Source, site, and propagation parameters are inverted from a U.K. database of weak-motion events (2.0>ML>4.7). This results in the complete spectral parameterization of over 3200 velocimetric records of 273 events from the year 1992 to 2006. The S wave is extracted from the vertical records and is processed using a multitaper Fourier transform. We initially use a nonlinear least-squares log-space optimization to obtain estimates of the attenuation parameter for each spectrum. The estimates of t* are then used to geometrically constrain a depth-dependent Q model using a technique adapted from velocity tomography. We then invert for the remaining frequency-dependent parameters and a collective amplitude parameter from the velocity spectra while fixing the newly computed attenuation parameters based on raytracing through our Q model. The resultant amplitude parameters are then split into source moments, apparent geometrical spreading, and site correction factors. We find a frequency-independent depth-dependent Q structure. A linear relationship proportional to 0.7 ML between moment magnitude (Mw) and local magnitude (ML) is found in the range of 2–4.7 ML. The majority of stress drops are found to range on the order of 0.1–10 MPa. A multiple segment apparent geometrical spreading model is found to best describe the amplitude decay with distance, accounting for factors such as geometrical spreading and scattering, along with multiple phase interference in the analysis window. Site response functions are found to broadly correlate with regional geology, mean amplification occurring in the Cenozoic sedimentary rock sites to the southeast of England relative to the harder Palaeozoic rock sites of Wales and Scotland. We use a bootstrap analysis technique to analyze the dependence of our results on the data in order to estimate the variance of the results and check the robustness of different inversions. Synthetic spectra are also computed in order to obtain minimum variance and bias of model parameters associated with the method. In applying a geometrical Q constraint, through the use of Q tomography, we find that the robustness of the results is significantly increased. A thorough analysis of the trade-offs involved in the inversion is performed using synthetic datasets. We find strong trade-offs between the parameters, but we are able to show that this covariance is reduced when adopting the Q-tomography approach.

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