Hino et al.
Progress in Earth and Planetary Science(2022) 9:73
https://doi.org/10.1186/s40645-022-00526-y

Progress in Earth andPlanetary Science

Open Access

RESEARCH ARTICLE

Assessment of S‑net seafloor pressure data
quality in view of seafloor geodesy
Ryota Hino1* , Tatsuya Kubota2, Naotaka Y. Chikasada2, Yusaku Ohta1 and Hideto Otsuka1

AbstractLong-term continuous observation of seafloor pressure is effective for detecting seafloor vertical deformations thatare associated with transient tectonic phenomena such as slow slip events. Since the aseismic slip event prior to the2011 Tohoku earthquake, several discoveries have been made on spontaneous slow slip events and various othertypes of slow earthquake along the Japan and Kuril Trenches. Seafloor observation network for earthquakes and tsunamis along the Japan Trench (S-net) is expected to provide invaluable information on slow slip activities via geodetic
signals that are detected by pressure observation. This study inspects the quality of the S-net pressure data in viewof seafloor geodesy by comparison with records obtained by more than 100 autonomous ocean bottom pressurerecorders (OBPRs) deployed along the Japan Trench. OBPRs have long been standard tools in seafloor geodesy, andthe data collected are considered a benchmark in terms of quality. Most of the S-net stations showed noise levels thatare considerably higher than those of the OBPRs over periods of more than 2 d. We speculate that a strong correlation between pressure and temperature accounts for much of the long-term noise. In this study, the temperaturedependent fluctuation component was estimated by prediction filtering and removed from the original data, leading
to a significant reduction in the noise level at 51 stations, which reached levels almost equivalent to those of OBPRs.
Although no significant pressure changes have been identified as associated with the 2018 Boso SSE or repeatedtremor bursts in the northern Japan Trench thus far, our findings indicate that these stations are sufficiently sensitive
to detect slow slip events occurring nearby.
Keywords: S-net, Seafloor pressure observation, OBPR, Slow slip events, Pressure–temperature correlation
1 Introduction
The 2011 Tohoku earthquake triggered an increase inresearch in the number of studies on the slow slip activity
that occurs along the Japan and Kuril Trenches. The slow
slip that preceded the main shock was indicated by analysis of foreshock and tectonic tremor activities (Kato et al.,2012; Ito et al., 2015; Katakami et al., 2018) and seafloorpressure observations (Ohta et al., 2012; Ito et al., 2013);
the relationship between slow slips and the occurrenceof large earthquakes has thus attracted attention (Obara
and Kato, 2016). Accelerating aseismic slips in this region*Correspondence: hino@tohoku.ac.jp
1
Graduate School of Science, Tohoku University, 6‑6 Aramaki‑Aza‑Aoba,
Aoba‑Ku, Sendai, Miyagi 980‑8578, Japan
Full list of author information is available at the end of the article

have also been reported as afterslips following major
earthquakes (Kawasaki et al., 1995; Heki et al., 1997;
Iinuma et al., 2016; Itoh et al., 2019). Ohta et al. (2019)
reported on the tectonic tremor activity promoted by
the afterslip of the 2011 Tohoku earthquake in the shallow plate boundary in the southern Japan Trench. However, evidently, spontaneously accelerating slips occur not
only immediately after major earthquakes, but also continuously and periodically (Uchida et al., 2016). Recently,
frequent very low frequency earthquakes, a type of slow
earthquake, have been reported by onshore broadband
seismic observations in the region (Matsuzawa et al.,2015; Baba et al. 2020).
The 2011 Tohoku earthquake led to the developmentof an offshore observation network, Seafloor observation
network for earthquakes and tsunamis along the Japan© The Author(s) 2022. Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which
permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to theoriginal author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images orother third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line
to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory
regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of thislicence, visit http://​creat​iveco​mmons.​org/​licen​ses/​by/4.​0/.

Hino et al. Progress in Earth and Planetary Science(2022) 9:73

Trench (S-net), which was established to observe submarine earthquakes and tsunamis (Aoi et al., 2020). Using
S-net short-period seismograms, Nishikawa et al. (2019)and Tanaka et al. (2019) discovered that tectonic tremor
activity is widely distributed over the shallow part of the
subduction zone across the Japan Trench and the southwestern edge of the Kuril Trench. This finding strongly
suggests the occurrence of shallow slow slip events (SSEs)
in the subduction zone. However, most SSEs occur awayfrom the terrestrial geodetic networks that cannot detect
the associated crustal deformation. Thus, only Honsho et al. (2019) indicated an association between thehorizontal displacement resulting from an SSE and anincrease in the number of small repeating earthquakes in
2015, which was detected by a series of campaign surveys
using GNSS-Acoustic seafloor measurement.
Compared to that of the SSEs that occur on the downdip side of the seismogenic zone, knowledge of shallow
SSEs is based on only a few observations. However, shallow SSE activity is key to understanding the frictional
behavior that occurs at shallow plate boundaries, which
has been the focus of attention since the Tohoku earthquake, when a seismic slip reached the trench axis (Fujiwara et al. 2011; Iinuma et al., 2012; Kodaira et al, 2020).
Seafloor pressure observation is expected to be an effective tool for shallow SSE observation because it enables
long-term continuous observation of the vertical movement of the Earth’s surface just above the shallow boundary of the plate. Crustal deformation due to an SSE off
Hikurangi in 2014 was observed by both the terrestrial
geodetic network and a network of autonomous ocean
bottom pressure recorders (OBPRs), indicating that theslip extended close to the trench axis (Wallace et al.,2016). Seafloor pressure observations are thus being conducted in several locations globally (Davis et al., 2015;
Fredrickson et al., 2019).
The main purpose of the S-net is to detect offshore
tsunamis, and it has thus far provided important information concerning various tsunami events (Kubota
et al. 2021a, 2021b, 2022). Kubota et al. (2020) detectedtsunamis with a wave height of less than 1 cm that weregenerated by a local M 6.0 earthquake just below the network, indicating the high resolution of S-net pressure
observation in a short-period band of less than 1 h. If thesensitivity to water pressure changes, such as those associated with SSEs, remains constant over a longer period
and is as high as it is in the tsunami frequency range,
we can expect SSEs to be detected from pressure dataobtained continuously over longer periods by the broadseafloor pressure monitoring network. Seafloor pressure gauges sense vertical changes in the elevation of theseafloor after removing fluctuations due to the motionof the overlying oceans and atmosphere (Bürgmann andPage 2 of 18

