Using more than 500 accelerometric records from three vertical arrays located in Japan, we performed a regression analysis in order to derive attenuation relationships at underground sites with depths ranging from 100 to 950 m. Analyses were conducted on both peak ground acceleration and pseudo-velocity response spectra. Because of a positive correlation between magnitude and distance, a two-step regression technique was employed. Results show that, compared with surface ground motion, peak accelerations at underground sites are lower by a factor ranging from 1.5 to 4 according to the depth. In the case of response spectra, differences between ground surface and underground spectra are dependent on geological conditions. For the three sites considered in the study, underground pseudo-velocity response spectra show amplitudes lower by a factor ranging from 1.5 to 10 according to the depth or the period considered.
Ratios between the receiver responses obtained at different depths provided average transfer functions. Those were compared with transfer functions calculated by averaging ratios of observed response spectra between different depths. A good agreement between the two techniques was found. Finally, theoretical transfer functions were estimated using both one-dimensional SH and complete wave modeling. It was shown that the characteristics of the incident wave field can play an important role in the estimation of theoretical transfer functions.