Use of Nakamura's spectral ratio (horizontal versus vertical components) is investigated theoretically for deep sedimentary basins by considering semi-circular and semi-spherical valleys. The ratio is evaluated from the steady-state surface response for different incident waves. Based on this ratio, both the resonant frequencies and ground motion amplification are determined. The results based on Nakamura's ratio are compared with those based on the sediment-to-bedrock spectral ratios (Kagami's ratio).

The results show that for both two- and three-dimensional models, Nakamura's technique predicts well the fundamental resonant frequency, but it could not determine higher resonant frequencies of the basins. The error in Nakamura's estimate of the fundamental resonant frequency increases for stations near the valley center. For alluvial valleys considered in this article, Nakamura's ratio failed to predict accurately surface ground-motion amplification.

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