesis. Furthermore, a strong spatial variability of back-calculated coupling coefficients with large values at the sites on the basin slope verified the 2D effects of the small Sendai basin and justified the numerical simulation results. The outcome provides the first observed evidence for shear-wave coupling due to a small-scale basin and shows its influence on site amplification characteristics, especially for the high-frequency range.

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