Estimates of Coda-Q Using a Non-Linear Regression

Abstract

A non-linear regression technique (Gauss-Newton method) is used to fit the single-scattering model of coda wave generation to experimental data. Comparisons between these results and those obtained applying the technique used in seismological practice (logarithmic linearization of the model equation and least-squares fit) are made. Data used are: a) a synthetic coda generated by white Gaussian noise modulated with an attenuation factor, exp(–kt), and a geometrical spreading factor; b) seismograms provided by two seismic series that occurred in the Abruzzo (Italy) and Antequera (Southern Spain) regions. The study from synthetic data shows that when the signal-to-noise ratio of the final part of the coda is greater or equal to 5, there are no significant differences in the values of Qc inferred by both techniques. When the signal-to-noise ratio is less than 5, we observed that the log-log technique produces a systematic overestimation of the values of Qc. Results obtained with real seismograms show that the log-log technique overestimates the Qc values when compared with the Gauss-Newton method, when the whole coda is used. When a long coda is used, the Qc dependence on frequency estimated using log-log is different in some cases from the one obtained with the Gauss-Newton technique. The Qc dependence on the lapse-time is less pronounced when the Gauss-Newton technique is used. This effect is more evident when different coda durations are obtained fixing the start-time of coda analysis, and increasing the end-time of the same coda. This pattern is also observed for the Abruzzo (Italy) and Antequera (Spain) series; when the log-log technique is used, a lapse-time dependence is observed, but, when the Gauss-Newton technique is used, this dependence is less significant. © 1993, The Seismological Society of Japan, The Volcanological Society of Japan, The Geodetic Society of Japan. All rights reserved.