Quantitative Analysis of Early Seismograph Recordings - Historical Seismology: Interdisciplinary Studies of Past and Recent Earthquakes - page 381

While bothersome for the retrieval of waveforms, time marks are essential to control
the record speed and convert distance on the seismograms to differences in time.
Especially for uneven recording speed or for distorted raster images of seismogram
sections (e.g. due to the process of photographic reproduction), time marks are key
to recover the time series. Between time marks, fluctuations of the recording drum
angular velocity may distort the apparent frequency contents of the record. As the
real instantaneous velocity of the drum is unknown, Herrmann (1987) suggested
interpolating linearly between time marks. After these corrections are applied, the
records can be interpolated to a constant sampling rate.
After such preprocessing, the signal amplitude is still given in counts, and we
need to deconvolve the proper instrument response to restitute actual ground dis-
placement. The instrument transfer functions are defined by design characteristics
as are the damping and the magnification of the system, the free period of the pen-
dulum, and the free period of the coupled galvanometer in case of electromagnetic
recording systems. Above the free period of the instruments, the magnification drops
rapidly, following a − 3 slope for

electromagnetic sensors (e.g. Kanamori 1988, Batll o 2004). Below the free period,
nominal sensor sensitivity is nearly flat for purely mechanical sensors and drops
proportional to

− 2 slope for purely mechanical sensors, and a

for electromagnetic sensors. Near the free period, the response
curve is conditioned by the damping of the pendulum motion. Some of the earliest
instruments are essentially undamped except of friction effects, making a stable
restitution of ground motion problematic. The removal of the instrument response
through deconvolution is a task performed by many standard seismic processing
tools. Though most of them do not contemplate the responses of old mechanical and
electromagnetic instruments directly, it is possible to introduce the response as a se-
ries of poles and zeroes (Scherbaum 1996, Batll o and Bormann 2000, Batll o 2004).
For mechanical instruments a further problem arises. The inscription system (lev-
eler contacts and stylus) presents a non negligible amount of dry friction. Dry fric-
tion is a dissipative force and introduces a loss of signal energy. It is a problem that,
even early acknowledged (Reid 1925), still needs further studies to properly char-
acterize its importance. Also, sometimes, mainly for some mechanical instruments,
the transfer function may not be exactly linear (Herak et al. 1997, Ritter 2002). To
complete our description of possible pitfalls, we recall that even idealized instrument
transfer functions may be inappropriately estimated, since instrumental parameters
are sometimes insufficiently documented (if at all) in contemporaneous sources, and
furthermore may be subject to temporal drifts and fluctuations. Especially damping
on mechanical seismographs may depend on the daily variations of room tempera-
ture. This type of uncertainties is particularly critical for the restitution of intermedi-
ate period waveforms (e.g. Rodgers 1968, Stich et al. 2005). Given the uncertainties
of estimated transfer functions and the potential instabilities of deconvolution, a
more stable alternative for waveform modeling may be applying the convolution of
the corresponding instrument response to the synthetic Green functions instead (e.g.
Kikuchi et al. 2003, Ichinose et al. 2003), or - in case we want to compare two real
seismograms recorded with different instrument response- the re-convolution of the
records with the interchanged instrument responses (Rivera et al., 2002). In both