Volume 46, Issue 1 p. 303-310
Research Letter
Free Access

Seafloor Crustal Deformation on Ocean Bottom Pressure Records With Nontidal Variability Corrections: Application to Hikurangi Margin, New Zealand

Tomoya Muramoto

Corresponding Author

Tomoya Muramoto

Research Center for Earthquake Prediction, Disaster Prevention Research Institute, Kyoto University, Uji, Japan

Now at National Metrology Institute of Japan, National Institute of Advanced Industrial Science and Technology, Tsukuba, Japan

Correspondence to: T. Muramoto,

[email protected]

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Yoshihiro Ito

Yoshihiro Ito

Research Center for Earthquake Prediction, Disaster Prevention Research Institute, Kyoto University, Uji, Japan

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Daisuke Inazu

Daisuke Inazu

Department of Marine Resource and Energy, Tokyo University of Marine Science and Technology, Tokyo, Japan

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Laura M. Wallace

Laura M. Wallace

GNS Science, Lower Hutt, New Zealand

Institute for Geophysics, University of Texas at Austin, Austin, TX, USA

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Ryota Hino

Ryota Hino

Graduate School of Science, Tohoku University, Sendai, Japan

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Syuichi Suzuki

Syuichi Suzuki

Graduate School of Science, Tohoku University, Sendai, Japan

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Spahr C. Webb

Spahr C. Webb

Lamont-Doherty Earth Observatory, Columbia University, Palisades, NY, USA

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Stuart Henrys

Stuart Henrys

GNS Science, Lower Hutt, New Zealand

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First published: 28 December 2018
Citations: 19

Abstract

Ocean bottom pressure (OBP) observations are a powerful tool for determining vertical crustal displacements, especially due to earthquakes and slow earthquakes, with centimeter-level resolution. In these studies, removal of oceanographic noise (tens of centimeters) is required to identify centimeter-level crustal deformation. We undertake barotropic modeling to remove oceanographic signals from data from an OBP array deployed offshore New Zealand in 2014/2015. We show that removing the nontidal component calculated from a barotropic ocean model reduces the variance in the data by about 66% and provides a feasible means to resolve pressure changes due to crustal deformation during the slow slip events. We also discuss the vertical displacements from slow slip events that occurred in late September to mid-October 2014, and we outline our procedure for processing OBP data.

Key Points

  • The oceanographic corrections from our model help to reduce noise in ocean bottom pressure data recorded during slow slip event
  • We show a barotropic oceanographic model can be used to reduce the variance in seafloor pressure measurements by about 66%
  • Our oceanographic model is particularly valuable for the shallower-water sites

Plain Language Summary

We developed a new method for determining pressure changes due to slow slip events (SSEs) on offshore subduction plate boundaries by using information from the ocean bottom pressure records and numerical simulation. We use an oceanographic model to correct the seafloor pressure data for oceanographic signals, so that centimeter-level vertical deformation of the seafloor during the SSEs can be isolated. We show that this method can be used to identify SSEs that occurred off the coast of New Zealand in 2014. Our results indicate that our ocean model can be a useful tool to use ocean bottom absolute pressure gauge data to resolve crustal deformation.

1 Introduction

Slow slip events (SSEs) involve transient aseismic slip across a fault that can last weeks to months. The presence and spatiotemporal evolution of SSEs in the shallow portions of subduction zones (near the trench) have been particularly difficult to document due to the submarine nature of the near-trench region. There are relatively few observations of this phenomenon near the trench (e.g., Araki et al., 2017; Davis et al., 2015; Wallace et al., 2016). Ocean bottom pressure (OBP) observation networks are becoming more widely used to measure offshore crustal deformation because they enable centimeter-level resolution of continuous vertical seafloor displacement during SSEs, earthquakes, and other transient deformation events.

Pressure changes observed at the seafloor are dominated by the influence of oceanic variations, such as tidal and nontidal components (e.g., Hino et al., 2014). Conventionally, to detect centimeter-level crustal deformation, oceanographic noise is removed by taking the difference between pressure records at OBP sites in the deforming zone and one or more nearby reference sites (preferably outside of the deforming zone, often on the subducting plate), which cancels out any common-mode tidal and nontidal components (e.g., Ito et al., 2013; Wallace et al., 2016). However, an alternative approach is to estimate the nontidal component through oceanographic modeling, in order to eliminate this component from the raw data. This is particularly useful to help isolate vertical displacement of the seafloor during SSEs, as the duration of the SSEs and nontidal oceanic variations often overlap.

