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JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 111, B11307, doi:10.1029/2006JB004311, 2006
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Comparison of fluid tiltmeter data with long-period
seismograms: Surface waves and Earth’s
free oscillations
A. M. G. Ferreira,1 N. F. d’Oreye,2 J. H. Woodhouse,1 and W. Zürn3
Received 26 January 2006; revised 17 July 2006; accepted 2 August 2006; published 17 November 2006.
[1] We compare observations of long-period seismic surface waves and free oscillations
recorded by high-resolution long-base fluid tube tiltmeters and by nearby broadband
seismometers after large earthquakes. The quality of the tiltmeter data is comparable to
that of the best horizontal component seismic data, recording some of the gravest free
oscillations of the Earth, as well as successive passages of seismic surface waves circling
the globe. We compare the observations with theoretical seismograms and with
theoretical tilt. The predicted and observed surface wave tilt waveforms are very similar
provided that we take into account horizontal acceleration effects on the tiltmeter. Phase
and amplitude anomalies between the waveforms are well explained by the theoretical
transfer function of the instrument. Likewise, observed horizontal seismograms
converted into tilt match the tiltmeter data very well. Long-base fluid tube tiltmeters
could potentially contribute to obtain high-quality measurements of the long-period
seismic spectrum.
Citation: Ferreira, A. M. G., N. F. d’Oreye, J. H. Woodhouse, and W. Zürn (2006), Comparison of fluid tiltmeter data with longperiod seismograms: Surface waves and Earth’s free oscillations, J. Geophys. Res., 111, B11307, doi:10.1029/2006JB004311.
1. Introduction
[2] The observation of the Earth’s free oscillations has
some of the most demanding data requirements among all
global seismology applications. The Earth’s free oscillations
are sensitive to large scale volumetric averages of structure
on scale lengths comparable to the planet’s radius, being an
important data set to improve the three-dimensional elastic
and anelastic picture of the Earth’s deep interior. They are
sensitive to both shear and compressional velocities, which
allows insight into the physical interpretation of anomalies
imaged by seismic tomography [e.g., Li et al., 1991] and
into the driving forces of mantle flow. Moreover, free
oscillations are the only data with the potential to give
direct information about the 3-D density structure [e.g., Ishii
and Tromp, 1999, 2001; Resovsky and Ritzwoller, 1999].
The potential rate of relative rotation of the inner core with
respect to the mantle is constrained by accurate normal
mode measurements, which can also further constrain
core structure and inner core anisotropy [Sharrock and
Woodhouse, 1998; Laske and Masters, 1999]. In addition,
recent studies have been devoted to the study of the Earth’s
‘‘hum,’’ consisting of faint spheroidal fundamental modes
observed in the frequency range 2 – 7 mHz in the absence of
1
Department of Earth Sciences, University of Oxford, Oxford, UK.
National Museum of Natural History and European Center for
Geodynamics and Seismology, Luxembourg.
3
Black Forest Observatory, Schiltach, and University of Karlsruhe,
Wolfach, Germany.
2
Copyright 2006 by the American Geophysical Union.
0148-0227/06/2006JB004311$09.00
earthquakes [Nawa et al., 1998; Suda et al., 1998; Tanimoto
et al., 1998; Kobayashi and Nishida, 1998; Tanimoto and
Um, 1999; Ekström, 2001; Fukao et al., 2002; Rhie and
Romanowicz, 2004]. After the great 2004 Sumatra earthquake, data records from more than 400 stations from global
seismic networks had sufficient quality to observe the
Earth’s free oscillations with unprecedented signal-to-noise
ratios [Park et al., 2005]. This was only possible due to the
very large moment of the earthquake and to the broadband
seismic technology of high-quality global networks (IRIS,
GEOSCOPE, MedNet, GEOFON, etc). The bulk of normal
mode observations in the past 40 years has relied on
recordings of spring gravimeters deployed in the International Deployment of Accelerometers (IDA) network and,
more recently, on the Streckeisen STS-1/VBB seismometers
deployed in the Global Seismic Network (GSN). However,
the signal-to-noise ratio (SNR) of seismic records from
many broadband seismometers used in global seismic networks decreases at low frequencies, hindering studies of the
Earth’s gravest normal modes (frequency lower than
1 mHz). Furthermore, some GSN sensors are now near
the end of their lifetime, forcing the international seismological community to consider designing the next generation broadband seismic sensors. The most recent
superconducting gravimeters exhibit lower noise levels at
frequencies lower than 0.8 mHz, allowing the Earth’s
gravest free oscillations to be studied, after correction for
fluctuations in atmospheric pressure [e.g., Zürn et al., 2000;
Widmer-Schnidrig, 2003]. However, measurements using
superconducting gravimeter records have not yet been used
as constraints in global mantle tomography, in spite of
suggestions that these measurements can make a significant
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contribution to the study of the three-dimensional (3-D)
structure of the mantle [Widmer-Schnidrig, 2003].
