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消除海纜式海底地震儀中之低頻雜訊
郭本垣 林慶仁
中央研究院地球科學研究所
許麗文 林祖慰 李伊婷
中央氣象局地震測報中心
摘
要
本計畫旨在研究中央氣象局海纜式地震站 EOS1 之資料進而擴大其綜效。上
一期計畫末期開始了 EOS1 之噪聲分析，並初步嘗試建立了轉換函數，以消除垂
直分量上的長週期噪聲。這一期計畫將著重於改善此一轉換函數，並初步建立順
從函數(compliance function)，以逆推 EOS1 下的地殼構造。我們重新檢討海洋學
與地震學基本理論，發現因海浪引起的重力效果不容忽視 修正了重力因素後對
EOS1 進行逆推便得到較合理的結果。在此我們呈現一個簡單的 5 層模型，顯示
EOS1 與另外兩個海底地震儀下方地殼構造的特性。
The CWB cabled seafloor observatory hosts a shallow-buried seismometer and
an absolute pressure gauge. This pair of instrument is assigned a station name EOS1
and has long enough frequency range that can support studies of long-period noise
from ocean waves registered in seismic data and how to use this noise to investigate
crustal structure. We have established the compliance function, i.e., the ratio
between vertical displacement and pressure, for EOS1, and compare it with that
from the 2 portable broadband OBSs deployed further offshore into the Okinawa
trough, S002 and S005. However, we found that, the long period part of EOS1
compliance is hard to fit. We then realized that the gravitational attraction by the
mass perturbation at the sea surface is large enough to pull the seafloor up and down
to an amplitude 1/10 of the total amplitude. After correcting this effect, the inversion
of the crustal structure of EOS1 become reasonable. In this report we show a simple
5 layer model for the crust beneath EOS1, S002, and S005.
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1. Constructing the compliance function
The compliance function measures the ratio of the vertical displacement of seafloor
to the pressure induced by ocean waves in the infragravity waves frequency band, and
thus consists of information of the crustal structure beneath an OBS (Crawford et al.,
1998). The compliance function 𝜂𝑑𝑝 is defined in frequency domain (f) as
𝐺
(𝑓)
𝜂𝑑𝑝 (𝑓) = 𝛾𝑑𝑝 (𝑓) ∙ √𝐺𝑑𝑑(𝑓)
𝑝𝑝
(1)
where 𝐺𝑑𝑑 and 𝐺𝑝𝑝 are auto-spectra of vertical displacement and pressure,
respectively, and 𝛾𝑑𝑝 is the coherence between vertical displacement and pressure
defined as
𝛾𝑑𝑝 (𝑓) =
𝐺𝑑𝑝 (𝑓)
√𝐺𝑑𝑑 (𝑓)∙𝐺𝑝𝑝 (𝑓)
(2)
with 𝐺𝑑𝑝 being cross-spectrum between displacement and pressure. Formal error is
calculated from equation 4 of Crawford et al. (1991) while here its minimum value is
set to be 1% of the compliance value. These are the same equations for the
construction of transfer function in Kuo et al. (2014) except that, in the latter, velocity
data without any corrections are adequate. Kuo et al. (2014) demonstrated that the
bottom motions forced by the infragravity waves can be isolated and removed from
these OBS data to recover seismic signals. In this study, we utilize the compliance as
a signal. The observed compliance functions for S002, S005, and EOS1 are shown in
Figure 2. The compliance is multiplied by wavenumber (k) to produce a constant
value from a uniform half space.
2. Gravitational attraction
While seafloor motion is predominantly driven by water pressure, the gravitational
attraction on the seafloor by the sea surface mass perturbation is the second largest
force, which may not be ignored at low frequencies especially when seafloor is
shallow (Crawford et al., 1998). For EOS1 where water depth is only 300 m, the
seafloor pulled gravitationally by the wave height can reach 1/10 of the observed
displacement at periods of ~200 s (Figure 3). We corrected this effect from the
observed compliance for each OBS (Figure 4). The effect is not a simple function of
water depth but is a sum of the contributions from water depth, magnitude of the
waves, and frequency.
3. Inversion : a 5-layer model
To invert for crustal structure from the compliance measurements, we started with a
simple model by dividing sediment into 2 layers and crust into 3 layers. Sediment
thickness h is estimated from seismic reflection profiles running closest to each OBS
(Kuo et al., 2014), and the first and second layers are assumed to be 200 m and h-200
m thick, respectively. The first crustal layer (crust 1) is 1 km thick, overlying a 2 km
thick second layer (crust 2) and a half space. We systematically search for the density
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(), VP, and VSof the sediment and crust that best fit the observed compliance data.
