Shear wave attenuation estimated from the spectral decay rate in the vicinity of the Petropavlovsk station, Kamchatka

Аннотация

The parameters of S-wave attenuation (the total effect of absorption and scattering) near the Petropavlovsk (PET) station in Kamchatka were estimated by means of the spectral method through an original procedure. The spectral method typically analyzes the changes with distance of the shape of spectra of the acceleration records assuming that the acceleration spectrum at the earthquake source is flat. In reality, this assumption is violated: the source acceleration spectra often have a high-frequency cutoff (the source-controlled f_max) which limits the spectral working bandwidth. Ignoring this phenomenon not only leads to a broad scatter of the individual estimates but also causes systematic errors in the form of overestimation of losses. In the approach applied in the present study, we primarily estimated the frequency of the mentioned high-frequency cutoff and then constructed the loss estimates only within the frequency range where the source spectrum is approximately flat. The shape of the source spectrum was preliminarily assessed by the approximate loss compensation technique. For this purpose, we used the tentative attenuation estimates which are close to the final ones. The difference in the logarithms of the spectral amplitudes at the edges of the working bandwidth is the input for calculating the attenuation. We used the digital accelerograms from the PET station, with 80 samples per second digitization rate, and based on them, we calculated the averaged spectrum of the S-waves as the root mean square along two horizontal components. Our analysis incorporates 384 spectra from the local earthquakes with M = 4–6.5 at the hypocentral distances ranging from 80 to 220 km. By applying the nonlinear least-square method, we found the following parameters of the loss model: the Q-factor Q₀ = 156 ± 33 at frequency f = 1 Hz for the distance interval r = 0–100 km; the exponent in the power-law relationship describing the growth of the Q-factor with frequency, γ = 0.56 ± 0.08; and the loss parameter beneath the station κ₀ = 0.03 ± 0.005 s. The actual accuracy of the estimates can probably be somewhat lower than the cited formal accuracy. It is also established (with a confidence level of 10%) that the losses decrease with distance.