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“N”shaped Y/X coda spectral ratio observed for inlinetype OBS networks; Snet and ETMC: interpretation based on natural vibration of pressure vessel
Earth, Planets and Space volume 72, Article number: 130 (2020)
Abstract
We have identified “N”shaped Y/X amplitude spectral ratios in Scoda records from a significant number of OBSs (ocean bottom seismometers) belonging to inlinetype ocean bottom networks of Snet and ETMC deployed around the Japan Trench and Sagami Trough, respectively. The “N”shape reflects a sharp peak and notch at approximately 5–13 Hz and 10–23 Hz, respectively. This shape does not characterize OBSs belonging to nodetype ocean bottom network of DONET deployed near the Nankai Trough. For Snet stations, the “N”shape is not clearly formed for stations installed within grooves dug in the seafloor. We interpret the “N”shaped Y/X amplitude spectral ratio is caused by the natural vibrations of a cylindrical pressure vessel that is placed sideways (longaxis lies in the horizontal plane) on the seafloor. The notch and peak frequencies in the Y/X amplitude spectral ratio likely correspond to natural frequencies of longitudinal (Xdirection) and torsional and/or bending (Ydirection) vibrations, respectively. These natural vibrations are not observed for buried OBSs or those installed within grooves in the seafloor probably because they are better coupled to the seafloor. We propose a simple model to evaluate the extent to which the peak and notch have formed, which depends on the natural frequencies and coupling of the pressure vessel. We suggest users of inlinetype OBSs carefully examine if there are different responses between the X and Y components when frequencies about > 3 Hz are used. When installing OBS networks in the future, installing OBSs and cables within grooves dug in the seafloor or by burial will be effective in suppressing such natural vibrations.
Introduction
After the 2011 TohokuOki earthquake (M_{W} 9.0) and tsunami, which resulted in at least 18,000 dead and missing people, National Research Institute for Earth Science and Disaster Resilience (NIED) installed the Seafloor Observation Network for Earthquakes and Tsunamis (Snet) along the Japan Trench (e.g., Kanazawa et al. 2016). Snet was designed to detect tsunamis and earthquakes much earlier than existing seismic networks. It was also expected to provide valuable data that may advance marine seismology. The Snet records have already produced new discoveries, such as nonvolcanic tremors (e.g., Tanaka et al. 2019; Nishikawa et al. 2019) and small tsunamis (e.g., Kubota et al. 2020) that have not been detected by land or coastal observations.
Since ocean bottom seismic observations are different to land seismic observations in many ways, problems specific to ocean bottom observations should be shared as much as possible. For example, Takagi et al. (2019) measured the orientation of threecomponent seismometers in Snet using DC offsets and farfield waveforms from accelerograms. This showed that, unlike land seismic observations, the orientations of Snet seismograms require correction with respect not only to azimuth but also the tilt and rotation angles of the installed pressure vessel. Nakamura and Hayashimoto (2019) detected a significant change in the DC offset before and after strong ground motion in inlinetype OBSs installed at SanrikuOki, Japan. This change was interpreted to reflect rotation of the pressure vessel due to decoupling from the ocean bottom during the strong ground motion. Using seismograms affected by such rotation may lead to an overestimation of earthquake magnitude.
These issues are related to the asymmetric shape of the observation system that is specific to inlinetype OBS networks, and insufficient coupling with the seafloor. Given these factors, the two horizontal components from inline type OBSs may respond to incident waves differently. Previous studies have examined this issue by polarization analysis of artificial shots (e.g., Woje et al. 2002; Bagaini and Muyzert 2004; Landschulze and Mjelde 2014). However, artificial shots are too expensive to be applied to a largescale seismograph network such as Snet, and can also have a negative impact on the environment. Noise records can also be used to evaluate the response of the two horizontal components (e.g., Landschulze and Mjelde 2016). However, the noise wavefield itself typically has polarity in the oscillation direction due to contamination of various types of waves such as Rayleigh waves and Twaves (e.g., Ardhuin et al. 2019). Therefore, it is difficult to resolve responses specific to installation from the natural properties of noise.