Chadwell, 2014; Wilcock et al., 2021). OBPRs, which arecapable of continuous observation for 1 to 2 years, havethus far been used for SSE detection (e.g., Ito et al., 2013;
Wallace et al. 2016). However, OBPR observations arelimited with respect to both period and spatial coverage.
Observation data from a wide-area multi-point observation network are expected to provide a more comprehensive picture of SSE activity. Suzuki et al. (2016) reported
on a possible shallow SSE based on the pressure datathat were obtained from the Dense Ocean floor Network
system for Earthquakes and Tsunamis (DONET), which
is deployed along the Nankai Trough. In this paper, thequality of S-net pressure records obtained at lower frequencies than those focused upon in tsunami observations was evaluated and the possible detection of crustal
deformation resulting from shallow SSEs was discussed.
This study focused on the power spectrum of the S-net
pressure data to investigate the characteristics over awide frequency range and compare them with OBPR datapreviously obtained for the Japan Trench. We found thatthe noise level at many S-net stations was more than 10times higher than that associated with OBPR in the frequency bands of geodetic interest, rendering it difficult to
detect small crustal deformations at the cm level, while
the noise level was at least as high as that associated withdata collected by OBPRs at the remaining 51 stations.
Deformation that was associated with SSE events withmagnitudes > Mw 6 occurring in the vicinity of such quiet
stations is therefore likely to be detected.

2 Data
2.1 S‑net seafloor pressure observation

Although the details of the S-net system have previously
been described by Aoi et al (2020), we reiterate the partthat is related to pressure observation in this section.
S-net consists of 150 seafloor seismic and water pressure stations (Fig. 1). The network is divided into six submarine fiber networks; subsystems S-1 to S-5 along thelandward slope of the trench, and S-6, which is deployedon the incoming plate outside the trenches. The observation equipment is packed into anti-pressure cylindricalhousing that is separated into wet and dry sections. The
pressure sensors are placed in the wet section, filled withfluid and is isolated from seawater by bellows and diaphragm, constructed using flexible materials that allow
equivalency of internal and external pressure. The dry
section contains devices such as seismic sensors, electronic signal amplification and processing units, communication equipment, and power supply. The instruments
at each station belonging to one subsystem are connected
serially via submarine cables, much like the repeaters
used for commercial communication. Observation systems that use this type of geometry are known as inline

Hino et al. Progress in Earth and Planetary Science(2022) 9:73

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more than 1500 m were not buried and just placed on theseafloor.
2.2 Characteristics of S‑net data

Fig. 1 Map showing distribution of the observation points(stations). Circles indicate S-net stations and are colored according tosubsystems. Squares show locations of OBPRs deployed from 2008
to 2019. Not all stations were operating simultaneously. Diamonds
denote stations in the TM system. Crosses are seafloor benchmarksin the GNSS-Acoustic geodetic survey. Epicenters of tectonic tremors(Nishikawa et al., 2019) are plotted as gray dots. Water depth contours
are in 500-m intervals

systems, and a similar structure is used in many othercable-based submarine earthquake and tsunami observation systems in Japan (Kanazawa and Hasegawa, 1997;
Hirata et al., 2002).
As the location where the instruments are installed
is an active trawl fishing area, instruments were placed
beneath the seafloor in water at depths of up to 1500 m,
which is the operational range for trawling. The instruments were buried using a plow-type burial machine,which is also used for laying commercial submarine
cables, and covered by soft sediments just below the seafloor to a thickness of several tens of centimeters. Meanwhile, the instruments at the stations in water depths of

The sensor, Paroscientific 8B7000-2–005 or 8B80002–005, provides continuous recording of pressure andtemperature at a sampling frequency of 10 Hz. To investigate the nature of the seafloor pressure data for the
purpose of detecting crustal deformation, continuous
data comprising 1-h samples for the period from the
beginning of observation in May 2016 to June 2022 weregenerated and analyzed. Power spectra for all 150 stations were obtained, allowing us to attain an overall picture of the characteristics obtained by S-net. The spectra
were obtained using a moving 4096-h time window thatwas shifted 24 h, and the median value was taken as therepresentative spectrum for each individual observation station. An example of an obtained power spectrais shown in Additional file 1: Fig. S1a. Significant diversity was observed in the power spectra for the different
stations (Additional file 1: Fig. S1b); thus, a probability
density distribution of the power spectrum was createdto understand the characteristics of this diversity (Additional file 1: Figs. S1c and Fig. 2a). The results show that
the S-net stations can be classified according to the characteristics of the pressure data in the frequency domain.
The power spectra show broad distribution at the lowest frequency. To observe the variation in power forthe lower frequency components, root-mean-square(RMS) amplitudes of the pressure records were obtainedby applying a low-pass filter with a cutoff frequencyof 1.39E-3 cph (cycles per hour) or a period of 30 d,
3.86E-7 Hz (1 cph = 2.78E-4 Hz). The inherent sensor
drift in the pressure sensors is a well-known cause oflong-period variation (Watts and Kontoyiannis, 1990;
Polster et al., 2009). Therefore, the RMS was calculated
after the drift, expressed as exponential plus linear function of time, and subtracted from the filtered waveform.
Figure 3a shows the difference in the RMS for pressure
data obtained at all S-net stations. Considering that 1 hPa ofwater pressure change is roughly equivalent to 1 cm of vertical seafloor motion, it would be difficult to detect crustal
deformation at stations where the RMS is > 10 hPa or 10 cm.
Figure 4a and 4b shows examples of pressure records withlarge RMS. The records from station ’a’, indicated in Fig. 3a(Fig. 4a) showed annual variations with large amplitudes
that are highly correlated with changes in the temperature,
whereas irregular fluctuations were observed in the records
from station ’b’ (Fig. 4b). These fluctuations were not correlated with temperature variation and were suspected tobe due to the mechanical instability of the instruments thatare associated with pressure sensing. The S-net pressureHino et al. Progress in Earth and Planetary Science(2022) 9:73

