Empirical Improvements for Estimating Earthquake Response Spectra with Random-Vibration Theory

The stochastic method of ground-motion simulation is often used in combination with the random-vibration theory to directly compute ground-motion in- tensity measures, thereby bypassing the more computationally intensive time-domain simulations. Key to the application of random-vibration theory to simulate response spectra is determining the duration (Drms) used in computing the root-mean-square oscillator response. Boore and Joyner (1984) originally proposed an equation for Drms, which was improved upon by Liu and Pezeshk (1999). Though these equations are both substantial improvements over using the duration of the ground-motion ex- citation for Drms, we document systematic differences between the ground-motion intensity measures derived from the random-vibration and time-domain methods for both of these Drms equations. These differences are generally less than 10% for most magnitudes, distances, and periods of engineering interest. Given the systematic nature of the differences, however, we feel that improved equations are warranted. We empirically derive new equations from time-domain simulations for eastern and western North America seismological models. The new equations improve the random-vibration simulations over a wide range of magnitudes, distances, and oscil- lator periods. Online Material: SMSIM parameter files, tables of coefficients and model parameters, and shaded contour plots of TD/RV ratios for two WNA models.