[3] Tiltmeters, and in particular long-base tiltmeters, have
been primarily designed for monitoring deformation in
various contexts [Agnew, 1986], such as volcanoes (for a
review, see, e.g., Dzurisin [2003]), gas fields [e.g., Sleeman
et al., 2000], tunnelling [e.g., Feldman et al., 1998], mining
[e.g., Chrzanowski et al., 1986], Earth tide studies [e.g.,
Melchior, 1983; Zürn et al., 1986], postglacial rebound
[e.g., Kääriäinen, 1979] and tectonic crustal deformation
[e.g., Wyatt et al., 1994; Anderson et al., 1997]. However,
some instruments have achieved very low noise levels in a
wide frequency range, allowing observations in the normal
mode frequency band [e.g., Zürn et al., 1999, 2000; d’Oreye
and Zürn, 2005; Braitenberg et al., 2006]. These instruments are relatively inexpensive since they do not require a
sophisticated mechanical design. For example, the water
tube tiltmeter devised by d’Oreye and Zürn [2005] only
requires aluminum pots, circular aluminum capacitive
plates, polyethylene tubes, water and some silicone oil.
The only relevant costs are associated with the data acquisition system and with the preparation of the site for
installation, if necessary. Furthermore, they are easily installed (given an appropriate site for installation), so the
question now arises whether they could contribute to longperiod seismology studies.
[4] In this paper we compare long-period data from the
long-base capacitive water tube tiltmeter WTH2O at Walferdange, Grand Duchy of Luxembourg [d’Oreye and Zürn,
2005] with records from seismometers at two seismic
stations nearby: WLF (GEOFON network) at Walferdange,
and BFO (IRIS network) at the Black Forest Observatory,
Schiltach, Germany. BFO also operates a long-base differential pressure fluid tiltmeter, HF3, so we will also show
data from this instrument. In addition to the comparison of
long- period surface waves and free oscillations recorded by
the different instruments we also compare the records with
theoretical seismograms and with theoretical tilt. These
comparisons are important not only to assess the potential
of tilt data for long-period seismology studies, but also to
better understand the response of fluid tube tiltmeters.
Physics dictates that tiltmeters cannot distinguish between
horizontal inertial acceleration and components of the
gravity vector coupled into the sensor by tilt. In this paper
we study the influence of these effects on observed tilt.
[5] In section 2 we describe the data and some characteristics of the instruments used in the comparison. In section 3
we revisit the work of Gilbert [1980] and explain how to
calculate synthetic tilt. Since the great 2004 Sumatra earthquake provided Earth free oscillations data with unprecedented quality, we present comparisons for this earthquake.
In section 4 we show the results of such comparisons, and in
section 5 we draw the conclusions of this paper.
2. Data
[ 6 ] The long-base capacitive water tube tiltmeter
WTH2O is a very simple instrument, without moving parts,
which has shown great reliability and a fairly high stability
(linear drift rate of 5 109 rad/month). The WTH2O is
composed of two aluminum vessels with an inner diameter
of 20 cm, and interconnected with two 43 m long polyeth-
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ylene tubes. A 2 cm thick layer of MetylSyloxane oil covers
the free surface of the water in each end vessel to prevent
evaporation. A capacitive sensor employing the change of
resonance frequency records the vertical liquid displacement in each head by measuring the displacement of the
water-oil interface (for a detailed description of WTH2O,
see d’Oreye [2003]).
[7] Given the length of the apparatus (43 m long), it is
installed in an old 100 m deep gypsum mine in Walferdange
at a latitude of 49.66°N, longitude 6.15°E and at an azimuth
of 23.26°N-E. Its high resolution and its very low noise
level has enabled Earth tide observations in excellent
agreement with theoretical models, with the lowest root
mean squared errors among all the results obtained with
other tiltmeters in Walferdange [d’Oreye and Zürn, 2005].
