Abstract

Regressions of 2700 horizontal-component broadband seismograms from 213 seismic events recorded by the German Regional Seismic Network (67 earthquakes and 146 large mining explosions and rockbursts) are carried out to study the scaling relationships of high-frequency S-wave motion for central Europe. At a set of sampling frequencies, regressions were performed on the logarithms of the peak amplitudes of narrow bandpass-filtered seismograms, as well as on the logarithms of the Fourier components of the velocity spectra. At a fixed frequency f, these values are written as  
\[\mathrm{AMP}(f,{\ }r)=\mathrm{EXC}(f,{\ }r_{\mathrm{ref}})+\mathrm{SITE}(f)+D(r,{\ }r_{\mathrm{ref}},{\ }f).\]
EXC(f, rref) is the excitation at an arbitrary reference hypocentral distance, rref, SITE(f) is a site term, and D(r, rref, f) describes the crustal attenuation in the region.
The crustal propagation term, empirically estimated in the (0.5–16.0 Hz) frequency band and (40–600 km) distance range, is modeled using a complex geometrical spreading function and a frequency-dependent crustal Q. We suggest  
\[Q(f)=Q_{0}{\cdot}\left(\frac{f}{f_{\mathrm{ref}}}\right)^{{\eta}},{\ }\begin{array}{ccc}Q_{0}&=&400\\{\eta}&=&0.42\\f_{\mathrm{ref}}&=&1.0{\ }\mathrm{Hz}\end{array}\]
and a log-log quadrilinear geometrical spreading.
A factor exp(-πκ0f) is used to fit the high-frequency roll-off of the inverted excitation terms. Since we deal with two different kinds of sources (explosions-rockbursts and earthquakes), we use  
\[{\kappa}_{0}=\begin{array}{l}0.08{\ }\mathrm{sec}{\ }(\mathrm{for\ explosions});\\0.05{\ }\mathrm{sec}{\ }(\mathrm{for\ earthquakes}).\end{array}\]
The same Brune spectral model, characterized by a stress drop Δσ = 30 bars, is used to fit both earthquakes and explosive excitation terms.

A regression on the effective duration of the ground motion following the S-wave onset is also carried out. In central Europe, duration is observed to be almost frequency-independent. This property might be explained in terms of a self-similar distribution of crustal scatterers.

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