Inazu et al. (2012) developed a global barotropic ocean model driven by assimilated wind vectors that has been used to remove nontidal oceanographic signals to isolate seafloor vertical displacement using OBP data. Applying this ocean model to the 2011 Tohoku-Oki earthquake data, the authors succeeded in detecting crustal deformation due to afterslip during the largest foreshock, which occurred just before the 2011 earthquake (Inazu et al., 2012). These results suggest that detailed modeling of the nontidal component can help to remove this noise from OBP records, to resolve transient tectonic deformation, potentially without the need for nearby reference sites to undertake oceanographic noise removal. In this study, we performed a quantitative evaluation of the method using reference sites compared to a new approach outlined here using a nontidal ocean model, to remove noise from OBP data acquired at the offshore Hikurangi subduction zone during large SSEs in 2014.

2 Seafloor Pressure Data at Offshore Hikurangi to Detect Slow Slip

The Hikurangi margin is the site of westward subduction of the Pacific Plate beneath the east coast of the North Island of New Zealand. It is an area of well-documented shallow SSEs (e.g., Wallace et al., 2012, 2016; Wallace & Beavan, 2010). The northern Hikurangi margin is an ideal location to investigate shallow SSEs using seafloor geodetic methods, owing to the proximity of SSEs to the onshore geodetic network, short SSE recurrence interval of 1–2 years, and a short SSE duration of 2–3 weeks (e.g., Wallace et al., 2012).

The Hikurangi Ocean Bottom Investigation of Tremor and Slow Slip experiment began in 2014 to investigate offshore SSEs and their relationship to tectonic tremor and earthquakes along the northern Hikurangi margin. In 2014, 24 autonomous OBPs and 15 Ocean Bottom Seismometers were deployed from May 2014 to June 2015 off the eastern coast of the North Island (Wallace et al., 2016). During the experiment, two SSEs were observed by the onshore Global Navigation Satellite Systems network in September/October 2014 and December/January 2014/2015 (e.g., Figure 1; the SSEs spanned days 265–285 and 350–370, where day 1 is 1 January 2014). By using reference sites on the subducting Pacific plate to remove the common mode oceanographic noise, Wallace et al. (2016) were able to resolve 1–5 cm of uplift of the seafloor during the September/October SSE. As an alternative to using reference sites to remove oceanographic noise, we attempt to detect SSE signals from the September/October event in the observed OBP data by using a barotropic model to remove the nontidal component of the OBP changes.

Details are in the caption following the image
(a) Regional map of New Zealand and location of the study area. Diamonds denote station locations. Red and dark blue arrows respectively denote horizontal displacement during the slow slip events on the number of days 265–285 (e.g., Wallace et al., 2016) and 350–370 after 1 January 2014 in Hikurangi Ocean Bottom Investigation of Tremor and Slow Slip 2014/2015. (b) Observed coordinates (east component) from GPS sites Gisborne (GISB) and Mahia Peninsula (MAHI). Eastward (positive) jumps denote slow slip events on the number of days 265–285 (e.g., Wallace et al., 2016; red bar) and 350–370 (dark blue bar) after 1 January 2014.
The bottom pressure anomaly or perturbation from reference pressure, corresponding to the depth of water, can be represented as follows (e.g., Inazu et al., 2012):
urn:x-wiley:00948276:media:grl58466:grl58466-math-0001(1)
urn:x-wiley:00948276:media:grl58466:grl58466-math-0002(2)
where ∆PB(t) denotes the pressure anomaly around a reference pressure level according to depth (Pref); ∆Pc(t) is the pressure change due to vertical crustal deformation; ∆PT (t) is the pressure change due to ocean and Earth tides (~100 hPa, 0.5- to 1-day cycle; e.g., Park et al., 2008); ∆Po(t) is the nontidal ocean mass variation, such as ocean currents and eddies driven by atmospheric disturbances (~15 hPa; e.g., Inazu et al., 2012); ∆PA(t) is the pressure change due to the sea surface pressure change (Ponte & Ray, 2002); and ∆PD(t) is the pressure change due to instrument drift. The instrument drift component varies greatly depending on the equipment (Kajikawa & Kobata, 2016) and can be on the order of several centimeters per year or more on Paroscientific Absolute Pressure Gauges (Polster et al., 2009). The ϵ(t) includes other unmodeled noise, such as instrument noise. Seafloor pressure changes, ∆Pc(t), due to transient uplift or subsidence during offshore Hikurangi SSEs, are expected to be up to 5 hPa (1 hPa ≃ 1 cm; e.g., Wallace et al., 2016). All of the components discussed above are independent from each other from a geophysical perspective.

