Reply to "Comment on 'Empirical-Stochastic Ground-Motion Prediction for Eastern North America' by Behrooz Tavakoli and Shahram Pezeshk" by Kenneth W. Campbell

Abstract

The shape of earthquake source spectrum and how it is scaled with earthquake parameters (e.g., seismic moment, stress parameter, and rupture area) has been widely examined and used as a guide for the prediction of earthquake ground motion at a specific region. As we discussed in our 2005 article, the most commonly used earthquake source model is based on Brune’s spectrum (Brune, 1970, 1971) that has had remarkable success in predicting a variety of measures of strong ground motion over the magnitude range from 4 to about 7. The basic seismological model of a ground acceleration spectrum has a simple ω 2 shape (Brune, 1970, 1971). This model assumes that the earthquake source is modeled as a circular fault source and the ground acceleration spectrum from this simplified source has an inversely ω 2 decay for frequencies below a source-corner frequency and a flat level for frequencies greater than source-corner frequency and less than site-corner frequency. The amplitude spectrum level begins to drop faster at higher frequencies beyond the site-corner frequency. The choices of source- and site-corner frequencies depend mainly on the earthquake size given by the seismic moment and the site condition (e.g., κ ), respectively. The seismic moment defines the size of the earthquake based on the product of the rigidity modulus, the area of fault rupture, and the average slip along the fault rupture. For small earthquakes, both the length and width of the fault rupture must increase in the same quantity with increasing magnitude based on assuming a circular fault source model. In Brune’s source spectrum model, the measure of the stress parameter is used as a parameter controlling the level of the amplitude spectrum above the source-corner frequency. The value of the stress parameter can be derived by differences between evaluating Fourier spectra in …