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Fig. 2 Probability density of S-net pressure power spectra. a Raw pressure data. b Temperature-corrected pressure data. Curves ‘a’ to ‘e’ are thepressure spectra at the corresponding stations shown in Fig. 3aFig. 3 Noise level of S-net stations defined by various quantities. a Root-mean-square (RMS) amplitude of long-period (longer than 30 d)component. RMS was calculated after the drift, expressed as exponential plus linear function of time, was subtracted from the filtered waveform.
Pressure power spectra and pressure/temperature records obtained at stations indicated as ‘a’ to ‘e’ are shown in Fig. 2 and Fig. 4, respectively. b
Logged power ratio (LPR) before temperature correction. c LPR following temperature correction. LPRs are calculated from 24 to 720 h in period

data also suffered from other factors that may reduce longterm stability, such as offsets due to strong ground motions
that are irrelevant to the static displacement resulting fromfault motions (Kubota et al., 2020), suggesting that it is difficult to detect long-term fluctuations exceeding one monthfrom the S-net pressure data.

Hino et al. Progress in Earth and Planetary Science(2022) 9:73

Focusing on frequency bands that are higher than 0.001
cph or for periods of < 1000 h, there are two prominent
peaks in the probability density of the spectral shape(Fig. 3a). One peak lies around the lowest power level inthe entire spectrum, and we classified stations with thispeak as Group 1. The other peak is located at a power
level of approximately a couple of hundred times higher
than that observed in the results of Group 1. Stations
with this peak comprised the majority of the S-net stations and were classified as Group 2. A few other stations demonstrated much higher power than the average
power observed in Group 2.
An example of the records from a station in Group 1(’c’) is shown in Fig. 4c. The RMS for the long period was
4.5 hPa, which is one of the lowest among all stations.
Although the record at station ’a’ (Fig. 4a) has a large,
long-period RMS (110.2 hPa), its power spectrum wasclose to that of Group 1 at high frequencies. The power
spectrum was quiet in the short-period band, but rapidly
and abruptly increased in the long-period side.
Examples of waveforms obtained at a Group 2 station(’d’) and a station with much higher power (’e’) are shownin Fig. 4d and 4e, respectively. The pressure fluctuations
obtained at these stations may have a clear correlation
with temperature changes.
Long-period instability can be expected to be removed
as linear trends for periods of less than one month orthereabouts (~ 720 h). If the level of fluctuation within
this period is small, it may be possible to detect shortterm transient signals such as those caused by short-term
slow slip events, even at stations with large, long-period
fluctuations such as station ’a’.
The power spectra of the S-net observations were compared with those obtained by OBPRs, which have been
proven to be sufficiently quiet to detect small tectonic
signals (Ito et al., 2013; Hino et al., 2014; Wallace et al,2016). The OBPR records are expected to more accurately
elucidate the actual pressure variation on the seafloor
because OBPR sensors are directly exposed to seawater.
The probability density distribution of the OBPR power
spectrum using records obtained from 122 OBPRs, whichhave been deployed since 2008 by Tohoku University, isshown in Additional file 2: Fig. S2. All deployed OBPRs
were equipped with pressure sensors in the Paroscientific8000 series, with specifications identical to those used in
S-net. The time window for spectral estimation was set
to 2048 h because of the short observation period overwhich the OBPRs function. The shape of the power spectrum was stable with little variation although the OBPRs
were deployed at various times and locations. Therefore,
the median value of the OBPR power spectra can be
regarded as the standard for seafloor pressure changes inthis area. Superimposing the median spectrum onto the

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probability density of the S-net power spectra (Fig. 2a)
indicates that almost all of the S-net data are much noisier than the average OBPR data in all frequency bands,
and this difference may be due to noise that is inherent in
the S-net data.
As an indication of the quality of the S-net data, thelogged power ratio (LPR) was calculated as follows:
N
 
 
1 
log10 PkS - net fi − log10 P OBPR fi
N
i=1
(1)
 
S - netwhere Pkfi represents the pressure power  at the kth
S-net station, ith frequency band; P OBPR fi represents
the median of the OBPR spectra at the ith frequency
log10 PkS - net fi − log10 P OBPR fi represents
band;
the deviation of the S-net logged power from the OBPR
logged power at the ith frequency band; and LPRk represents the mean of the deviations in the frequency range(i = 1, N), namely from 1.4E-3 to 2.1E-2 cph or from 24
to 720 h.
The LPRs of the data from the Group 1 stations are
distributed over a range of < 1. Compared to the OBPR
data, the pressure data obtained at these stations differ bya factor of 10 in terms of power, or by up to a factor of
3 in amplitude, and may thus be useful for detecting oftransient tectonic signals. Figure 3b shows the LPRs for
all the S-net stations, and it is apparent that several stations with small LPRs are located near zones with active
tectonic tremor.