3 Methods

3.1 Tidal and Nontidal Effect

We used a global barotropic ocean model driven by assimilated surface wind vectors and air pressure at the sea surface from an atmospheric model to remove nontidal oceanic variations from the OBP records (Inazu et al., 2012). This model is based on a nonlinear, single-layer barotropic ocean model in a spherical coordinate system (e.g., Inazu et al., 2006, 2012). It can simulate wind-driven circulation and effects on OBP, especially in low latitudes and midlatitudes (Inazu et al., 2012). The governing equations of the model are as follows (equations 35):
urn:x-wiley:00948276:media:grl58466:grl58466-math-0003(3)
urn:x-wiley:00948276:media:grl58466:grl58466-math-0004(4)
urn:x-wiley:00948276:media:grl58466:grl58466-math-0005(5)
where v is the horizontal velocity (ocean current); η is the sea level anomaly; PA is the sea level pressure; τ is the wind stress vector; H, ρ, g, and f are the depth, sea-water density, gravitational acceleration, and Coriolis parameter, respectively; γb and AH are the bottom friction parameter and horizontal eddy viscosity; and ρa, Cd, and W are the bulk coefficient, air density, and wind vector, respectively. Using this model, we calculated the high-frequency sea level anomaly caused by wind stress and converted it to a pressure anomaly (equation 6):
urn:x-wiley:00948276:media:grl58466:grl58466-math-0006(6)

As an external forcing, we used 6-hourly surface air pressure and surface wind vector data published by the 55-year Japanese Reanalysis Project (Harada et al., 2016; Kobayashi et al., 2015) and bathymetry and coastline data provided by GEBCO_08 (http://www.gebco.net./). Numerical simulations with a horizontal resolution of 1/12° were carried out, following Inazu et al. (2012), who found that this resolution is optimal when using ocean bottom topography data with similar resolution to that of GEBCO_08. Each fixed parameter setting of the model, including the grid size, was optimized using in situ OBP data (Inazu et al., 2012).

First, we subtracted the tidal components from the raw data using Baytap-G (Tamura et al., 1991). After subtracting the tidal component, we applied a 1-day corner decimation filter to the time series. Following this, we corrected the nontidal oceanic variation predicted by the ocean model described above.

3.2 Evaluating Vertical Displacement and Drift Component

We subsequently corrected the instrument drift by fitting the sum of an exponential term and a linear trend function to represent instrument drift (equation 7) for the entire observation period. We simultaneously estimate the vertical crustal displacement by also estimating v * U(t), which represents the vertical crustal deformation due to SSE. The model parameters, a, b, c, d, and v (instrument drift and vertical displacement during the middle of the SSE, t1), are estimated using the least squares method.
urn:x-wiley:00948276:media:grl58466:grl58466-math-0007(7)
where
urn:x-wiley:00948276:media:grl58466:grl58466-math-0008(8)
where t is the time. The a, b, c, and d are model parameters describing the exponential and linear components of the drift. The v * U(t) represents the vertical crustal deformation due to SSE. We used two procedures to evaluate instrument drift by fitting equation 7, with or without the vertical displacement term, v * U(t), depending on whether the OBP site is landward or seaward of the trench; we assume vertical deformation during SSEs will be negligible for sites deployed seaward of the trench: LOBS4 and TXBPR1 (supporting information Figure S1). We applied equations 7 and 8 to all of the overriding plate sites above the SSE source (landward of the trench) to evaluate the amount of vertical displacement and instrument drift simultaneously (e.g., Sato et al., 2017; Figure S2). The t1 was set as the middle day of the SSE (275 after 1 January 2014), which was confirmed by onshore Global Navigation Satellite Systems data.

3.3 Variance Reduction

Next, we evaluated how much the variance of the OBP data is reduced when using a nontidal ocean model compared to using reference sites by calculating the variance reduction (VR; equation 9) for each approach. We used TXBPR1, LOBS4, and an average of the reference sites for the reference data. We excluded the time period during the SSE from the time series when we calculate the VR.
urn:x-wiley:00948276:media:grl58466:grl58466-math-0009(9)
where Pcorr(ti) is the time series of either the reference data or output of ocean model. Pobs(ti) is the OBP time series after subtracting the tidal component and detrending the data using equations 7 and 8.

