Reply to "Comment on 'Comparison of Time Series and Random-Vibration Theory Site-Response Methods' by V. Graizer"

Abstract

We appreciate the comments of Graizer (2013) and agree that the accuracy of all site‐response methods should be evaluated with respect to recordings from downhole array sites. However, the goal of our study was not to evaluate the absolute accuracy of a specific method of site‐response analysis, but rather to evaluate two approaches to the same method of site‐response analysis. Namely, we aimed to evaluate the random‐vibration theory (RVT) and time‐series (TS) approaches to equivalent‐linear site‐response analysis using frequency‐domain transfer functions. Because these two types of analysis use the same algorithm to model wave propagation, we felt that the most insight would be gained by comparing the RVT and TS results to each other rather than with downhole recordings. When evaluating site‐response methods with downhole recordings the comparisons are influenced by several factors, including the quality of the site characterization, the applicability of the 1D assumptions and boundary conditions, and these factors would potentially obscure understanding the differences between RVT and TS analyses. Nonetheless, we feel that the results presented in Graizer (2013) regarding the Treasure Island site complement and reinforce the conclusions from Kottke and Rathje (2013). In particular, the results support the need for a correction to the ground‐motion duration for RVT motions computed at the surface of soil sites. The dynamic response of a soil deposit will change the duration of shaking. This effect is modeled in current ground‐motion prediction equations for duration (e.g., Bommer et al. , 2009) and it is clearly shown by the recorded motions from the Treasure Island downhole array. Qualitatively, figure 2 in Graizer (2013) reveals a significant increase in duration between the motions at 122 m depth and at the surface. Quantitatively, one may compute the significant duration ( D 5–75, defined as the time interval between the occurrence of 5% and 75% …