LPRk =

3 Results
3.1 Reduction in temperature dependence

As apparent in the pressure and temperature records
in Fig. 4, high correlations were observed between thepressure and temperature variations. Histograms of thecross-correlations and the lag times that produce themaximum correlations are shown in Fig. 5. Lag (h) is positive when the pressure record appears to result from atemperature lag. The cross-correlation coefficients were
nearly 1 at most stations. It should be noted that negative
lag times dominated the results. The clear peak at ~ –8 hindicates that changes in temperature lead to pressurechanges after ~ 8 h. Such significant temperature correlations were not observed in the OBPR data and are considered to be inherent in S-net records.
It is unlikely that inaccurate temperature compensation for the pressure sensor output accounts forthe high correlation. If it were, the time lag would beshorter. The temperature-dependent pressure variation would be in the form of mechanical noise resulting from the structure of the observation device. Since
the correlation seems to be more prominent at noisierstations (Fig. 4), we can assume that the dependenceHino et al. Progress in Earth and Planetary Science(2022) 9:73

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Fig. 4 Examples of pressure (black) and temperature (red) records. Typical examples with different pressure change characteristics areshown. a Example of large periodic fluctuations. b Example of slow and large irregular variations. c Example of small-amplitude fluctuations. dModerate-amplitude high-frequency fluctuations. e Large-amplitude high-frequency fluctuations. Subpanels a–e) are records at stations ‘a’ to ‘e’ inFig. 3aof pressure fluctuation on temperature changes is the
major source of noise in the S-net pressure data. If it
can be eliminated, the signal-to-noise ratio of the pressure data may be improved.
To reduce the effect of temperature variation, prediction filtering was applied to the pressure and temperaturerecords. A filter that predicts the apparent temperaturedependent pressure variation from the temperature recordand subtracts the output of the filter from the pressurerecord was expected to remove any noise resulting fromtemperature disturbances. We assume that the observedpressure fluctuation consists of the sum of the apparent
pressure fluctuation and the true pressure fluctuation:p(t) = p̂(t) + p′ (t, T )(2)where p(t) is the observed value, p′ (t, T ) is the apparent
pressure fluctuation due to the temperature disturbance,and p̂(t) is the true pressure fluctuation.
We further assume that the apparent pressure variation can be obtained from the temperature time series
T (t) by applying filter F:

p′ (t, T ) = F (t) ∗ T (t).

(3)

Here, the asterisk denotes convolution. OBPR observations indicate that the actual seafloor pressure does
not correlate with temperature. Therefore, the equation
below can be used to estimate the filter coefficients by
the least-square method.

F (t) ∗ T (t − τ ) = p(t).

(4)

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Fig. 5 Histograms of a normalized cross-correlations between pressure and temperature, and b lag times of pressure changes following
temperature changes

Note that time shift τ (< 0) needs to be applied to ensurecausality in the S-net data because p(t) leads to T (t) lag.
Once a filter that can predict the apparent pressure variation from temperature is obtained, the true pressure variation can be determined using the predicted error and isexpressed using the following equation:p̂(t) = p(t) − F (t) ∗ T (t − τ ).

(5)

Since the filter estimation is equivalent to the divisionin the frequency domain,
 
 
P f
F f ∝  ,
(6)
T fthe filter coefficientscan diverge if the temperature spec trum T f is much smaller than pressure spectrum P f
in a certain frequency range. In such cases, a component
proportional to the time-shifted temperature T (t − τ ) is
subtracted from p(t).
To evaluate the effect of the temperature correction
using least-square filtering, the corrected S-net pressure records were compared with the pressure record
obtained by an OBPR located ~ 4 km from station ’c’(Fig. 6). The LPR which was 0.50 before the temperaturechange decreased to 0.28 as a result of the temperaturecorrection. Although there is a high similarity between
the corrected waveform and the OBPR waveform, thelong-period component is not in good agreement.
However, we found that the similarity increased after aband-pass filter that covered the 48–720-h period component was applied to both this station and the S-net
data following temperature correction.
Figure 2b shows the probability density of the power
spectra obtained by applying the temperature correction to the results from all stations. The power was
significantly reduced for stations in Group 2, to whichmost S-net stations belong. The Group 1 stations also
showed improvement, as demonstrated in the above
example (station ’c’), and the noise level was significantly reduced by removing the components correlatedwith temperature for many of the stations. However,
the gap between Groups 1 and 2 remains, although it
has been reduced. In addition, at stations where longperiod irregular variations that do not correlate withtemperature predominate [e.g., station ’b’ (Fig. 4b)],the noise level has increased due to the temperaturecorrection, leading to a relative increase in the frequency of higher power compared to the levels prior tocorrection.
The spatial distribution of LPRs in the temperaturecorrected data is shown in Fig. 3c. Compared to Fig. 3b,
the number of stations with LPR < 1, which is the noiselevel expected for OBPRs, increased from 40 before
the correction to 51 after the correction. However, theLPRs are still > 1 at many stations even after correction,and stations that can detect small tectonic transientsare limited and sparsely distributed along the Japan and
Kuril Trenches.

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Fig. 6 Waveforms of S-net pressure data before (gray) and after temperature correction (black). Red traces show pressure data obtained by the
OBPR located ~ 4 km from a S-net station. a Before application of band-pass filter. b After a pass-band filter was applied for 24 to 720 h

3.2 Reduction in common‑mode noise

Examples of the temperature-corrected records of stations with a LPR < 1 are shown in Fig. 7a. As data gaps
can introduce noise, time periods were selected in which
continuous records from all stations with a LPR < 1 wererecorded without any data gaps. Although a significant
variation was observed in the noise level among all stations, the temperature-corrected time series shows acoherent component attributed to pressure disturbancesof a non-tidal oceanographic origin. Several methods
have been proposed to reduce such disturbances in order
to increase the detectability of tectonic signals in theseafloor pressure data. Examples include a deterministic approach in which the seafloor pressure fluctuations
calculated by ocean circulation models were subtracted
from the results of observation (Inazu et al., 2012; Muramoto et al., 2019; Dobashi and Inazu, 2021), and estimation using obtained auxiliary oceanographic observations(Watts et al., 2021). Another is to find a proxy of theoceanographical fluctuation using a combination of pressure observations obtained in different locations. Here,
we try to apply the latter approach.