In this study, we examined the difference between the amplitude spectra of two horizontal components recorded by OBSs using Scoda waves in seismograms. Figure 1 shows examples of amplitude spectral ratios of an Scoda wave amongst the three components (Y/X, X/U, and Y/U) observed at Snet stations N.S1N01 and N.S6N14. Hereafter, the X, Y, and U components correspond to directions along the cable axis (horizontal), perpendicular to the cable axis (horizontal), and vertical, respectively. For N.S1N01 (Fig. 1b), the amplitude spectral ratios of X/U and Y/U are similar and Y/X is close to unity from 0 to 30 Hz. This behavior is typical for an Scoda wave because it is composed of multiply scattered Swaves and the oscillation direction is, in theory, horizontally isotropic (e.g., Sato et al. 2012) unless strong horizontal anisotropy exists below the seafloor. However, for N.S6N14 (Fig. 1d), the amplitude spectral ratios of X/U and Y/U show peaks at different frequencies (i.e., 18 and 7 Hz), and Y/X shows a notch and peak at these frequencies, respectively. As a result, the Y/X amplitude spectral ratio shows an “N”shape. In fact, such an “N”shaped Y/X amplitude spectral ratio has been observed from many Snet OBSs. Related observation was reported by Hayashimoto et al. (2016) from inlinetype OBSs installed at KushiroOki, Japan, where the spectral amplitude of the Xcomponent is much larger than the Ycomponent at frequencies of > 10 Hz.
We examined the Y/X amplitude spectral ratios of Scoda waves from Snet seismograms, and also those from OBSs of the Earthquake and Tsunami Monitoring Cable (ETMC) installed along the Sagami Trough and the Dense Oceanfloor Network system for Earthquakes and Tsunamis (DONET) installed close to the Nankai Trough. Since these three types of OBS network are different in many aspects, they enable us to identify the cause of the “N”shaped Y/X amplitude spectral ratio.
OBS networks of Snet, ETMC, and DONET
There are two main types of permanent ocean bottom seismic observatory system deployed around the world. One is composed of geophysical sensors integrated into a submarine cable with a power feed and optical fiber, which is sometimes referred to as an “inline system” (e.g., Fujiwara et al. 2010). Stations can be deployed rapidly and for low initial cost by installing the cable into ocean bottom areas from a cable ship without using a remotely operated vehicle (ROV). The other type is a system composed of sensors and science nodes (or junction boxes) that are physically connected or disconnected to a cable by a ROV. This system enables expansion of observatory areas by connecting a new cable to interfaces at the nodes and by adding sensors. Hereafter, we refer to this as the “nodetype” system following Fujiwara et al. (2010). The ETMC (Eguchi et al. 1998) and Snet (Kanazawa et al. 2016; Mochizuki et al. 2016; Uehira et al. 2016) deployed in eastern Japan are classified as the former system, whereas DONET (Kaneda et al. 2015; Kawaguchi et al. 2015) in southwestern Japan is the latter system.
Snet
Snet comprises 150 oceanbottom stations and optical fiber cables installed along the Japan Trench (Fig. 2a). The stations and cables installed at water depths shallower than 1500 m (Fig. 2a) are mostly installed within grooves dug to at least 1 m below the seafloor to avoid the risk of cable damage due to fishing (Kanazawa et al. 2016). Each station is equipped with a velocity seismometer (OMNI2400; OYOGeoSpace), accelerometers, and pressure gauges to monitor earthquakes and tsunamis. All sensors at each station are housed in a cylindrical pressure vessel that is placed sideways on the seafloor (longaxis lies in the horizontal plane). Both ends of the pressure vessel are connected to optical fiber cables. Ground motion and water pressure records are transmitted to land station via the cables. We used velocity seismometers in this study, which have a natural frequency of 15 Hz, and electrical signal is digitized at 100 Hz sampling.
To restore X, Y, and U components from the original three components, we used the tilt and rotation angles of the pressure vessels determined by Takagi et al. (2019). Although Takagi et al. (2019) referred to the restored components as X’, Y’, and U, we use X, Y, and U, respectively, in this study.
The seismograms of Snet have been openly available online from 15 August 2016, apart for records of segment 6 (S6; mostly installed on the outer rise) from 13 April 2017. Kanazawa et al. (2016) described the Snet system in detail.
ETMC
The ETMC seismic network comprises six oceanbottom stations and optical fiber cables installed along the Sagami Trough (Fig. 2b). Like the Snet system, each ETMC seismic station consists of a velocity seismometer and an accelerometer (both produced by Akashi Co.). Both sensors are housed in a cylindrical pressure vessel that is placed sideways on the seafloor. We used velocity seismometers in this study that have a flat frequency response from 1 to 30 Hz, and electrical signal is digitized at 100 Hz sampling. Unlike the Snet system, each seismometer is maintained horizontally by a gimbal mechanism. Therefore, we did not correct the orientations of the X, Y, and U components. Each pressure vessel is equipped with a “coupling cover” to improve coupling with the seafloor. None of the stations are buried beneath the seafloor.