Theoretical models of this instrument taking into account
the damping produced by the flow of liquid between the
plates of the capacitive sensors have been used to derive an
accurate theoretical transfer function, as confirmed by the
successful comparison with observed frequency responses
[d’Oreye and Zürn, 2005, 2006]. The WTH2O tiltmeter has
acquired continuous data since November 1997, recording
local, regional and global large earthquakes (Figure 1).
Notably, it has recorded some signals rarely measured with
a water tube tiltmeter, such as the gravest toroidal and
spheroidal modes of the Earth’s free oscillations excited by
large earthquakes and the successive passages of surface
waves circling several times around the globe after large
earthquakes. In this paper we examine such observations
following the great 2004 Sumatra earthquake (Figure 1,
bottom). In order to corroborate our findings with WTH2O
we shall also show results from the long-baseline fluid
tiltmeter, HF3, at station BFO. This instrument consists of
two end vessels connected by thin tubes with a central
differential pressure sensing unit. The instrument is filled
with a fully substituted fluorocarbon FC 40 fluid. A thin
elastic beryllium-copper diaphragm senses the pressure
differences arising from tilts or horizontal accelerations of
the instrument. This type of fluid tiltmeter was first constructed by Horsfall and King [1978] and is described by
Agnew [1986, paragraph 4.2.3]. At BFO the instrument has
a baseline of 110.65 m, an azimuth of 331.23°N-E and is
installed behind an airlock at an overburden of 170 m. A
more detailed description is given by Otto et al. [1998].
[8] The seismic station BFO is equipped with, among
other instruments, a set of STS-1/VBB seismometers and
the seismic station WLF is equipped with a STS-2/VBB
seismometer. Currently, the seismometer with the best very
long-period resolution (with the exception of a few gravimeter/barometer combinations) is the Wielandt-Streckeisen
STS-1/VBB [Wielandt and Streckeisen, 1982; Wielandt and
Steim, 1986]. It is most widely deployed in the IRIS GSN and
GEOSCOPE global networks as well as in some regional
networks (e.g., MedNet). In the permanent GEOFON network, mostly Streckeisen-Wielandt STS-2/VBB and a few
STS-1/VBB instruments are used. Compared to the STS-1/
VBB, the second generation triaxial seismometer STS-2/
VBB is more compact and less expensive. It has a passband
with a slightly higher low-frequency corner (0.00833 Hz
instead of 0.00278) and a significantly higher high-frequency
corner. The seismic station WLF is located at a latitude of
49.66°N, longitude 6.15°E, a few meters from the tiltmeter
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Figure 1. Examples of local, regional, and global earthquakes recorded by the WTH2O tiltmeter. (top)
Location of the WTH2O tiltmeter (triangle) and of the earthquakes (stars). (bottom) Tilt records (in
nanoradians) band-pass-filtered between T = 15 s and T = 75 s. The earthquake magnitudes and focal
mechanisms are as given by the Harvard CMT catalogue [e.g., Dziewonski et al., 1981; Dziewonski and
Woodhouse, 1983]. The earthquake-tiltmeter azimuth (clockwise from north) is superimposed on each of
the focal mechanisms. Note the different time lengths of the plots for each earthquake.
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Figure 2. Comparison of vertical component acceleration noise power spectral density for a series of
seismic stations from the Global Seismic Network. We highlight the curves for the seismic stations WLF
(dashed) and BFO (solid). The curve corresponding to the new low noise model (NLNM) of Peterson
[1993] is also shown (dotted).
WTH2O. BFO is at latitude 48.33°N, longitude 8.33°E,
about 200 km away; the sites are sufficiently close that the
long-period signals of interest are comparable.
[9] Figure 2 compares the vertical noise power spectral
density for a series of seismic stations from global networks
for a representative period of 2 weeks between 20 April
2005 and 4 May 2005, given by the Harvard Waveform
Quality Center [Ekström, 2000]. We highlight the curves for
the seismic stations WLF (dashed) and BFO (solid). The
New Low Noise Model (NLNM) of Peterson [1993] is also
shown for reference (dotted). The well-known low level of
background noise at BFO is clear, particularly at very long
periods, where its noise power spectral density is very close
to the NLNM curve. WLF is significantly noisier at very
long periods, but still less noisy than most of the other
stations from the global networks.
