Geophys. J. R. astr. SOC.(1983) 73,517-521
Research note
Seismograms from phaseless seismographs
R. c. Stewart
Department of Geology, University of Reading, Whiteknights,
Reading and MODIPE), Blacknest, Brimpton, Reading R G7 4RS, Berks
A. Douglas MOD(PE), Blacknest, Brimpton, Reading RG7 4RS, Berks
Received 1982 May 12
Fig. l(a) shows a P-wave seismogram from an earthquake in the New Hebrides recorded
at Wolverton (WOL) UK on a broad-band (BB) seismograph which has a displacement
response that is constant from around 0.1 to 5 H z (Fig. 2). The P seismogram shows an
initial negative deflection followed by a broad positive deflection. Fig. l(b) shows the same
P signal as Fig. l(a) except that the phase shifts due to the BB seismograph have been
cancelled out: this was done by multiplying the spectrum of the recorded seismogram by
ia(w)l/a(w) and transforming back into the time domain; a ( o ) is the response of the BB
seismograph at frequency w . It is clear that removing the phase shift removes (as might be
expected) the instrument overswing and produces, in this case at least, a seismogram that is
easier to interpret than the standard BB-seismogram (Fig. la): the signal on the phaseless
seismogram (Fig. lb) is now seen to consist of two pulses, the first and largest has negative
polarity (A the second ( A z ) positive polarity.
The phaseless seismogram (Fig. lb) can be thought of as representing the ground displacement filtered with a symmetric non-causal filter with amplitude response as a function of w
identical to that of the BB seismograph (Fig. 2). Such filters, as is well known, generate precursors which may make the onset of a signal difficult to observe. For the New Hebrides
earthquake shown here the onset is so gradual that the effect of any precursor is negligible the onset is no more distinct on the standard than on the phaseless seismogram. Fig. l(c
and d) show the standard and phaseless BB-seismograms respectively, recorded at WOL from
a Sea of Okhotsk deep earthquake: for this example the phaseless seismogram does show a
precursor to the signal but this is easily allowed for when interpreting the seismogram. The
form of the pulse radiated by the Sea of Okhotsk earthquake is more clearly seen in the
phaseless than the standard BB-seismogram so that for example the pulse length (D) and
pulse area can be estimated; from the area of the pulse an estimate of the seismic moment of
the source can be obtained. The examples shown in Fig. 1 demonstrate that phaseless seismoDarns may sometimes be easier to interpret than standard seismograms and these are not
holated examples.
It is the purpose of this research note t o draw attention to the value of phaseless seismograms. Many papers have been published on deconvolving seismograms to remove the effects
of the seismograph (see for example Fukao 1972) and as far as we can tell this has usually
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R . C.Stewart and A . Douglas
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1-...
85
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Figure 1. (a) Broad-band P-wave seismogram recorded at WOL from New Hebrides earthquake of 1976
January 9. Origin time: 23 :54 :35.6. (b) Seismogram (a) after removal of phase shifts due to broad-band
seismograph. (c) Broad-band P-wave seismogram recorded at WOL from Sea of Okhotsk earthquake of
1975 December 21. Origin time: 10:54 :17.7. (d) Seismogram (c) after removal of phase shifts due to
instrument response.
meant correcting the seismogram for both amplitude and phase effects. However, Strelitz
(1980) shows an example of a World Wide Standard Station Long Period seismogram after
filtering with what he calls a moving-window matched-filter (but gives no further details)
which seems to have a similar effect to using a filter to cancel out the phase shift as proposed
here.
Fig. 3(a) is the SP P-seismogram (for response see Fig. 2) from an earthquake near Alma
Ata, USSR as recorded at Yellowknife, Canada. On this seismogram P is clearly of positive
polarity but the polarity of p P is less clear. On Fig. 3(b), however, where the phase shifts of
the SP instrument have been cancelled out, the polarity of pP is clearly seen to be the
opposite of P. To obtain Fig. 3(c) the SP P-seismogram (Fig. 3a) has been converted to the
seismogram that would have been recorded by a phaseless BB-seismograph and then filtered
with a high-pass phaseless-filter cutting off at 2 s period to reduce the low-frequency noise
that is amplified by the conversion process. (The conversion from SP to phaseless BB was
done by multiplying the spectrum of the SP P-seismogram by l a ( w ) J / b ( o ) ,where b(w) is
the response of the SP seismograph at frequency w , and converting back into the time
domain.) The result of this processing of the SP P-seismogram is to produce a slightly broader
Seismograms from phaseless seismographs
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I
I
l
l
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Frequency I Hzl
A l l 1 1
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Figure 2. Relative magnification and phase shift for broad-band (BB) and short-period (SP) seismographs.