The seismograms of ETMC have been openly available online from 1 April 2004. Eguchi et al. (1998) described the details of the ETMC system.
DONET
DONET1 (eastern segment) and DONET2 (western segment) comprise 22 and 29 oceanbottom stations, respectively, which are installed close to the Nankai Trough (Fig. 2a and c). Each DONET station is equipped with an accelerometer, a broadband seismometer (CMG3 T; Güralp), a hydrophone, a differential pressure gauge, a waterpressure gauge, and a thermometer. These multiple sensors are used to detect not only normal earthquakes, but also slow earthquakes, tsunamis, and even crustal deformation. We used broadband seismometers in this study, which have a flat frequency response from 1/360 to 50 Hz and electrical signal is digitized at 100 Hz sampling. Unlike Snet and ETMC, science nodes (Fig. 2c) are connected to the backbone cable, and four or five stations are connected to each science node via an extension cable. All sensors at each station are housed in a cylindrical pressure vessel that is placed upright (longaxis is vertically oriented). Burial of the pressure vessels depends on the site and time period, as summarized in Table 1. Like ETMC, each seismometer is maintained horizontally by a gimbal mechanism.
The seismograms of DONET1 and 2 have been openly available online from July 2011 and March 2016, respectively. Since the background seismicity of the Nankai Trough is relatively low and we could not collect enough number of seismograms for DONET2, we only used DONET1 data in this study. To examine the effects of burial, we analyzed records of nonburied and buried time periods separately (Table 1). Figure 2c shows stations used only for nonburied time period, buried time period, and both time periods. Kaneda et al. (2015) and Kawaguchi et al. (2015) described the DONET system in detail.
Table 2 summarizes the specifications of each OBS network that are relevant to this study.
Data and methods
We used 139, 6, 14, and 18 OBS stations from Snet, ETMC, nonburied DONET1, and buried DONET1, respectively. Based on the Japan Meteorological Agency (JMA) unified hypocenter catalog, we selected earthquakes with both epicentral distances and depths of < 80 km and magnitudes of 3–6. In total, 40566, 2867, 552, and 2260 event waveforms were used for Snet, ETMC, nonburied DONET1, and buried DONET1, respectively. At least 10 event waveforms were used for each station.
The time window of Scoda wave begins 70 s after the origin time and is 20.48 s (2048 samples) long (Fig. 1a and c). This time window corresponds to the multiple scattering regime, in which the oscillation direction of Scoda wave is considered to be horizontally isotropic (e.g., Sato et al. 2012). Therefore, the amplitude spectra of two horizontal components should be similar for this time window, in theory, unless strong horizontal anisotropy exists in the subsurface and/or installation. To evaluate the signal to noise (S/N) ratio of the coda amplitude spectra, we also set a noise time window that begins either before the Pwave onset time or > 220 s after the origin time. By rotating X and Y components in a horizontal plane and taking the amplitude spectral ratio for each rotation angle θ, we search for the direction in which the “N”shape forms.
The data processing procedure is as follows.

1.
For Snet seismograms, convert the original three components to X, Y, and U components following the method of Takagi et al. (2019).

2.
Remove the mean.

3.
Rotate X and Y components every 10° in a horizontal plane. We obtained nine pairs of orthogonal horizontal components U_{X}(θ) and U_{Y}(θ) (i.e., θ ranges from 40° to + 40°).

4.
Apply a 2% cosine taper.

5.
Compute the power spectra using the Fast Fourier Transform (FFT).

6.
Smooth the power spectra by applying a Hann window 15 times in frequency domain. The bandwidth of this smoothing is approximately 0.5 Hz (e.g., Ohsaki 1994).

7.
Compute the amplitude spectral ratio \(\left{U}_{Y}\left(\theta ,f\right)/{U}_{X}\left(\theta ,f\right)\right\).

8.
Compute the logarithmic average A_{Y/X} and logarithmic standard deviation S_{Y/X} of the amplitude spectral ratio using all event waveforms recorded at each station as
$${A}_{Y/X}\left(\theta ,f\right)={10}^{\frac{\sum_{i}\mathrm{log}\left{U}_{Yi}\left(\theta ,f\right)/{U}_{Xi}\left(\theta ,f\right)\right{W}_{i}\left(\theta ,f\right)}{\sum_{i}{W}_{i}\left(\theta ,f\right)}}$$(1)
and
respectively, where i is the number of event waveforms. The weight function W is defined as
where n_{X} and n_{Y} represent the orthogonal two components of the noise spectra. Equation (3) indicates W is close to unity if amplitude of the coda spectra is much larger than that of the noise spectra. As the amplitude of the coda spectra approaches the noise level, W decreases and approaches almost zero.