[ 10 ] Figure 3 compares records from the tiltmeter
WTH2O with those from the two seismometers 12 hours
after the great Sumatra earthquake. A theoretical tidal signal
has been calculated [Wenzel, 1998] and subtracted from the
original tilt data. Instrument response deconvolution is
conducted on the recorded seismograms. We apply the same
band-pass filters between 180s and 400s to both seismograms and tilt records. All the records show many Earth
circling surface waves, up to the orbits 7 and 8 for Rayleigh
and Love waves, respectively.
[11] In order to study the Earth’s normal modes, we applied
a Fourier transform to the corrected tilt data and to the
deconvolved seismograms, after multiplication by a Hanning
window. Figure 4 shows the corresponding amplitude spectra. In the higher frequency range (frequency larger than
2 mHz) it is clear that the seismograms have higher SNR than
the tilt record, except for the transverse component seismogram from WLF. However, in the range of frequency lower
than 2 mHz, the data from WLF become very noisy, notably
for frequencies smaller than 1 mHz, inhibiting the study of the
gravest free oscillations. The data from the vertical component of BFO have the highest SNR in the lower frequency
range, followed by the tilt record, which shows oscillations
consistent with spheroidal and toroidal normal modes. Indeed, the tilt data show clear peaks associated to the modes
0S3, 0S4, 0S6, 0S8, 0S9, and 0T3 0T9. The longitudinal record
(L) at BFO shows three peaks immediately to the left of 0S3,
the leftmost one is 0T2, which is unresolved, and the two at the
right are two singlets of the widely split 2S1. All three are
visible with good SNR in the tilt record, but much less clearly
in the transverse (T) record of BFO. This clearly illustrates the
quality of WTH2O data at very low frequencies. In addition
to toroidal modes, the horizontal component spectra may
show different spheroidal singlets or even different multiplets
from those shown by vertical components, depending on the
source radiation pattern and on the relative positions of the
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Figure 3. Examples of many Earth-circling Rayleigh (R) and Love (G) surface waves recorded at threecomponent seismic stations WLF and BFO and at the water tube tiltmeter WTH2O over a time window
of 12 hours after the Sumatra earthquake. The seismograms have been rotated into longitudinal (L) and
transverse (T) components. Z is the vertical component. A theoretical tidal signal has been calculated and
subtracted from the original tilt data. Instrument response deconvolution has been conducted on recorded
seismograms. All the records have been band-pass-filtered between 180 s and 400 s. The amplitudes of
the seismograms are in meters, and the tilt record is in nanoradians.
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Figure 4. Comparison of observed linear amplitude spectra of 72 hour seismograms recorded at seismic
stations WLF and BFO and of a 72 hour record of tilt. Dot-dashed lines indicate fundamental toroidal
frequencies as predicted using the spherically symmetric model, whereas dashed lines indicate
fundamental spheroidal modes. Instrument response deconvolution has been conducted on recorded
seismograms. Note that there is a different amplitude scale on the right and on the left of the dot-dashed
line (the right-hand side plot is multiplied by 10).
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source and receiver. Potentially, tilt data may be important to
study such modes.
[12] To further interpret our observations, we compare
them with theoretical calculations.
3. Modeling
[13] We here consider the calculation of synthetic records
for tilt using normal mode theory. For a spherically symmetric, nonrotating, perfectly elastic, isotropic (SNREI)
reference Earth model the problem is tractable, so that many
applications in global seismology have been based on the
assumption of such an Earth model. Under these assumptions, and for a point source, the displacement field following an earthquake is obtained by calculating the excitation
of each mode and then summing the displacement or
acceleration associated with each mode at the receiver
[e.g., Gilbert, 1970; Gilbert and Dziewonski, 1975].
[14] It has been shown by d’Oreye and Zürn [2005] that
the WTH2O instrument responds to effective horizontal
acceleration in the direction in which the instrument is
oriented. We shall refer to the output signal h(t) of the
WTH2O instrument as apparent tilt. Omitting the final term
on the right side of equation (1) of d’Oreye and Zürn
[2005], which is negligible, we can write
w
w
aðwÞ
2 þ 2b i þ 1 hðwÞ ¼
;
w0
g0
w0
2
ð1Þ
where w0 and b are the natural frequency and damping
constant of the instrument, as described by d’Oreye and
Zürn [2005]. In equation (1), h(w) is the spectrum of
apparent tilt, which is pure tilt in the limit w ! 0. a(w) is the
spectrum of the input signal, which is the effective
acceleration; a(w) includes the effects of tilt, perturbed
gravitational potential and actual horizontal acceleration.