One method that is often used for common-mode
noise reduction is to use the pressure difference from areference station (Ito et al., 2013) located far from thesource location of the tectonic event representing theoceanographic signals. Wallace et al. (2016) set a reference station on the incoming plate side of the trench,where no vertical variations were expected, to detect an
SSE signal in the OBPR data distributed on the landward
slope. Fredrickson et al. (2019) and Inoue et al. (2021)
showed that the non-tidal oceanographic fluctuations
tend to be coherent among the sites located at stations
with similar water depth and pointed out the advantage
of using common-depth station pairs to obtain pressure
differences with reduced noise.
Records that were obtained from stations on theincoming plate and landward sides with similar water
depths were extracted from the high-quality S-net
records obtained at 51 quiet stations (LPR < 1 after thetemperature correction) in Fig. 7a and are displayed inFig. 7b. The waveforms at stations 3–20 and 4–22 on the
landward side of the trench were notably similar; however, few correlations were observed between the otherHino et al. Progress in Earth and Planetary Science(2022) 9:73

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a)

b)

hPa
300

S1

140˚

144˚

146˚

5-05

0

42˚

142˚

0

0
-200

S2

4-22

40˚

0

-600

3-20

-2
00
0

38˚

S3
hPa
50

150

S4

40

c)

2-06
2-21

36˚
0

200

00

0

-60

-4000

250

1-07

6-17

1-07
2-21

30

2-06
3-20

50

S5

20

4-22
5-05

S6

10

6-17

0
0

Fig. 7 a Pressure records after the temperature correction at stations with LPR < 1. b Station distribution. c Traces of selected stations close to thedepth contour of 4000 m and a station on the incoming plate. Locations of selected stations are highlighted in b

stations. S-net does not provide a high degree of freedom
in the combination of stations used for common-mode
noise reduction via pressure difference. The difference
between the records from stations 3–20 and 4–22, withrelatively high similarity, was therefore investigated totest the theory, and we found that the RMS of the pressure data at station 3–20 was 1.14 and that at station
4–22 was 1.25, showing a reduction of 1.02 hPa.
Hino et al. (2014) showed that the common-mode
noise can be reduced by subtracting the first principal
component obtained by principal component analysis(PCA) without the use of pressure differences from areference station. Similarly, we attempted to remove thecommon-mode noise in the S-net data in the same way.
In applying PCA to the S-net data, it should be noted thatthe noise level varies greatly across stations. Here, we
performed PCA weighted by the inverse of the variancesof input temperature-corrected pressure data. Additional
file 3: Figure S3 shows the results of PCA using all therecords shown in Fig. 7a. The common-mode variations
were reduced by subtracting the estimated first principal

component. To evaluate the effect of PCA-based noise
reduction, we determined the reduction rate of RMSs at
all the stations and calculated their median, which was
81%. At stations 3–20 and 4–22, where we attempted toreduce the common-mode noise by taking pressure differences, the RMS decreased from 1.14 to 0.82 (72%reduction) and from 1.25 to 1.07 (86%), respectively.
From Fig. 7a, the non-tidal oceanographic component
was not necessarily coherent over a wide area, and thecorrelation of waveforms decreased with increasing distance between stations. We, therefore, expected the noise
reduction using PCA to be more effective if the rangeof stations used was limited to a relatively narrow area.
Below, we applied the PCA-based common-mode noise
reduction to the pressure records obtained at 13 quiet
stations belonging to the S-4 system in the northern partof the Japan Trench. We chose these stations because
their number and density of quiet stations were the largest in the region (Fig. 7b).
Figure 8a shows the temperature-corrected pressurerecords and the first principal components obtained

Hino et al. Progress in Earth and Planetary Science(2022) 9:73

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142˚

a)

41˚

hPa

1st PC
40

40

145˚

07
14

16
40˚

144˚

03

02
15

b)
hPa

143˚

18 19 20

17

21
4-22

27

4-02
4-15
30

30

4-16
4-17
4-03
4-14

20

20

4-18
4-27
4-19
4-20

10

10

4-07
4-21
4-22

0

0

Fig. 8 a Pressure records after correction with LPR < 1 at stations belonging to S-4. Traces are colored according to the depth at which stations arelocated. Thick, red trace at the top is the first principal component (1st PC) obtained by PCA. b Pressure records after subtracting the 1st PC

from the temperature-corrected pressure records at the
S-4 quiet stations selected from Fig. 7a. The color of the
traces changes according to the depth of the stations,and it is apparent that the correlation was high between
stations at similar depths, whereas the similarity of the
waveforms decreased when stations at different depths
were compared. Figure 8b shows the pressure records
after the contribution of the first principal component
was subtracted. The median of the RMS reduction rate
was 66%, indicating a better performance when using
stations within a narrow subarea than that when using
broad network data. However, the noise reduction rate at
station 4–22 was 89% (from 1.25 to 1.11), slightly worse
than that after the noise reduction using broad networkdata.
One possible reason for the poor performance at thestation can be the water depth dependence of waveform

similarity. Station 4–22 was the deepest one among thequiet S-4 stations, the only station deployed at ~ 4,000 m
depth, whereas six more stations located at depths similar to 4–22 were included in the PCA using all the quiet
stations. The water depth-dependent components would
be extracted as principal components of second or higher
orders. However, subtracting the second principal component did not substantially reduce the RMS values. The
reduction rates between the records after removing thefirst component and those after removing the first andsecond components were 96% and 86%, when applied to
all the quiet stations and to the S-4 stations, respectively.
The high level of instrumental noise likely remained in
the record even after the temperature correction, andthe noise hinders the extraction of depth-dependent
components.

