It is a well-known fact that the uncertainties in measuring relative attenuation factors within a local or regional seismic network are usually high, due to noise of different kinds and unrealistic assumptions. Numerical experiments using nine synthetic seismograms, created using t* values ranging from 0.1 to 0.9 sec, reveal that the commonly used spectral ratio method is strongly affected by the selection of data processing parameters such as width of the spectral smoothing window, reference station, and so on. The numerical experiments demonstrate that a Bayesian nonlinear inversion approach that directly matches the spectra is better at finding the correct parameters used to generate the synthetic seismograms. The Bayesian inversion approach uses a priori information to simultaneously search for the t* values, the common spectrum for all the records from an event, and the near-receiver amplification factors by using all the recordings from an event. When z, the ratio of Gaussian noise to signal, ≦ 0.1, the spectral ratio and Bayesian methods yield similar results with mean t* measurement errors <0.05 sec. For 0.1 < z ≦ 0.8, the mean errors of the spectral ratio method are larger than 0.1 sec and in some cases as large as 0.6 sec, while those of the Bayesian method are less than 0.08 sec. Frequency-independent t* and near-receiver amplification factors are assumed. A multi-step procedure is proposed to reject records with a large misfit.

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