This is exactly the same signal as is sensed by a horizontal
seismometer. Thus we can calculate the effective acceleration associated with each mode using formulae given by
Gilbert [1980]; for a given mode, having unit excitation, we
have
aq ðt Þ ¼ B @q Ylm þ C csc q @f Ylm
ð2Þ
af ðtÞ ¼ B csc q @f Ylm C @q Ylm ;
ð3Þ
with
0
1
B P
g0 U C
Cð1 cos wk t Þ
B ¼ w2k V cos wk t þB
þ
@
|fflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflffl}
a
a A
|{z}
|{z}
V
ð4Þ
C ¼ w2k W cos wk t ;
|fflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflffl}
ð5Þ
ga
Vpot
Vtilt
Wga
where U, V, W are the scalar modal eigenfunctions evaluated
m
at the Earth’s surface, Ym
l = Yl (q, f) are the spherical
harmonics, wk are the eigenfrequencies of the kth multiplet,
a is the radius of the Earth, P(r) is the gravitational potential
perturbation due to the redistribution of the Earth’s mass by
the displacement field of the kth multiplet and g0 is the
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surface gravitational acceleration. In addition to the ground
acceleration, Vga and Wga, the effective acceleration
includes a term Vtilt, which is due to ground tilt and a term
Vpot, which arises from the perturbation P in the gravitational potential due to the redistribution of the Earth’s mass.
[15] In the next sections of this paper we will study the
influence of these effects on observed apparent tilt. We shall
refer to the term Vtilt in equation (4) as actual tilt. If we take
all the terms in equations (2) – (5) into account, we shall
refer to apparent tilt. We will compute both synthetic and
observed apparent tilt. The latter will be calculated from
observed seismograms using equation (1), where a(w) is
the observed horizontal acceleration projected in the
tiltmeter axis recording direction.
[16] It should be noted that this methodology to calculate
theoretical tilt can be adapted for calculations on a realistic
laterally varying Earth using, for example, modal splitting
and coupling theory for normal modes [Dahlen, 1968, 1969;
Woodhouse and Dahlen, 1978; Woodhouse, 1980, 1983] or
surface wave full ray theory [Woodhouse, 1974; Woodhouse
and Wong, 1986; Tromp and Dahlen, 1992a, 1992b;
Ferreira and Woodhouse, 2006].
4. Results
4.1. Surface Waves
[17] Figure 5 compares three-component surface waves
recorded at the seismic station BFO with synthetic seismograms calculated by normal mode summation using the
spherically symmetric Earth model PREM [Dziewonski and
Anderson, 1981], for the 26 December 2004 Sumatra
earthquake. The theoretical calculations are performed using
source parameters from Tsai et al. [2005], who carried out a
multiple centroid moment tensor (CMT) analysis of the
2004 Sumatra earthquake. They found a final source model
consisting of five point sources to mimic a propagating slip
pulse following the great Sumatra earthquake. We see that
in this example the observed seismograms are very well
matched by the synthetic 1-D normal mode seismograms.
We have also calculated surface wave full ray theory
synthetics using the 3-D mantle model S20RTS [Ritsema
et al., 1999] combined with the global crust model
CRUST2.0 [Bassin et al., 2000] and the fit to the data is
similar to that by 1-D normal mode seismograms.
[18] We now turn our attention to surface waves recorded
by the tiltmeter WTH2O. We start by comparing observed
apparent tilt with predictions of actual tilt (Vtilt) using the
spherically symmetric model (Figures 6a and 6b). We see
that there is no agreement at all between them. The apparent
tilt record shows arrivals consistent with the arrival of Love
waves, which cannot be explained by actual tilt. Furthermore, the observed signal has much larger amplitude than
actual tilt predictions. Therefore the contribution of horizontal ground acceleration to observed apparent tilt is significant. We calculate theoretical apparent tilt as described in
section 3 and Figures 6c and 6d compare such predictions
with observations. All the traces are band-pass-filtered
between T = 180 s and T = 400 s; in this frequency range
the fit to the data is very good. Moreover, we also compare
tiltmeter records (corrected using the theoretical transfer
function derived by d’Oreye and Zürn [2005]) with apparent
tilt obtained from ground acceleration recorded at the seis-
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Figure 5. Comparison of observed three-component surface wave seismograms at seismic station BFO
(black) with synthetics calculated using the spherically symmetric PREM model (red). (top) Vertical
component. (middle) Longitudinal component. (bottom) Transverse component.
