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Reply to “Comment on `Attenuative Dispersion of P Waves in and near the New Madrid Seismic Zone' by L. Cong, J. Mejia, and B. J. Mitchell” by Robert B. Herrmann

Manuscript received 24 July 2001.

Herrmann (2002) has raised concerns about what he describes as two major problems in the method of Q determination developed by Cong et al. (2000) (hereafter, the years for the two preceding citations will be omitted). First, he notes that there is a sign reversal in the equation that they used and, second, based on his computations of waveforms in a uniform medium, he asserts that the first cycle of the waveform for ground velocity (the time duration that they used) is too short to produce correct results.

He is correct on the first point, but because the two terms are so small and because they partially cancel one another, the sign reversal does not affect the conclusions of Cong et al. , and mean values of Q m (the largely flat portion of the Q -1 spectrum) obtained using the correct equation are nearly the same as those originally plotted in Figure 5 of those authors. His second concern arises from what amounts to an attempt to quantify the effects of systematic errors due to using a truncated waveform. This type of error was discussed by Cong et al. (2000) in a nonquantitative way. Herrmann showed that inversions of group delays for short, theoretically predicted pulses yield unrealistic dispersion curves. Such unrealistic dispersion, however, does not occur for the observed pulses that we tested, suggesting that the Q results obtained from measurements of dispersion for short pulses are correct within reasonable uncertainty. We will address those issues in the following sections entitled “Group-Delay Equation” and “Examination of Herrmann's Computational Results.”

We will also address two other issues raised in Herrmann's comment. He criticizes Cong et al. (2000) because (1) they did not tabulate all values obtained for the high-frequency relaxation time (τ2) and …