9. To examine the horizontal anisotropy of amplitude spectra, two indices defined by
and
are introduced. D_{1} represents the degree of dissimilarity between the two orthogonal components, and D_{2} represents the frequency average of the logarithmic standard deviation. The evaluated frequency range is f_{1} = 3 Hz and f_{J} = 25 Hz, within which the Scoda wave is considered to be composed of multiply scattered Swaves (e.g., Sato et al. 2012). D_{1} is equal to zero if A_{Y/X} is unity within the target frequency range and increases as A_{Y/X} deviates more from unity. This deviation becomes statistically more significant as D_{1}/D_{2} increases.
Results
Snet stations
The “N”shaped nonunity curve of A_{Y/X} (Fig. 1d) indicates that the oscillation direction is not horizontally isotropic. Two possibilities can explain this anisotropy: one is contamination by a nonisotropic wavefield, such as by Rayleighwaves and/or Twaves, and the other is strong horizontal anisotropy in the subsurface and/or installation. We confirmed the former is not likely because the “N”shape appears even if we use only the earthquakes located near 45° back azimuth with respect to the X and Y axes. See Appendix for detail of this confirmation.
Figure 3 shows the θ dependence of A_{Y/X}, D_{1}, and D_{2} at station N.S6N14. Note that the θ dependence of D_{1} and D_{2} has a 90° periodicity. The “N”shaped amplitude spectral ratio is observed most clearly at θ = 0° (i.e., pairing of X and Y components). As expected from this clear “N”shape, D_{1} has the largest value at θ = 0° and is much larger than D_{2}.
We refer to the θ that gives the maximum D_{1} as θ_{max}, and to corresponding D_{1} and D_{2} values as \({D}_{1\mathrm{max}}={D}_{1}\left({\theta }_{\mathrm{max}}\right)\) and \({D}_{2\mathrm{max}}={D}_{2}\left({\theta }_{\mathrm{max}}\right)\), respectively. Figure 4a shows a plot of θ_{max} versus D_{1max} and D_{2max} for all the used Snet stations. Most of the large and statistically significant D_{1max} values are observed at θ_{max} = 0°. This result indicates that strong horizontal anisotropy of amplitude spectra tends to appear for the pair of alongcable (X) and perpendiculartocable (Y) components. Since the orientation of the cable is not related to topography or geological structure, the observed horizontal anisotropy of amplitude spectra is unlikely to arise from subsurface structures; instead, it reflects the installation of the pressure vessel at each station.
In Fig. 5a, we map D_{1max} using a color scale for all the used Snet stations. Stations with large D_{1max} are located in relatively offshore regions, although not all offshore stations have large D_{1max}. On the other hand, most of the near coast stations installed within grooves (orange triangles in Fig. 2a) have relatively small D_{1max} values.
Figure 6a shows a plot of the installed water depth versus D_{1max} and D_{2max} for all the used Snet stations. D_{1max} is smaller than D_{2max} for most of Snet stations installed at water depths shallower than 1500 m (vertical dotted line), while a significant number of stations at water depths deeper than 1500 m have much larger D_{1max}. This depth dependence occurs abruptly at the threshold depth of 1500 m. As described in Table 2, most of Snet stations at water depths shallower than 1500 m are installed within grooves dug in the seafloor. Therefore, this result indicates installation within a groove is related to the suppression of horizontal anisotropy of amplitude spectra.
Figure 7 shows A_{Y/X} curves of 12 selected Snet stations with different D_{1max} values amongst those installed at water depths deeper than 1500 m. Most stations form an “N”shaped Y/X amplitude spectral ratio, although it becomes less obvious as D_{1max} decreases. The peak and notch tend to appear at 5–9 Hz and 10–23 Hz, respectively. Because the instrumental responses are the same for the X and Y components in the specification, we think the common “N”shape at different sites must be due to the installation situation of each OBS.
Figure 8 shows A_{Y/X} curves of 12 Snet stations with the largest D_{1max} amongst those installed at water depths shallower than 1500 m. All stations except for N.S1N08 do not form an “N”shape even for those having relatively large D_{1max}. Actually, N.S1N08 station is not installed within a groove although it is installed at water depths shallower than 1500 m (Uehira, personal communication). In comparison with Fig. 7, we think the Snet stations installed within grooves are not characterized by the “N”shape regardless the value of D_{1max}.