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Figure 6. Comparison of observed surface waves at the tiltmeter WTH2O (black) with theoretical tilt
calculated using the spherically symmetric model (red). Figures 6a and 6b compare data with theoretical
actual tilt. Note that the actual tilt synthetic has been multiplied by a factor of 8 for clarity. The poor
match between actual tilt synthetics and data shows that the contribution of actual tilt (Vtilt) to tiltmeter
records is much smaller than that of horizontal ground acceleration. This is confirmed by Figures 6c and
6d, which compare observed tilt with theoretical apparent tilt (i.e., taking both actual tilt and horizontal
acceleration into account). Note that for each type of synthetics we show comparisons for 12 hours of
records and for 4 hours of records.
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Figure 7. Comparison of observed surface waves at the tiltmeter WTH2O corrected for the instrument
response (black) with apparent tilt at the nearby seismic station WLF (red). (top) The 12 hours of records.
(bottom) First 4 hours of records.
mic station WLF projected to the direction of WTH2O
(Figure 7). We see that the two records match very well.
[19] In order to check if this result also applies for waves
filtered around other frequencies, we measured phase and
amplitude anomalies at various frequencies between the raw
tiltmeter record and the apparent tilt recorded at the seismic
station WLF and compared them with the theoretical
transfer function (Figure 8). The phase measurements agree
very well with the theoretical transfer function, with some
discrepancy only for higher frequencies. For amplitudes, the
agreement is also quite reasonable, but not as good as for
phase measurements. This may be due to local effects such
as strain-tilt coupling, which can locally distort observed
amplitudes and, in principle, affects broadband seismometers more significantly than long-baseline tiltmeters like
WTH2O [e.g., Harrison, 1976; King et al., 1976]. Furthermore, the observed discrepancies in amplitude may also be
due to atmospheric perturbations.
4.2. Normal Modes
[20] Figure 9 compares the amplitude normal mode
spectra of the tiltmeter record with predictions using the
spherically symmetric Earth model and the five CMT source
parameters determined by Tsai et al. [2005]. Figure 9 (top)
shows predictions of actual tilt, whereas Figure 9 (bottom)
shows theoretical apparent tilt, following the same procedure as that used for surfaces waves (see section 4.1). As for
surface waves, the horizontal acceleration contribution to
observed apparent tilt is more important than the contribution of actual tilt. Overall, there is a good fit to the data.
Some modes of oscillation are underestimated by predictions, which may be due to several effects that are not taken
into account, such as lateral heterogeneity and spheroidaltoroidal mode coupling due to the Earth’s rotation [see e.g.,
Dahlen and Tromp, 1998].
[21] We also convert observed seismograms at BFO into
apparent tilt (projected to the direction of WTH2O) to
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Figure 8. (top) Amplitude and (bottom) phase theoretical transfer function of the tiltmeter (solid lines)
compared with measured phase and amplitude anomalies between raw tiltmeter records and WLF
apparent tilt records (circles). The records have been all filtered in the same way around the indicated
frequencies. Note that the lowest frequency is 2 mHz, since for lower frequencies the ground motion
records at WLF are very noisy (see Figure 4).
compare its amplitude spectra with that of records from
WTH2O. Since the sites of the instruments are only about
200 km apart, this comparison is valid in the free oscillation
range, as confirmed by comparing synthetic apparent tilt at
the two sites (Figure 10, top). Comparing the apparent tilt
amplitude spectra observed at BFO with that at WTH2O
(Figure 10, bottom), they have very similar shapes and the
amplitudes at WTH2O are often smaller at the lower
frequencies. This may be due to very local strain-tilt
coupling effects, which have been shown to be quite
significant for the horizontal components of BFO [Lambotte
et al., 2006].
[22] It is also interesting that the noise level of the
apparent tilt amplitude spectra observed at BFO is very
similar to that of the tiltmeter data, confirming that the
quality of WTH2O data is comparable to that of the best
seismic data.
