STOLBERG (DE)

Multiple filter technique (Dziewonski, Bloch & Landisman, 1969), applied in your browser to the raw signal of the station (100 samples per second), the very file of the seismograms above: trend removed, ends tapered over 2 s, spectrum divided frequency by frequency by the instrument response (sensitivity, poles and zeros of the sensor, and digital filters of the digitiser, from the ORFEUS inventory), then, for each of the 81 frequencies from 50 to 0.5 Hz, a Gaussian filter exp(−α ((f − f₀)/f₀)²) with α = 18 and the envelope of the analytic signal; the power (squared envelope) is smoothed in time with a Gaussian whose standard deviation equals the filter’s, √(2α) T₀ / 2π (the smoothing operator of Torrence & Webster, 1999, used by Grinsted et al., 2004), and the displayed amplitude is its square root, the RMS amplitude at the filter’s resolution, free of the fades of the instantaneous envelope; one sample every 0.04 s. Up to normalisation, this is a continuous wavelet transform with the Morlet wavelet, ω₀ = √(2α) = 6, the usual value (Torrence & Compo, 1998). The filter is taken as zero where the digitiser’s anti-alias filter attenuates the signal by more than 80 % (or, when the inventory does not describe it, above 0.8 times the Nyquist frequency); the rows whose filter extends beyond that limit are hatched. Amplitudes in ground velocity, in decibels relative to the station’s maximum; below −40 dB, the background colour.

Colour scale, as chosen: “station”, 0 dB at the maximum of the selected station (vertical and transverse together); “earthquake”, at the maximum of all plotted stations, to compare colours from one station to another; “absolute”, 0 dB at 1 µm/s, from −40 to +40 dB (from 10 nm/s to 100 µm/s), the same on every page, saturated above. The levels are not recomputed: only their mapping to colours changes.

Above each spectrogram, the signal of its component, processed like the seismograms: trend removed, ends tapered over 2 s, 4th-order Butterworth band-pass applied in both directions between 0.5 Hz and the station’s limit, scaled to its maximum in the displayed window; that maximum, written on the right, is the signal divided by the instrument sensitivity, without correcting its frequency response. The time window is shared by the seismograms and the spectrogram.

Transverse component: −E·cos β + N·sin β, β being the back azimuth, the direction from the station to the epicentre (ObsPy convention), computed on the ellipsoid from the instrument position in the ORFEUS inventory; both horizontal components are converted to velocity by their sensitivity before the rotation, then corrected for their common response. It is only computed when the uncertainty on the epicentre location leaves this direction known to within 10°, atan(uncertainty / distance): beyond that, more than 17 % of the radial component, on which the P wave and part of the S wave arrive, would leak into the transverse one. Both components share the same 0 dB.

Computation checked against a second, independent implementation (ObsPy and NumPy) on recordings from the catalogue: instrument response compared with ObsPy’s (evalresp), envelopes and colour levels with NumPy. Response compared with ObsPy’s (evalresp), digital filters included, up to each station’s limit. Signals: public archive of ORFEUS (EIDA), networks BE.