4 Results and Discussion

As a result of calculating VR for each case, we found a depth dependence of VR when we used reference data to cancel oceanographic noise (Figure 2). For the approach using reference sites, shallower-water ( urn:x-wiley:00948276:media:grl58466:grl58466-math-0010 1,000 m) sites LOBS8, TXBPR2, and LOBS1 show lower VR (50–60%), compared to the remaining deeper-water sites ( urn:x-wiley:00948276:media:grl58466:grl58466-math-0011 1,000 m), where VR from using the reference sites was as high as 80–90% (installation depth is shown in Table 1). This is not surprising because there is a much larger horizontal distance between the shallow-water sites and the reference sites compared to the smaller distance between deep-water sites and the reference sites. Thus, the oceanographic signals between the shallow water sites and the reference sites are less similar, and less of this noise can be removed. Differencing pressure data from adjacent shallow water sites also removes most of the variance; however, using that procedure would also remove any slow slip signals that are common to those sites. In contrast, using the barotropic model produces a slightly higher VR for the shallow-water sites TXBPR2 and LOBS8 (58–69%) compared to using the reference data (54–58%) for these two sites (Figures 2 and 3a). However, the VR achieved by using the barotropic model at the remaining sites was 52–75%. This is a substantially smaller VR compared to the approach of using reference sites, suggesting that the reference site data may be more effective in removing the oceanographic noise in this particular case, with the exception of some of the shallow water sites (Figure 2). Overall, when using the barotropic model the average VR is ~66%, and when using reference data, it is ~80%. Calculated formal uncertainties are 44% higher when using the oceanographic model compared to that using reference data.

Details are in the caption following the image
Variance reduction of time series using the ocean model and reference site data.
Table 1. Characteristics of Ocean Bottom Pressure (OBP): Installed Depth, Site Position, and Recording Period
Site Installed depth Site position Start End
(m) Longitude (°E), latitude (°N) (day/month/year) (day/month/year)
LOBS1 993 178.82, −38.59 14/05/2014 21/06/2015
EBPR3 1031 178.65, −38.69 12/05/2014 21/06/2015
TXBPR2 779 178.57, −38.71 17/05/2014 25/06/2015
SBPR1 2453 178.89, −38.72 13/05/2014 26/06/2015
EBPR2 1013 178.62, −38.73 11/05/2014 20/06/2015
EBPR1 989 178.68, −38.75 13/05/2014 20/06/2015
LOBS8 651 178.46, −38.84 14/05/2014 26/06/2015
SBPR2 2116 178.88, −38.85 12/05/2014 23/06/2015
SBPR3 1360 178.76, −38.89 12/05/2014 23/06/2015
TXBPR5 1246 178.57, −38.95 11/05/2014 26/06/2015
LOBS6 1874 178.80, −38.98 14/05/2014 25/06/2015
LOBS9 1457 178.52, −39.07 11/05/2014 23/06/2015
LOBS10 1444 178.31, −39.13 11/05/2014 23/06/2015
TXBPR1 3532 179.00, −38.76 16/05/2014 27/06/2015
LOBS4 3441 178.98, −39.12 17/05/2014 26/06/2015
Details are in the caption following the image
(a) Processed ocean bottom pressure records (Hikurangi Ocean Bottom Investigation of Tremor and Slow Slip 2014/2015) time series associated with slow slip event (SSE) indicated by the squared period (data from LOBS8 and TXBPR2). Solid dark blue and red lines show the processed time series and estimated trend and vertical displacement, respectively. (b) Power spectra of each ocean bottom pressure data for two of the sites. Solid green, red, and dark blue show the time series of observed data (not corrected), processed time series corrected by ocean model, and reference data, respectively.

We calculated power spectra of the original data time series and the data time series after applying the reference correction or the oceanographic model correction to compare which frequency bands the two methods provide the most VR. The short time series leads to high variance in the spectra, but the comparison shows that the oceanographic model reduces the variance most at periods between 50 and 20 days (Figure 3b). At shorter period the reference data produce more VR, while the oceanographic model may increase the variance slightly at the shortest periods. The net result is that the oceanographic model provides less VR than the reference site data (Table 2) due to insufficient correction of short-period components.