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Figure 9
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Figure 10. (top) Comparison of synthetic amplitude spectra of apparent tilt at WTH2O (black) with that
at the BFO site (red). Both synthetics are calculated using the spherically symmetric model. (bottom)
Comparison of observed amplitude spectra of records from WTH2O (black) with that of apparent tilt at
BFO (red).
[23] In this paper we carry out a case study focused on the
WTH2O fluid tube tiltmeter. Nevertheless, as we mentioned
previously, there are other long-base fluid tube tiltmeters
deployed in a few other places. Figure 11 compares the
normal mode spectra of observed tilt at WTH2O with that
from the long-base fluid tube tiltmeter HF3 located at BFO
(see section 2), for the great Sumatra earthquake. It is clear
that the data from HF3 have very high quality, comparable
to that of WTH2O data. Zürn et al. [1999] also show an
example of a normal mode spectrum of observed tilt at HF3
following the 25 March 1998 Balleny Islands earthquake,
clearly illustrating the quality of this instrument. This
emphasizes that fluid tube tiltmeter data are indeed competitive with some of the best horizontal component seismic
data recorded by STS-1 seismometers of the GSN.
[24] Various examples of long-period seismology observations using tiltmeters have been previously reported. For
example, Braitenberg et al. [2006] show normal modes
recorded by the Grotta Gigante pendulum tiltmeter (Trieste)
after the great Sumatra earthquake. In the N-S component
records the most prominent peaks of the very long-period
range of the spectra correspond to toroidal modes (0T4, 0T5,
0T6, 0T8, 0T9). Another example is given in Figure 1 of Zürn
et al. [2000], where a spectrum of the N-S component of the
Figure 9. (top) Comparison of observed amplitude spectra of tiltmeter records (black) with theoretical actual tilt
calculated using the spherically symmetric model (red). (bottom) Same as on the top, but apparent tilt is now calculated
(red). All the spectra are calculated over 72 hour seismograms. As for surface waves, the fit to the data dramatically
improves when taking into account horizontal acceleration effects (i.e., when calculating apparent tilt).
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Figure 11
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Askania tiltmeter after the Balleny Islands earthquake (Mw
8.2) of 25 March 1998 shows very strong lowest-degree
toroidal modes. These studies did not compare the toroidal
signals with theoretical calculations. As shown in this study,
such observations of toroidal oscillations must arise from
the sensitivity of the instruments mostly to inertial horizontal accelerations when the lowest degree modes of oscillation are recorded, and much less to actual tilt. Furthermore,
these reported observations also have very high quality,
suggesting that records from these tiltmeters could potentially be used in long-period seismology studies. This is
particularly interesting for the Askania tiltmeter, as it has a
very compact design. However, this instrument is no longer
manufactured and even when it was it involved very high
cost, especially when including the cost of a borehole. It is
possible that other short-baseline tiltmeters also record highquality long- period signals. A thorough comparison for this
type of instruments goes beyond this study. Nevertheless, in
principle, they are more sensitive to strain-tilt coupling
[Harrison, 1976] as well as to very small-scale heterogeneity, so that it is expected that long-baseline tiltmeters offer a
higher resolution and SNR than short-baseline instruments.
5. Air Pressure Effects
[25] It is well known that horizontal seismic noise at a
given station is larger by a factor between five and fifteen
than the vertical noise, especially at low frequencies, where
tilts are an important mechanism for production of noise
signals on horizontal seismograms. The air pressure effects
can be of different kinds: (1) a purely instrumental effect
(direct effect on the instrument, its casing and/or its ground
coupling); (2) an indirect effect due to a local atmospheric
loading of the surrounding surface near the station that
induces a true tilt (and strain) of the crust; and (3) to a much
lesser extent (negligible), a direct effect due to the gravitational attraction of the air masses.
[26] In the case of the WTH2O tiltmeter, direct instrumental effects are minimized due to the differential measurement principle. Visual inspection of the records as well
as simple correlation tests between tilt and air pressure data
easily confirm this. We have also applied a statistical, timeindependent method based on the inversion of a transfer
function between air pressure and seismic signals [Beauduin
et al., 1996], which did not lead to noticeable improvement.
HF3 is sensitive to ambient barometric pressure [Otto et al.,
1998], but pressure variations at the instrument are reduced
by the airlock at BFO, especially for frequencies higher than
0.03 cph (36 hours).