Hino et al. Progress in Earth and Planetary Science(2022) 9:73

4 Discussion
4.1 Processed OBP records describing short‑term SSEs

The S-1 subsystem of S-net is located off the Boso peninsula, where SSEs occur on a regular basis. The significant
crustal deformation that was associated with an event
in June 2018 was captured by terrestrial GNSS observations (Ozawa et al., 2019). An event at almost the same
location also occurred in 2014, and Sato et al. (2017)
reported that associated vertical seafloor movementof ~ 2 cm was detected by OBPR observations. According to Ozawa et al. (2019), the event in 2018, which was
the first following deployment of the S-net, was larger
in scale than that in 2014, and the seafloor displacement
should have been captured by the S-net seafloor pressure

Page 11 of 18

observations. The records of the four S-net stations closest to the SSE source estimated by Ozawa et al (2019),
with small LPRs (1–07: 0.67, 1–08: 1.47, 1–11: 1.03, 1–22:
1.23) following temperature correction and common
component removal by PCA, are shown in Fig. 9. PCA
was performed on the records of four stations. The RMS
amplitude of the OBPR records was evaluated to be 1 hPa
when Sato et al. (2017) observed the crustal deformation associated with the 2014 event. An RMS of 3.10 hPa(5.2 hPa before common-mode reduction) was observedin the post-processing record for 1–12, which is closest to
the epicenter; however, the high noise level of the S-net
pressure data rendered it difficult to detect the tectonic

Fig. 9 S-net pressure records during 2018 Boso SSE. Records at four relatively quiet stations (indicated by colored circles in the inset) are shown.
Records at other noisy S-net stations (shown in open circles) are not shown. Three components terrestrial GNSS data are also indicated. Notethat vertical component is flipped in sign so that positive change means subsidence and is equivalent to a pressure increase on the seafloor. Slip
distribution (Ozawa et al., 2019, contours in cm) is shown in the inset

Hino et al. Progress in Earth and Planetary Science(2022) 9:73

signals corresponding to the 2018 SSE, although it waslarger (Mw 6.8) in scale than the 2014 event (Mw 6.5).
It has been pointed out that the SSEs comprise thebackground of the increased activity that is associatedwith tectonic tremor in many subduction zones. Since
tremors occur constantly in the northern Japan Trench
region where subsystem S-4, which includes several quiet
stations, is located, we investigated whether any significant fluctuations associated with tremor activity can beobserved in the S-net seafloor pressure records. The target period of August 2016 to August 2018 was selected
because tremor activity has been reported by Nishikawa
et al. (2019) for some of this period. We focused on thedata at station 4–22, which was closest to the tremor
area and has the lowest LPR among the S-4 stations. As
in the previous section, PCA analysis and calculation of
the pressure difference from a reference point were used.
Since an anomalous large fluctuation was observed in the

Page 12 of 18

data prior to October 2017 at 3–20, which is the reference point for differential pressure, only the differential
pressure after this date was used. The resulting waveforms are shown in Fig. 10. The RMS of the records for
4–22 was 1.10 hPa following noise reduction with PCA
using the S-4 data set, and the RMS amplitude for thedifferential pressure record was 1.41. We compared thetemporal changes of the tectonic microtremor activity
with the processed records but could not find any change
in the tectonic microtremor activity that could be associated with increases in tremor activity. Although the noiselevel was much lower than that of S-1 off Boso, the scaleof the SSE-associated tremor bursts occurring in this area
is much smaller than that of the Boso SSEs, rendering it
difficult to detect such transient tectonic events using
S-net.
Hino et al. (2014) discussed the relationship between
the OBPR noise levels and the detection ability of SSE.

Fig. 10 Tectonic tremor activity and S-net pressure records from 2016 to 2018 in the northern Japan Trench. a Cumulative number of tremors.
b Pressure record at station 4–22, the closest station to the tremor swarm. Black: Temperature-corrected trace. Red: Trace after common-mode
reduction using PCA. Orange: Pressure difference from station 3–20

Hino et al. Progress in Earth and Planetary Science(2022) 9:73

They reported RMS amplitudes of ~ 1.5 hPa for the analyzed OBPR records, which were reduced by ~ 0.5 hPa
to ~ 1.0 hPa following PCA-based noise reduction. They
further estimated the lower detection limit of the slip
events by considering the noise level of the OBPR records
and concluded that events of Mw 6.0 or larger that occur
on shallow plate boundaries near the trench can bedetected by nearby OBPRs. The RMS amplitude at station 4–22 was comparable to those of the OBPRs, andwe therefore assume that the station has the same levelof detection capability for tectonic transients. Therefore,possible SSEs that yield repeating tremor bursts in thenorthern Japan Trench would not be significantly larger
than ~ Mw 6, the possible size of detectable SSEs taking
place immediately below the quiet S-net stations.
Honsho et al. (2019) suggested that an SSE occurredalong the shallow subduction interface in the northern
Japan Trench in 2015, prior to the S-net deployment,
based on small repeating earthquakes and seafloor horizontal motions observed using GNSS-A. The source
location is located within the coverage of the S-4 subsystem and its magnitude is estimated to have been Mw
6.5. If an SSE of similar magnitude were to occur in the
future, S-net would certainly be able to detect the crustal deformation. The vertical motions obtained by S-net,
together with the horizontal displacements obtained by
the GNSS-A, will thus play an important role in constraining the source model of SSEs.
As a case study, we examined the detectability of crustal
deformation in a simple manner, focusing on two regions.
For events that are likely to occur repeatedly, such as thosein the northern Japan Trench, significant crustal deformation could be identified by stacking the noisy data referring to the timings of tremor burst events (e.g., Frank et al.,2015). However, owing to the high noise level, accumulating data to increase the number of stacking is important.
To improve the detection of tectonic signals related to
SSEs, it is also necessary to improve the performance of
reduction in common-mode variations originating from
non-tidal oceanographic fluctuations. It is essential tounderstand the spatiotemporal characteristics of thecommon-mode components, and comprehensive studies
performed by changing the combinations of the used forthe analyses will be an important subject. Milliner et al.
(2018) discussed the superiority of independent component analysis (ICA) over PCA when it is applied to thedecomposition of components with non-Gaussian distribution. Fluctuations of seafloor pressure are likely tofollow non-Gaussian distribution, and application of ICA
to the pressure data obtained by the seafloor network is
worth investigating in the future.

