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cases the resulting traces are directly comparable since they correspond both to the
same transfer function.
4 Inversion of Source Parameters from Historical Seismograms
Digitized and corrected time series from old seismogram recordings can -in prin-
ciple - be used in any state-of-the-art digital inversion procedure to derive point
source seismic source parameters or the distribution of rupture parameters over a
finite fault. However, there are evident differences between modern recordings of
the seismic wavefield at dense networks of modern-standard accelerometers or very
broadband velocity sensors with force feedback technology and 24 bit digitizing
systems (Wielandt 2002), and sparse early XX century recordings. Beneath station
coverage, the main limitation is due to the small dynamic range and bandwidth of
early instruments. The dynamic range is nominally limited between the most tiny
amplitude differences we can resolve and digitize on analogue recordings, about
0.2-0.3 mm under most favourable conditions, and the full width of the recording
medium, which does not exceed 30 cm. This corresponds to about 60 dB. To trans-
late this into the language of the digital seismologist: The double amplitude of digi-
tized waveforms is intrinsically limited to 1,000 meaningful counts, which would be
equivalent to the performance of a 10 bit digitizer. Considering the enormous ampli-
tude range of seismic ground motion in nature, only for small subsets of earthquake
magnitudes and epicentral distances the input signal could be recorded appropriately
at those instruments. In practice, the dynamic range will be even smaller due to
background noise at the low end, or due to nonlinearity and imaging issues at the
high end of the recording range.
The frequency bandwidth of early instruments is conditioned by the free period
of the pendulum, as well as the free period of the coupled galvanometer where ap-
plicable. By early XX century standards, long period recording meant free periods
for either seismometer or galvanometer to be 10-25 s at horizontal components, and
less for vertical sensors (e.g. Kanamori 1988, Batllo 2004). For longer periods, the
decrease of instrument magnification is proportional to
−
2
for mechanical sensors,
−
3
for electromagnetic sensors, usually corresponding to just the same de-
cay of dynamic range for the longer period component of recorded ground motion
(12 dB/octave and 18 dB/octave, respectively). At the high frequency end, band-
width is practically limited at about 1-4 Hz by an instrument-specific ratio between
the effective pen width and the velocity of the recording media: high frequency wig-
gles in quick succession may be drawn onto one another and cannot be distinguished
readily anymore. In this case, aliasing effects may be introduced into the digitized
waveforms (c.f. Scherbaum 1996), and recordings with too low drum speed are not
suitable for digital waveform analysis.
Teleseismic recordings of early XX century recordings are a comparably reli-
able source of information. Teleseismic body waves with periods of a few sec-
onds carry a lot of information on the source process and are recorded with low
and
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