[27] On the other hand, the air pressure loading effect on
the surface surrounding the instrument depends on many
time- and space-dependent parameters (e.g., the azimuth of
the air pressure front with respect to the azimuth of the
instrument, the wavelength of air pressure waves, and/or the
frequency of air pressure variations). A network of micro-
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barographs installed around the tilt/seismic station would be
necessary to get a precise picture of the air pressure field.
Nevertheless, preliminary simple 1-D models using the
local air pressure data and considering a horizontally
propagating plane wave in the atmosphere over an elastic
half-space [Zürn and Neumann, 2002] can potentially
reduce the noise in the observed apparent tilt spectra.
Further work in that direction is in progress.
6. Discussion and Conclusions
[28] In this paper we show that the quality of seismic
records from the fluid tube tiltmeters WTH2O and HF3 is
comparable to that of horizontal component data from the
seismic station BFO, one of the quietest seismic stations of
the global network, equipped with a STS-1/VBB sensor. We
also perform comparisons with the nearby seismic station
WLF, equipped with an STS-2/VBB sensor. Although this
station provides high-quality records of surface waves, the
noise level is very high below 1 mHz, so that the data are
not competitive for grave normal mode studies. In contrast,
the tiltmeters record some of the gravest Earth’s free
oscillations as well as high-quality seismic surface waves.
[29] Modeling surface waves recorded at the seismic
stations using a spherically symmetric model and the five
CMT source parameters from Tsai et al. [2005] provides a
good fit to the data. Comparing recorded surface waves at
the tiltmeter with theoretical calculations of actual tilt, the fit
is poor, which shows that the contribution of horizontal
acceleration into observed apparent tilt is very important.
Indeed, when taking into account horizontal acceleration,
the predicted and observed apparent tilt waveforms are very
similar, showing that in the surface wave frequency range
the tiltmeter is behaving as a high-quality horizontal seismometer. Comparisons between raw apparent tilt recorded
by the tiltmeter and theoretical calculations as well as with
apparent tilt recorded in the nearby WLF seismic station in a
wide frequency range agree very well with the tiltmeter
theoretical transfer function derived by d’Oreye and Zürn
[2005, 2006].
[30] Comparing the normal mode amplitude spectra of
records at WTH2O with predictions using the spherically
symmetric model and the five CMT source parameters from
Tsai et al. [2005], we observe that overall there is a good fit
to the data. For some modes of oscillation the predictions
underestimate the observed amplitudes, which may be due
to several effects that are not taken into account, such as
lateral heterogeneity and spheroidal-toroidal mode coupling
due to the Earth’s rotation [see e.g., Dahlen and Tromp,
1998].
[31] The WTH2O tiltmeter is a relatively simple and
inexpensive instrument and is easy to install, given an
appropriate site for installation. The use of data from this
instrument as well as from other existing long-base fluid
tube tiltmeters could contribute to long-period seismology,
Figure 11. Comparison of (top) observed amplitude spectra of records from WTH2O with (bottom) those from the 120 m
fluid tube tiltmeter HF3 at the BFO site. Dot-dashed lines indicate fundamental toroidal frequencies as predicted using the
spherically symmetric model, whereas dashed lines indicate fundamental spheroidal modes. Note that the amplitudes of the
two spectra cannot be easily compared as the two instruments have different sensing directions. The noise level of HF3
starts to rise at about 2 mHz. This is due to the longer time constant and the corresponding instrumental correction.
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notably to normal mode studies, which involve some of the
most demanding data requirements in seismology.
[32] Acknowledgments. The initial ideas for this paper occurred
during the 2005 workshop on ‘‘Ocean Island Volcanism’’ in Sal Island,
Cape Verde. A.M.G.F. thanks support by the workshop organization for
attendance to the meeting and from NERC postdoctoral fellowship under
grant NE/C510916/1. We gratefully acknowledge the availability of global
seismograms from the IRIS/IDA/USGS and GEOFON networks and the
IRIS Data Centre. We thank Editor Michael Ritzwoller, Ruedi WidmerSchnidrig, and an anonymous reviewer for a number of constructive
comments, which improved this manuscript. We also thank Victor Tsai
for promptly providing us with the five moment tensor solutions used to
simulate the great Sumatra earthquake. A.M.G.F. is also grateful to Anna
Stork for insightful comments.
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