Page 13 of 18

Based on our evaluation, a third of the S-net stations
were as quiet as the OBPR observations and can be used
for monitoring the SSE activity in the region. Considering the uneven distribution of the station and large variation in noise levels across stations, pragmatic assessmentof detectability based on numerical modeling is anotherimportant scope for future study.
4.2 Characteristics of seafloor temperature data

As the noise level of S-net was greatly reduced by thetemperature correction, we expected that the noise levelof the pressure data is strongly related to the temperature
variation. Here, we examine the power spectrum of thetemperature data.
The most significant influence on the characteristics oftemperature variation observed by S-net is the location
at which the instruments were deployed on the seafloor.
Instruments are covered by sediments and are thus notin direct contact with seawater at depths shallower than
1500 m; thus, the temperature environment is significantly different from that of instruments that are not buried. The significantly higher mean temperature of ~ 10 °C
for buried stations is due to the effects of the insulating
sediment cover. Self-heating of the observation equipment accounts for the significantly high temperatureobserved at the buried stations. In a buried environment,
the generated heat is retained and not transferred to theseawater effectively.
The power spectra of the buried stations and the stations exposed to seawater are shown in Fig. 11a and b,
respectively. The spectra for the buried stations show asteep slope, reflecting the suppression of short-periodtemperature changes because of the thermal insulation.
The power of the temperature spectrum is very low in
the frequency band in terms of the LPR, and the temperature-correlated noise is expected to be small in theburied stations. The LPR tends to be smaller at stations
shallower than 1500 m in Fig. 3b.
The spectra of the unburied stations have smaller falloff slopes and higher temperature fluctuation levels thanthose of the buried stations. Although the temperature
variation tends to be greater at stations located at shallower depth, no significant depth dependence is observedin the LPR distribution (Fig. 3b). The power spectra of thetemperature data obtained by the OBPRs are superimposed in Fig. 11. Unlike the pressure data spectrum, the
OBPR spectral shape is not significantly different fromthat of the unburied S-net stations. This means that selfheating has little effect on the temperature data obtainedat unburied stations.

Hino et al. Progress in Earth and Planetary Science(2022) 9:73

Page 14 of 18

Fig. 11 Power spectra of temperature data at S-net stations. a Buried stations. b Unburied stations. Dot colors show the difference in station
depths. Thick black line shows the median of the OBPR spectra and dotted lines are 25 and 75 percentiles. Blue denotes the average from TM
stations

Hino et al. Progress in Earth and Planetary Science(2022) 9:73

4.3 Possible mechanism of temperature‑correlated noise

The temperature-correlated noise, a major reason for thelarge noise level in the S-net pressure observations, may
be a result of the actual structure of the S-net observation system. The noise character is very similar to that ofthe pressure records obtained by the off-Sanriku cabled
system (Inazu and Hino, 2011), hereafter the TM system.
The TM system was also designed as an “inline system,”and the structure of the observation unit was almost
identical to that of S-net. The shape of the pressure power
spectrum for the TM system was in the range of the spectra obtained for Group 2 in this study, indicating similarity to most S-net stations (Additional file 4: Fig. S4). The
shape of the temperature spectrum was also similar tothat of the unburied S-net stations (Fig. 11). The correlation between the pressure and temperature data obtainedby the TM system and calculated in the same manner as
the S-net data was very high (cross-correlation ~ 0.9) anda negative (–2 h) lag time was also observed. The strong
dependence of the TM system on pressure data has
already been pointed out by Inazu and Hino (2011). As
indicated by Baba et al. (2006) and Itoh et al. (2019), thecabled system that was deployed off Hokkaido, anotherinline system, also showed a high correlation between
pressure and temperature.
In contrast, there were no significant correlations
between the pressure and temperature records obtainedby the OBPR deployed in the Japan Trench, as pointed
out earlier. Gomberg et al. (2019) investigated the relationship between seafloor pressure and temperatureobserved in the Hikrangi subduction zone, New Zealand,
using the instruments of almost identical structure with
the OBPRs deployed in Japan. Although they pointed
out small correlations in time scale of ~ 10 d, the correlations were insignificant at lag times ~ 0 d. This report isconsistent with our OBPR observations, but completely
different from the characteristics identified in the S-net
data, or in other inline observation systems.
Based on the similarity among the data obtained for
inline systems, we suggest that the correlation between
the pressure and temperature records is related to themechanical structure of the inline system. The sensors
comprising the inline system are not in direct contact
with seawater, and bulkheads constructed using flexible
materials, such as the bellows or the diaphragm, affectthe results. If their motions were smooth, the internalpressure measured by the pressure sensor is expected to
be in equilibrium with the seafloor pressure; otherwise,a pressure differential is created. However, the pressuretransfer is insufficient and the internal and external pressures are not in equilibrium when the bulkheads are notin ideal conditions. Under poor pressure transfer conditions, the internal pressure is affected by the thermal

Page 15 of 18

deformation of the enclosure. This may be why the pressure data correlated with temperature change and qualitatively explains the time lag between temperature andpressure observed by S-net. Pressure responds instantaneously to temperature changes in the enclosure, but themeasured lag in temperature change occurs because thesensors are thermally shielded.
At several S-net stations, sudden and extremely large(> 1000 hPa) pressure increases were observed with nocorresponding change in temperature, indicating that thepressure step is neither due to temperature change nor a
failure in the measurement or data transmission system.
These incremental changes could correspond to events
that have occurred spontaneously in the bulkheads,
eliminating the disparity between internal and externalpressure. The pressure transfer mechanism, including thebulkhead, is composed of several parts made of different
materials. If we assume friction along the contact surfaces accounts for the pressure disparity, the events could
be slips on the surfaces. Some of these pressure steps
were accompanied by a marked decrease in the LPR. In
the case shown in Additional file 5: Fig. S5, the power ofthe pressure signal following the change was reduced to
the level of the OBPR spectrum. We interpret that theevent corresponding to this change improved the pressure transfer performance, thus reducing the noise level.
This observation supports the hypothesis that imperfectpressure transfer is a significant source of noise in the
S-net data.