ETMC stations
ETMC is an inlinetype ocean bottom observation network like Snet, but it is different from Snet in some aspects (Table 2). Figures 4b, 5b, and 6b correspond to Figs. 4a, 5a, and 6a, respectively, but for ETMC stations. Two of six ETMC stations have D_{1max} significantly larger than D_{2max}, and θ_{max} values of all six stations are within 10° and 10° (Fig. 4b). This result indicates that strong horizontal anisotropy of amplitude spectra tends to appear for pair of the alongcable (X) and perpendiculartocable (Y) components, as for Snet. However, unlike Snet, stations with relatively large D_{1max} are located at relatively shallow water depths (Fig. 6b).
Figure 9 shows A_{Y/X} curves of all six ETMC stations. Not only the two stations with large D_{1max} (N.ST3H and N.ST4H) but also some stations with smaller D_{1max} form “N”shape, although those for the latter are less obvious. Unlike Snet, each ETMC station is equipped with a coupling cover to avoid rotation and a gimbal system to maintain a horizontal state. However, considering the similarity of the “N”shape observed for both ETMC and nonburied Snet stations, the coupling cover and gimbal system do not appear to efficiently suppress the “N”shape of the Y/X amplitude spectral ratio. The peak and notch frequencies are observed at 6–13 Hz and 14–23 Hz, which are slightly higher than those of Snet in average.
DONET1 stations
Figures 4c, 5c, and 6c correspond to Figs. 4a, 5a, and 6a, respectively, but for nonburied DONET1 stations. Unlike Snet and ETMC, θ_{max} values are distributed relatively uniformly (Fig. 4c). Figures 4d, 5d, and 6d correspond to Figs. 4a, 5a, and 6a, respectively, but for buried DONET1 stations. D_{1max} values of the buried DONET1 stations are generally smaller than those of nonburied DONET1 stations (Fig. 5d), and are smaller than D_{2max} (Fig. 4d). Like ETMC, stations with relatively large D_{1max} are located at relatively shallow water depths (Figs. 6c and d).
Figure 10 shows A_{Y/X} curves of the six DONET1 stations with the largest D_{1max} in the nonburied time period (red). In each subfigure, we also show the A_{Y/X} curves obtained during the buried time period (blue) at the same station. The A_{Y/X} curves of DONET1 show greater fluctuations than those of Snet and ETMC because the number of used event waveforms is much smaller than the other two OBS networks. The A_{Y/X} curves obtained in the buried time period are closer to unity as compared with those in the nonburied time period. This indicates burial is effective in suppressing differences in the X and Y components.
Regardless of whether buried or nonburied, the “N”shape is not formed at all DONET1 stations. Unlike Snet and ETMC, the cylindrical pressure vessels of DONET are placed upright and have no directionality in a horizontal plane. We consider this is the reason why “N”shape is not formed for DONET1 stations even in the nonburied time period. As such, the “N”shape is likely to be specific to inlinetype OBSs whose pressure vessel is placed sideways on the seafloor.
Based on the survey results targeting the three OBS networks, we hypothesize that the cause of the “N”shaped Y/X amplitude spectral ratios observed at inlinetype stations is natural vibration of an insufficiently coupled pressure vessel. Although the water depth may be related to nonunity of the D_{1max} value, it may not be related to emergence of the “N”shape, and we neglect this effect in further discussion.
Discussion
Natural vibration model
To explore the natural vibration model and reproduce the observed “N”shaped Y/X amplitude spectral ratio, we considered two main sources that excite vibrations in the pressure vessel, as shown schematically in Fig. 11.
One source is incident Swaves (S_{X} and S_{Y}) affecting the coupling zone between the pressure vessel and the seafloor. We suppose that amplitude of the incident Swave is horizontally isotropic in Scoda time window and regard that \(\left{S}_{X}\left(f\right)\right=\left{S}_{Y}\left(f\right)\right\). If coupling between the pressure vessel and seafloor is sufficient, the incident wave is recorded as is. As the coupling decreases, the proportion of the wave amplitude that can pass through the coupling zone decreases. We denote this proportion as the coupling factor c, and assume a common c value for the X and Y components for simplicity.