The number of data in equal-spaced frequency is 41, 27, and 27 for EOS1, S002, and
S005, respectively.
The compliance is more sensitive to VS than to VP and , especially for structures with
high VP / VS or equivalently high Poisson ratio (Crawford et al., 1999). In previous
compliance studies, VP and  structures of the crust were often determined by activesource seismic modeling for the same OBS and thus fixed in the inversion. In this
study, such independent, in-situ constraints for each OBS are not available. The VP
models from Wang et al. (2004) are the closest but still 50 km away from EOS1.
Rather than fixing these parameters, we impose a maximum VP value of 2, 4, 5, 6, and
7.5 km/s on layers 1-5, respectively. These maximum values were chosen by
referencing the velocity of the shallow, unconsolidated sediment documented in the
ODP 1202 site report (Salisbury et al., 2002), that for consolidated marine sediment
(Shillington et al., 2008), and crustal models in this region (Wang et al. 2004,
Klingelhoefer et al., 2009). The respective maximum VS is given as VP /1.7 (see
below).
Using the forward calculation technique formulated in Crawford et al. (1991), a grid
search with progressive decreasing of grid interval was performed. The grid search
starts with a wide model range and grid intervals of 0.2 km/s for VP and VS and 0.2
g/cm3 for . A best-fit model is achieved when error-weighted misfit of compliance
in the logarithm scale reaches a minimum among all trials. The second run starts with
the best-fit model from the first run with a search range narrowed and search interval
halved. Two conditions were implemented to regularize the grid search: All model
parameters are allowed only to increase with depth, as the compliance data do not
display obvious peaks that suggest the presence of a low shear-strength zone, and VP
/ VS is set to be > 1.7 because porosity increase, faulting, hydration, and melting only
increase the velocity ratio from its nearly Poisson value. In the bottom half-space layer,
VP is fixed as VP = VS × 1.73 and  is fixed at 2.8 g/cm3 to speed up the search. There
are a total of 13 free parameters to be determined in the grid search. Under these
conditions, two or three runs can lead to a final model with a variance reduction >
99.5%. Table 1 summarizes the statistical performance of the best-fit model for each
OBS.
Figure 5 shows the best-fit 5-layer models of VS. The predictions in compliance from
these models are shown with the data in Figure 3. The first order feature from the 3
models is the decreasing VS in layers 1 - 4 from EOS1 to S002 and to S005. The
variation is most significant in the shallow crust, or “crust 1.” As a rule, the
compliance at a particular frequency is most sensitive to the VS at the depth about 1/6
of the wavelength of the infragravity wave at that frequency (Crawford et al., 1999).
Because of its shallow water depth, EOS1 has much shallower resolution depth than
the other 2 OBSs and that “crust 1” is the only part of the crust well constrained for
all 3 OBSs (Figure 4). We performed a series of grid-search with different thickness
for crust 1 and 2, and the pattern in this layer is robust until its thickness reaches 3 km
or above.
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References related to this report
Crawford, W. C., S. C. Webb, and J. A. Hildebrand (1991), Seafloor compliance observed
by long-period pressure and displacement measurements, J. Geophys. Res., 96,
16,151-16,160.
Crawford, W. C., S. C. Webb, and J. A. Hildebrand (1998), Estimating shear velocities in
the oceanic crust from compliance measurements by two-dimensional finite
difference modeling, J. Geophys. Res., 103, 9895-9961.
Crawford, W. C., S. C. Webb, and J. A. Hildebrand (1999), Constraints on melt in the
lower crust and Moho at the East Pacific Rise, 9 48’N, using seafloor compliance
measurements, J. Geophys. Res., 104, 2923-2939.
Hsiao, N. C., T. W. Lin, S. K. Hsu, K. W. Kuo, T. C. Shin, and P. L. Leu (2014),
Improvement of earthquake locations with the marine cable hosted observatory
(MACHO) offshore NE Taiwan, Mar. Geophys. Res., doi:10.1007/s11001-013-92073.
Klingelhoefer, F., C. S. Lee, J. Y. Lin, and J. C. Sibuet (2009), Structure of the
southernmost Okinawa trough from reflection and wide-angle seismic data,
Tectonophysics, 466, 281-288, doi:10.1016/j.tecto.2007.11.031.
Ko, Y. T., B. Y. Kuo, K. L. Wang, S. C. Lin, and S. H. Hung (2012), The southwestern
edge of the Ryukyu subduction zone: A high Q mantle wedge, Earth Planet. Sci.