5 Conclusions
If small vertical crustal deformations can be detectedusing long-term, wide-area seafloor pressure observation data from S-net, significant progress in understanding the SSEs occurring at shallow plate boundaries along
the Japan and the Kuril Trenches can be made. We therefore investigated the data obtained over the 7 years since
S-net started operation in 2016 to ascertain whether the
results obtained are suitable for geodetic application byevaluating the power spectra and correlations with temperature variation. Comparisons with data obtained by
OBPR observations accumulated in the Japan Trench,
which have previously been proven useful in geodetic
studies, were used to characterize the quality of the S-net
data for periods > 2 d, over which geodetic signals are
expected to emerge.
The seafloor pressure data obtained at most S-net stations contained large fluctuations that are > 100-foldthose obtained by OBPRs in terms of power. Owing
to the extremely high noise level, detecting tectonic
transients below the level of a few centimeters, which
are associated with SSEs at these noisy stations, wasdifficult. The noise in the pressure data is strongly

Hino et al. Progress in Earth and Planetary Science(2022) 9:73

correlated to temperature, which was simultaneously
observed at the same station. Although no significant
pressure–temperature correlations were identified in
the OBPR data, a high correlation has been reported
in previous studies and was confirmed in this study forthe data obtained by seafloor-cabled observation systems other than S-net. We suggest that the temperature dependence accounts for the high noise level andmay be caused by the mechanical structure characteristics of the inline systems. Furthermore, we deviseda method to remove the temperature-correlated noise
by applying a prediction filter to the S-net pressurerecords. Although the filter reduced the noise significantly, pressure records at more than half of the S-net
stations still have large fluctuations that are more than
10 times more powerful than those observed in the
OBPR data.
Based on processed records from stations with relatively low noise, we investigated whether any pressurechanges corresponded to the 2018 Boso SSE or to possible SSEs associated with repetitive tectonic tremor
bursts in the northern part of the Japan Trench. The
noise level at the stations near the source of the Boso
SSE meant that we could not detect any meaningfulpressure change associated with the 2018 event (Mw6.5). More than 10 stations have noise levels similar
to, or slightly higher than, those associated with the
OBPRs in the northern part of the Japan Trench. However, no transient changes were detected in the seafloorpressure corresponding to the reported tremor bursts
from 2016 to 2018. Based on previous studies focusing
on detection capability evaluated using OBPR records,
we believe that the S-net can detect geodetic signals in
the northern Japan Trench if SSEs larger than ~ Mw 6
occur in the vicinity of at least one station.
Abbreviations
S-net: Seafloor observation network for earthquakes and tsunamis along theJapan Trench; OBPR: Ocean bottom pressure recorder; SSE: Slow slip event;
DONET: Dense Ocean floor Network system for Earthquakes and Tsunamis;
RMS: Root mean squares; LPR: Logged power ratio; NIED: National research
institute for earth science and disaster resilience.

Page 16 of 18

Additional file 2: Fig. S2. Probability density of pressure power spectra
observed by OBPRs.
Additional file 3: Fig. S3. Pressure records after the temperature correction at stations with LPR < 1 (same as shown in Fig. 7a) with the firstprincipal component (1st PC). The 1st PC is indicated at the top by a thicktrace. b Pressure records after subtracting the 1st PC.
Additional file 4: Fig. S4. Probability density of pressure power spectraby S-net. Medians of OBPR and TM system superimposed onto the S-net
histogram.
Additional file 5: Fig. S5. a Example of S-net pressure (black) andtemperature (red) data. An extremely large step in pressure occurred in
January 2020. b Power spectra of pressure data before (period I) and after
the pressure step (period II).
Acknowledgements
We thank Prof. Roland Bürgmann and an anonymous reviewer and the Editor
Takeshi Iinuma for their review of the manuscript and insightful comments.
We also thank Syuichi Suzuki and Makiko Sato for their assistance in OBPR
observations and data curation and Dr. Shozaburo Ozawa of Geospace
Authority Japan for his kind provision of the geodetic data and the slip model
describing the 2018 Boso SSE. Some figures were created using generic mapping tools (Wessel and Smith 1991). We would like to thank Editage (www.​edita​ge.​com) for English language editing.
Author contributions
RH, TK, and NC proposed the topic and conceived and designed the study.
RH, TK, YO, and HO carried out the experimental study. RH analyzed the dataand helped with data interpretation. All the authors collaborated with thecorresponding author in the drafting of the manuscript. All authors have readand approved the final manuscript.
Funding
This work was partly supported by JSPS KAKENHI Grant Number 19H05596.
Availability of data and materials
The S-net pressure gauge data are available at the Web site of the National
Research Institute for Earth Science and Disaster Resilience (NIED 2019; https://​doi.​org/​10.​17598/​NIED.​0007). The OBPR data obtained by Tohoku University
are available from the corresponding author upon request.

Declarations
Competing interests
The authors declare that they have no competing interests.
Author details
1
Graduate School of Science, Tohoku University, 6‑6 Aramaki‑Aza‑Aoba,
Aoba‑Ku, Sendai, Miyagi 980‑8578, Japan. 2 National Research Institutefor Earth Science and Disaster Resilience, 3‑1 Tennodai, Tsukuba, Ibaraki
305‑0006, Japan.
Received: 8 September 2022 Accepted: 24 November 2022

Supplementary Information
The online version contains supplementary material available at https://​doi.​
org/​10.​1186/​s40645-​022-​00526-y.
Additional file 1: Fig. S1. a Example of power spectra obtained using
data from a S-net station. Spectrum fluctuations over time at single
stations indicated by the scattering of gray lines. Black line indicates themedian and defines the representative shape of the power spectrum forthe station. b Representative power spectra for all S-net stations. c Histograms showing power spectra of the 150 stations shown in b. Probability
density defined by normalized frequency is shown according to the color
code.

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