The other source is guided waves (longitudinal L_{X} and transverse T_{Y}) that propagate in the pressure vessel and cables. We suppose that the guided waves are excited by conversion of the incident Swave. We assume the relationship given by
where r is the efficiency of conversion. We assume a common r value for the X and Y components for simplicity. Natural vibrations are excited when guided waves are incident on the pressure vessel via the two cable connections at both ends of the pressure vessel. The amplitude response functions of the natural vibrations G_{X} and G_{Y} with respect to the longitudinal and transverse guided waves are approximated by
and
respectively (e.g., Landschulze and Mjelde, 2014), where we suppose natural vibrations with one degree of freedom and neglect higher modes. The parameters f_{X}, f_{Y}, h_{X}, and h_{Y} are natural frequencies and damping constants for the X and Y components, respectively.
Considering these two sources, the amplitude spectra of X and Y components excited in the pressure vessel are described by
and
respectively. These equations indicate that \(c+r{G}_{X}\left(f\right)\) and \(c+r{G}_{Y}\left(f\right)\) are amplitude response functions with respect to the incident Swave. Given that we assume \(\left{S}_{X}\left(f\right)\right=\left{S}_{Y}\left(f\right)\right\) at coda time window, the Y/X amplitude spectral ratio is given by
The c/r ratio is the parameter that controls emergence of the natural vibrations. As c/r increases (i.e., the coupling factor and conversion efficiency increases and decreases, respectively), the Y/X amplitude spectral ratio approaches unity.
Figure 12 shows Y/X amplitude spectral ratios modeled by Eqs. (7), (8), and (11) for several c/r values, where other values are fixed as f_{X}= 18 Hz, f_{Y} = 7 Hz, and h_{X} = h_{Y} = 0.05. The reproduced Y/X amplitude spectral ratios form a peak and notch at natural frequencies of f_{Y} and f_{X}, respectively. As c/r increases, the peak and notch become smooth and the Y/X amplitude spectral ratio approaches unity. The Y/X amplitude spectral ratio observed at Snet N.S6N14 is reasonably reproduced by the theoretical curve for c/r = 1. As evident from Eqs. (7), (8), and (11), the DC level of A_{Y/X} is unity regardless of the c/r value. In fact, the observed A_{Y/X} is close to unity in the frequencies of < 3 Hz at most stations having an “N”shape (Figs. 7 and 9).
Some strong assumptions are included in the proposed model. First, we assumed horizontal isotropy of incident Scoda wavefield and \(\left{S}_{X}\left(f\right)\right=\left{S}_{Y}\left(f\right)\right\) as a result. This assumption may break down if the used earthquakes are distributed nonuniformly and the nonisotropic component (e.g., Twaves, Rayleigh waves, etc.) is dominant in the incident wavefield. Moreover, since we neglected higher modes in evaluating amplitude response functions of the pressure vessel (G_{X} and G_{Y}), our model may not be appropriate at frequencies higher than the normal modes of the pressure vessel. In addition to this, although we assumed the coupling factor and the conversion efficiency are not frequencydependent and common for the X and Y components, these assumptions may not be realistic. Previous studies have reported that the coupling factor is unity at frequencies lower than a threshold value, while it decreases as the frequency increases above the threshold value (e.g., Duennebier and Sutton, 1995). Therefore, this model needs to be considered with caution, especially at frequencies higher than the notch frequency. Nevertheless, this model shows in a general sense how the “N”shape forms and how coupling affects excitation of the “N”shape.
Interpretation of natural frequencies
In general, longitudinal, torsional, and bending vibrations are candidates of the natural vibrations of a cylindrical rod (e.g., Weaver et al. 1990). We regard this as a simplification of natural vibration of the pressure vessel. The natural frequencies of each mode (f_{l}, f_{t}, and f_{b}, respectively) are given by
and
respectively, where L, E, ρ, G, I, and A are the length, Young’s modulus, mass density, shear modulus, second moment of area, and cross section of the cylindrical rod, respectively. I and A are described by \(I=\pi \left({R}_{1}^{4}{R}_{2}^{4}\right)/4\) and \(A=\pi \left({R}_{1}^{2}{R}_{2}^{2}\right)\), respectively, for a cylindrical rod with outer and inner radiuses R_{1} and R_{2}, respectively. λ_{n} and λ_{n}’ are coefficients of the nth mode; λ_{0} = π and λ_{0}′ = 4.73 for twofreeedges boundary condition. We suppose the Xcomponent is dominated by longitudinal vibration, while the Ycomponent can be dominated by both torsional and bending vibrations, although we do not assess which is dominant in the Ycomponent.
From Eqs. (12) to (14), we derive
and
Considering the relationship between the Young’s modulus and the shear modulus is given by \(E=2G\left(1+\nu \right)\), where the range of the Poisson’s ratio ν is usually from 0 to 0.5, we expect f_{l}/f_{t} ranges from 1.4 to 1.7. Considering the specifications of Snet (Kanazawa et al. 2016) and ETMC (Eguchi et al. 1998) pressure vessels summarized in Table 3 and R_{2} value ranging from 0 to R_{1}, we expect f_{l}/f_{b} ranges from 2.7 to 3.8 for Snet and from 2.4 to 3.5 for ETMC.