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6
Figure 3. (a) Short-period P-wave seismogram recorded at Yellowknife, Canada from Alma Ata earthquake of 1968 July 1. Origin time: l y :14:54.7.@) Seismogram (a) after removal of phase shifts due to
SP seismograph. (c) Seismogram (a) converted to phaseless BB-seismogram and filtered with a phaseless
high-pass filter cutting off at around 0.5 Hz.
band signal than the original and which shows more clearly than the phaseless SP-seismogram
the polarities and pulse shapes of P and p P .
As a final example to illustrate the value of phaseless seismograms consider Fig. 4(a)
which is a standard BB-seismogram recorded at WOL from an earthquake on the BurmaIndia border. Douglas, Hudson & Marshall (1981), who give details of the earthquake,
demonstrate by comparing the standard BB-seismogram with seismograms computed from
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R. C. Stewart and A . Douglas
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Figure 4. (a) Broad-band P-wave seismogram recorded at WOL from Burma -India-border earthquake of
1970 July 29. Origin time: 10:16:19.3. (b) Seismogram (a) after removal of phase shifts due to broadband seismograph.
various source models that arrival A 3 (Fig. 4a) is not associated with an arrival of positive
polarity, as might appear at first sight, but is in fact the stopping phase of a pulse of negative
polarity. On the phaseless BB-seismogram (Fig. 4b), however, the polarity of the pulse that
produces A is clearly seen to be negative.
From the above examples it is clear that phaseless seismograms sometimes have advantages over standard seismograms in showing more clearly the polarity, width and area of body
wave pulses. If the filter amplitude response is broad, as it is for the BB seismograph used
here, then precursors generated by removing seismograph phase-shifts are not a serious drawback in the interpretation of phaseless seismograms. For narrow-band filters such as the SP
seismograph, although precursors may be present, the polarities of pulses may nevertheless be
clearly seen. The effect of precursors can be reduced at least for pulses of short duration by
widening the pass band of the filter to be flat from 0.5 Hz upwards. The process of removing
the phase shifts and widening the pass band slightly is a simpler way of obtaining estimates
of pulse shapes than the method proposed by Douglas et al. (1972) who used spiking filters.
Note, however, that in using spiking fdters Douglas et al. (1972) were also attempting to
correct for the effects of anelastic attenuation in the Earth so that spiking filters at least as
used by Douglas et al. (1972) and filters for conversion to phaseless seismograms are not
directly comparable.
Rather than compensate for the phase shifts due to the seismograph a complete deconvolution could be attempted to remove both the amplitude and phase effects of the seismograph from the seismogram. The attraction of confining the process to removing phase shifts
with little or no widening of the pass band is that the signal-to-noise ratio seen on the
original seismogram is more or less preserved; removing the effects of the amplitude response
from a seismogram usually results in such a large amplification of noise - both system and
seismic noise - outside the pass band that the signal is swamped by the noise.
Acknowledgment
One of us (RCS) acknowledges support from a Natural Environment Research Council CASE
Studentship.
References
Douglas, A., Corbishley, D. J., Blarney, C. & Marshall, P. D., 1972. Estimating the ruing depth of underground explosions, Nature, 237,26-28.
Seismograms from phaseless seismographs
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Douglas, A., Hudson, J. A. & Marshall, P. D., 1981. Earthquake seismograms that show Doppler effects
.
due to crack propagation, Geophys. J. R. astr. Soc., 64, 163-185.
Fukao, Y., 1972. Source process of a large deep-focus earthquake and its tectonic implications. The
Western Brazil earthquake of 1963, Phys. Earth planet. Int., 5 , 61-76.
Strelitz, R. A., 1980. The fate of the downgoing slab: a study of the moment tensors from body waves of
complex deep-focus earthquakes, Phys. Earth plonet. h t . , 21,83-96.