Table 2. Estimated Vertical Displacement (Positive in Uplift Direction) and Standard Deviation (1σ) for Each Correction Method
Site Ocean model (displacement [cm]/σ [hPa]) Reference: TXBPR1 (displacement [cm]/σ [hPa]) Reference: (TXBPR1 + LOBS4) /2 (displacement [cm]/σ [hPa]) Reference: LOBS4 (displacement [cm]/σ [hPa])
LOBS1 0.20/1.66 0.31/1.54 1.16/1.61 1.15/1.58
EBPR3 −0.08/2.25 0.73/1.49 0.74/1.44 0.74/1.42
TXBPR2 0.47/1.53 0.80/1.63 0.80/1.60 0.79/1.60
SBPR1 0.28/1.31 0.92/0.51 1.19/0.56 1.11/0.64
EBPR2 −1.88/2.98 1.14/2.03 1.02/1.61 1.10/2.07
EBPR1 0.32/2.10 0.68/1.51 0.67/1.45 0.66/1.42
LOBS8 1.83/1.41 2.72/1.69 2.69/1.63 2.68/1.61
SBPR2 0.29/1.26 1.03/0.60 1.03/0.61 1.44/0.71
SBPR3 1.01/1.32 1.54/0.91 2.09/0.90 2.07/0.85
TXBPR5 1.14/1.34 2.09/1.13 2.07/1.05 2.05/1.01
LOBS6 0.87/1.26 1.37/0.66 1.36/0.64 1.92/0.74
LOBS9 1.29/1.21 1.95/0.82 1.97/0.75 1.98/0.74
LOBS10 0.78/1.47 1.01/0.80 1.67/0.85 1.68/0.82

The differences between the three choices of reference data (TXBPR1, LOBS4, and an average of the reference sites) used in this study were small. When we use reference data to remove oceanographic noise, the displacement estimates are on average 65% larger compared to those using the oceanographic model (Table 2). In almost all cases, we estimated uplift above the SSE source. These results are generally consistent with Wallace et al. (2016; Figure 4), although the estimated vertical displacements in this study are slightly smaller, we think, due to differences in our procedures used for drift removal.

Details are in the caption following the image
Vertical displacement estimated by this study (left panel) and Wallace et al. (2016; right panel) during slow slip event on the number of days 265–285 after 1 January 2014. For LOBS8 and TXBPR2, the displacements in the left panel are from pressure time series corrected by the Inazu oceanographic model, while for the others, displacements are derived from time series corrected with reference site data (an average of LOBS4 and TXBPR1).

Coherent signals exist in each time series after correction with the ocean model (Figures 3a and S3). The residual time series show that the barotropic model has some limitations in reproducing the amplitude of the nontidal components, but more of the variance in seafloor pressure in the Hikurangi area is explained by the oceanographic model compared to the average value of variance obtained by Inazu et al. (2012).

The standard deviation (1σ) after removing the nontidal ocean model is still on average 30% higher than the results from removing the oceanographic noise using an average of the reference sites as reference data (Table 2). Further studies with more sophisticated oceanographic models that can remove oceanographic noise more precisely, and that also include additional oceanographic effects, are required to enable more precise determinations of vertical displacement due to SSEs from OBP data.

5 Conclusions

Here we demonstrate a method to correct for nontidal oceanographic variations on OBP data, to help resolve seafloor crustal deformation. We apply this approach to OBP data that were collected during two SSEs offshore New Zealand in late 2014. Correcting the data with the nontidal oceanographic models provides on average a 66% VR, following removal of tidal and instrument drift components. This is 18% less on average than the VR provided by the conventional approach of using nearby reference sites (average VR 80%) to remove the common-mode oceanographic noise. The reference sites (located on the subducting plate) do a more effective job correcting oceanographic noise at the deep-water sites, where the oceanography is more similar to that at the reference sites. In contrast, the barotropic model does a better job reducing variance at some of the shallow-water sites, where the oceanographic characteristics are not as well characterized by the deep-water reference sites. Overall, our work suggests that barotropic models can remove a large component of the oceanographic noise present in OBP records but are not yet sufficient to accurately resolve centimeter-level deformation of the seafloor. We anticipate that future work incorporating improved oceanographic observations and modeling that also accounts for more realistic physical processes will help to further improve use of OBP records for seafloor geodesy.

Acknowledgments

We thank Motoyuki Kido and Makiko Sato for their cooperation in the observations. This research was supported by JSPS KAKENHI (grant 26257206) and JST-JICA SATREPS (grant 15543611) for Y. I. and T. M. and JSPS KAKENHI (grant 26000002) for R. H. and Y. I. The OBP data used in this study are provided by GNS science and Columbia University. Support for data acquisition and ship time was provided by the U.S. National Science Foundation, GNS Science, and Land Information New Zealand's Oceans 2020 program. L. M. W. acknowledges support from a New Zealand MBIE Endeavour grant and NSF grant OCE-1334654. We thank the captain and crew of the New Zealand R/V Tangaroa and U.S. R/V Roger Revelle for deployment and recovery of OBP instruments. GMT software (Wessel et al., 2013) was used to draw the figures.