Figure 13 shows a plot of peak frequency f_{p} (≃f_{Y}) versus notch frequency f_{n} (≃f_{X}) for Snet and ETMC stations with D_{1max} > 1.5D_{2max}. The f_{p} and f_{n} values are mostly distributed within 5–13 Hz and 10–23 Hz, respectively, and the f_{n}/f_{p} ratio is mostly between 1.4 and 3.8, as expected from Eqs. (15) and (16).
From Eqs. (12) to (14), the following frequency ratios are also derived:
where we assumed E and G are common for Snet and ETMC because the major structural component of both pressure vessels is beryllium copper. Substituting the values in Table 3 to Eqs. (17) and (18), we derive f_{l,ETMC}/f_{l,Snet} and f_{t,ETMC}/f_{t,Snet} are 1.6 and f_{b,ETMC}/f_{b,Snet} ranges from 1.3 to 2.6. In fact, the ETMC stations have relatively large f_{p} and f_{n} values as compared with most Snet stations (red circles in Fig. 13), and these values become comparable to the Snet counterparts after dividing by 1.6 (red dotted circles in Fig. 13).
Substituting f_{t} = f_{b}= 5–13 Hz and f_{l} = 10–23 Hz to Eqs. (12) and (13), we obtain the range of E and G as 10^{–3} to 10^{–1} GPa in the order. This result appears to be too low for the Young’s modulus of beryllium copper (ca. 130 GPa). However, we should note that computed E and G values correspond to the entire structure of the pressure vessel, including junctions and buffers. The elastic modulus of an entire structure is usually much lower than that of each component. Therefore, we think the ranges of the natural frequencies observed for the pressure vessel are physically possible, though the real value can only be confirmed through actual experiments.
Problems and solutions when using inlinetype OBS records
As we have shown, analyzing the X and Y components of inlinetype OBSs needs to be undertaken with care when the frequencies of > 3 Hz are used. For example, when estimating back azimuth using polarization of the first motion, the estimation will be seriously biased if the used record is suffered by natural vibrations of pressure vessel. The same is true for the Swave splitting analysis. For these analyses, it is necessary to correct phase spectra of the natural vibration as well as amplitude spectra to retrieve correct horizontal seismograms. Although estimation of the phase spectra was out of scope in this study, it is an urgent issue in near future. Analyses that require the vertical component (U) only, such as estimating earthquake magnitudes, source spectra, codaQ, etc. may not be seriously affected by the natural vibrations of the pressure vessel because the vertical component is much less affected by coupling.
Because the difference between the X and Y components is insignificant at frequencies of < 3 Hz, we think the natural vibrations of the pressure vessel are not excited at these low frequencies and analyses of these frequencies do not require correction of the X and Y components. Such analyses may include centroid moment tensor (CMT) inversion, waveformbased source inversion, receiver function analysis, seismic interferometry, and so on.
Our study has shown that the coupling of the pressure vessel to the seafloor influences the emergence of an “N”shaped Y/X amplitude spectral ratio. Installation of the pressure vessel within a groove and/or burial are effective in suppressing natural vibrations of the pressure vessel. In fact, some studies have demonstrated that noise is dramatically reduced after burying OBSs (e.g., Araki et al. 2013). Therefore, such installation using underwater technologies to enhance the coupling is desirable when constructing an OBS network, not only to avoid the risk of cable damage but also to ensure highquality records. In addition, it is recommended to carry out shaking experiments by placing the pressure vessel and cables on the bottom of water by imitating actual installation situation. Such experiments may enhance our understanding of how the natural vibrations are excited, and how much burial is needed to suppress these vibrations.
Conclusion
We examined Y/X coda amplitude spectral ratios for three OBS networks installed around Japan, and found anomalous “N”shaped amplitude spectral ratios characterize many inlinetype OBSs of Snet and ETMC. Distinct peak and notch are found at around 5–13 Hz and 10–23 Hz in the amplitude spectral ratio, respectively. Such “N”shape does not characterize buried inlinetype OBSs. Nodetype OBSs of DONET1 also do not form the “N”shape regardless of whether they are buried or not. We modeled the “N”shaped Y/X amplitude spectral ratio by considering different modes of natural vibrations excited in a pressure vessel and insufficient coupling between the pressure vessel and the seafloor. When analyzing inlinetype OBS records at frequencies of > 3 Hz, it is necessary to confirm whether the anomalous responses are included in the X and Y components. If necessary, correction of these components is required, or we should not use these components. It is recommended that OBSs be installed below the seafloor or within grooves dug in the seafloor to suppress natural vibration of the pressure vessel.