Lett., 335-336, 145-153, http://dx.doi.org/10.1016/
j.epsl.2012.04.041.
Kuo, B. Y., C. C. Wang, S. C. Lin, C. R. Lin, P. C. Chen, J. P. Jang, and H. K. Chang
(2012). Shear-wave splitting at the edge of the Ryukyu subduction zone, Earth
Planet. Sci. Lett., 355-356, 262-270, http://dx.doi.org/10.1016/
j.epsl.2012.08.005.
Kuo, B. Y., S. C. Webb, C. R. Ling, W. T. Liang, and N. C. Hsiao (2014),
Removing infragravity-wave induced noise from OBSs data deployed offshore
of Taiwan Bull. Seismol. Soc. Am., 104, doi:10.1785/0120130280.
Lin, C. R., B. Y. Kuo, W. T. Liang, W. C. Chi, Y. C. Huang, J. Collins, C. Y. Wang
(2009), Ambient noise and teleseismic signals recorded by ocean-bottom
seismometers offshore eastern Taiwan, Terr. Atmosph. Ocean.,
doi:10.3319/TAO.2009.09.14.01(T).
McIntosh, K., Y. Nakamura, T. K. Wang, R. C. Shih, A. Chen, and C. S. Liu (2005),
Crustal-scale seismic profiles across Taiwan and the western Philippine Sea,
Tectonophysics, 401, 23-54.
Park, J. O., H. Tokuyama, M. Shinohara, K. Sueyhiro, and A. Taira (1998), Seismic record
of tectonic evolution and backarc rifting in the southern Ryukyu island arc system,
Tectonophys. 294, 21-42.
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Shillington, D. J., T. Minshull, C. Peirce, and J. M. O’Sullivan (2008), P- and S-wave
velocities of consolidated sediments from a seafloor seismic survey in the North
Celtic Sea Basin, offshore Ireland, Geohys. Prosp., 56, 197-211, doi:11.1111/j.13652478.2007.00669.x.
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Figure 1. Bathymetry map in the Taiwan region showing tectonic elements of the
Okinawa trough-Rykyu subduction system and the locations of EOS1, S002, and S005,
the 3 broadband OBSs (red triangle) used in the study. S002 and S005 are deployed in
the northern flank of the Okinawa trough. EOS1 is installed on the Yilan ridge, the
western end of the Ryukyu arc. Filled arrow indicates oblique subduction of the
Philippine Sea plate (PSP). Open arrows indicate continental back-arc extension along
the Okinawa trough. The 2 grey dotted lines imply the tapering of the extension towards
Taiwan. The cross marks the location of the ODP1202 site.
Figure 2. The compliance data (dots) with error (vertical bar) for the 3 OBSs as labelled.
The color lines are predicted values from the 5-layer model for EOS1 (red), S002
(green), and S005 (blue). The variance reductions are all > 99%. The grey lines are
predicted values from a different set of model not described in the text and can be
ignored.
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Figure 3. Example of removing gravitational attraction effect of mass perturbation at the
sea surface. (Right) Orange curves are vertical displacement spectrum of EOS1
observed in the third hour of 339th Julian day of 2011. The wave height at the sea
surface can be inferred from the pressure recorded by the OBS on the seafloor. This
mass perturbation is then downward continued to obtain the displacement (black). Note
the gravitational effect can reach 1/10 of the total displacement at frequencies
approaching 0.005 Hz for EOS1 which is installed on a depth of only 300 m. (Right)
Compliance measurements without (orange) and with (red) the gravitational attraction
effect removed. The correction becomes significant and necessary at low frequencies.
Figure 4. Correction for gravitational attraction effect for all three OBSs. The gray
curves denote the uncorrected compliance and the red curves denote the corrected
compliance. The amplitude is always increased after correction.
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Figure 5. VS of the 5-layer models determined from a grid search. EOS1 in red, S002 in
green, and S005 in blue. Three models have different sediment thickness and they are
plotted such that the depths to the crust for S002 and S005 match that for EOS1. Note
the variation in the top, 1-km thick layer of the crust, or “crust 1. The decrease in VS
from EOS1 (red), to S002 (green), and to S005 (blue) in the upper crust is correlated to
the increasing rifting from Taiwan into the OT. Triangle and inverse triangle plotted
along with each model mark the depths of maximum sensitivity for the lowest and
highest frequencies of the data, respectively, an indication of the range of good
resolution. Dotted line denotes EOS1 model without the data at frequencies higher than
the highest frequency for S005. This is to test how these additional data dictate the
model, proving that even without this part of the data EOS1 still has an upper crust
stronger than the other OBSs.
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