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This study uses borehole array recordings to measure the propagation characteristics of bedrock waves traveling from pre-Tertiary basement (seismic bedrock) to engineering bedrock with an S-wave velocity of approximately 0.5–0.8 km/s. To avoid the destructive interference of surface-reflected down-going waves and incidence waves in seismic and engineering bedrock, borehole data recorded at sufficient depth levels are used in this study. This is the most important aspect of the fundamental basis of this study. The propagation characteristics, i.e., the transfer function, of bedrock motions for S-waves are well represented by a Butterworth-type low-pass filter model with a high corner frequency in excess of 15 Hz and a low decay rate of —3 power of frequency. The use of such a filter model is based on the concise representation of the transfer function from an engineering viewpoint. Simple one-dimensional ray theory with a plane wave approximation explains the characteristics of the model filter at low frequencies of less than approximately 5 Hz; however, one-dimensional ray theory with a plane wave approximation at high frequencies in excess of 5 Hz requires the unusual frequency characteristics of QS−1(f), which increases with increasing frequency, to explain the frequency characteristics of the model filter. These facts imply that the filter gain can be determined using the impedance ratio of seismic bedrock to engineering bedrock and the attenuation characteristics of the intervening media at low frequencies less than 5 Hz. However, the cutoff frequency and decay rate of the filter must be determined from observational data.

Propagation characteristics of bedrock waves traveling from pre-Tertiary basement to engineering bedrock