Availability of data and materials
Snet and DONET records are available from the NIED’s data repository (https://doi.org/10.17598/NIED.0007, https://doi.org/10.17598/NIED.0008). ETMC records are available from Hinet download site (https://hinetwww11.bosai.go.jp/auth/download/cont/?LANG=en). The JMA unified hypocenter catalogue, which was compiled in cooperation with MEXT Japan, is available from the JMA webpage (https://www.data.jma.go.jp/svd/eqev/data/bulletin/hypo.html).
Abbreviations
 OBS:

Ocean bottom seismometer
 Snet:

Seafloor Observation Network for Earthquakes and Tsunamis
 ETMC:

Earthquake and Tsunami Monitoring Cable
 DONET:

Dense Oceanfloor Network system for Earthquakes and Tsunamis
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Acknowledgements
We thank Naoki Hayashimoto for valuable discussions and comments. Kenji Uehira provided us the burial information of Snet. Comments by Takuji Yamada, the associate editor, and two anonymous reviewers were helpful to improve quality of the manuscript. Seismic Analysis Code (SAC; Helffrich et al. 2013) and Generic Mapping Tools (GMT; Wessel et al. 2013) were used for signal processing and figure plotting, respectively.
Funding
This research was funded by the Japan Society for Promotion of Science (GrantNo. 19H01982).
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KS analyzed the data and drafted most of the manuscript. TN partly drafted the section “OBS networks of Snet, ETMC, and DONET” and partly created some figures. Both authors read and approved the final manuscript.
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Appendix
Appendix
One important assumption of the Scoda analysis in this study is that the Scoda waves are composed of multiply scattered S waves and the wavefield is horizontally isotropic. However, the Scoda part may contain nonisotropic phases like Twaves and/or Rayleigh waves. These phases may be dominant in the radial component. For such a case, if the epicenters of the used earthquakes are distributed unevenly around the cable axis direction (Xdirection) and/or the direction perpendicular to the cable axis (Ydirection), the amplitude spectra of incident Rayleigh waves and Twaves cannot be cancelled out, which makes it difficult to interpret the “N”shape properly.
To check whether the observed “N”shape is influenced by nonisotropy of the incident wavefield or not, we compute the Y/X amplitude spectral ratios using only earthquakes whose back azimuth is distributed within 45 ± 15° with respect to the direction of X and Yaxes (we call this the 45 ± 15° criterion). The direction of the X and Yaxes was referred from Takagi et al. (2019) for Snet and Nakano et al. (2012) and Nakano (2017) for DONET1. For ETMC, the direction of the X and Yaxes was visually estimated from Fig. 3 of Eguchi et al. (1998). For earthquakes satisfying this criterion, even if phases on the radial (or transverse) component dominate the Scoda, they are projected on the X and Y components with similar amplitude because sin45° is equal to cos45°. The effects of incident wavefield will be removed from the Y/X amplitude spectral ratio for such a case.
Figure 14 shows the distribution of D_{1max}, which is the same as Fig. 5 except that only the earthquakes satisfying the 45 ± 15° criterion are used for computing the average Y/X amplitude spectral ratio. For Snet and ETMC stations, the pattern of D_{1max} distribution is similar to that shown in Fig. 5. Figure 15 shows the Y/X amplitude spectral ratios for the selected Snet stations located at the water depths deeper than 1500 m. The red and black curves are the spectral ratios using the earthquakes satisfying the 45 ± 15° criterion and those using all the available earthquakes (same as Fig. 7), respectively. The “N”shape is clearly observed even if the earthquakes satisfying the 45 ± 15° criterion are used. The difference between the red and black curves is hardly seen for most stations.
Considering these results, we conclude that the “N”shape is excited independently of the horizontal anisotropy of the incident wavefield. Note that this does not necessarily mean the incident wavefield is horizontally isotropic.
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Sawazaki, K., Nakamura, T. “N”shaped Y/X coda spectral ratio observed for inlinetype OBS networks; Snet and ETMC: interpretation based on natural vibration of pressure vessel. Earth Planets Space 72, 130 (2020). https://doi.org/10.1186/s40623020012556
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DOI: https://doi.org/10.1186/s40623020012556