Abstract: Based on the accelerations recorded from two downhole arrays instrumented by the Caltrans/CDMG project, the site amplification effects of deep liquefiable soil deposits are analyzed in both time and frequency domains, and several important features of the wave propagation from the bedrock to the overlying soil layers are observed: (1) The depth of soil deposit affects the site amplification considerably, and large part of the amplification occurs in the near-surface zone within the depth of 20~30 m; (2) The amplification differs from one to another direction, and the difference between the horizontal and vertical shakings is significant; (3) The amplification occurs when the input bedrock motion is small, while the de-amplification effects are observed when the bedrock input motion is large enough; (4) The amplification is frequency dependent, and the deep deposits amplify the bedrock ground motion in a wide frequency band. The underlying mechanisms are preliminarily analyzed. The simplified function accounting for the impedance contrast amplification and thickness attenuation effects is proposed based on the plane wave assumptions, and the parameters are improved for the quarter wave length method. The amplification ratios are predicted for all four events in conjunction with "free-surface effect", where the predictions are found in good agreement with the observations either in time or frequency domain. The present study provides a theoretical basis and simplified method for estimating the ground motions for liquefaction evaluation and seismic design of deep liquefiable soil deposits.