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Abstract Seafloor geodetic observation technology is a pivotal method for capturing plate boundary earthquakes and related phenomena. Currently, this task is performed by Global Navigation Satellite System-Acoustic ranging (GNSS-A), a technique that integrates GNSS observations with acoustic ranging. This method involves measuring the round-trip travel time of an acoustic signal between a surface platform and a preinstalled seafloor station, which is then converted into a distance for positioning. While the horizontal positioning accuracy can reach the centimeter level, the vertical accuracy tends to be loser. Recent research has revealed that equipment-dependent distortion of sound waves causes problems for accurate travel time identification, leading to a decrease in vertical component accuracy. In this paper, we conducted an analysis of distortion tendencies using water tank test data and quantitatively identified differences in distortion magnitude related to instruments, angle dependence, and directional dependence attributed to the sea surface platform. We proposed a new identification algorithm, Acoustic Ambiguity Reduction (AAR) method, using a catalog of distortions for each device, and improved the observational capabilities of the vertical component. Graphical Abstract

Seafloor geodetic observation technology is a pivotal method for capturing plate boundary earthquakes and related phenomena. Currently, this task is performed by Global Navigation Satellite System-Acoustic ranging (GNSS-A), a technique that integrates GNSS observations with acoustic ranging. This method involves measuring the round-trip travel time of an acoustic signal between a surface platform and a preinstalled seafloor station, which is then converted into a distance for positioning. While the horizontal positioning accuracy can reach the centimeter level, the vertical accuracy tends to be loser. Recent research has revealed that equipment-dependent distortion of sound waves causes problems for accurate travel time identification, leading to a decrease in vertical component accuracy. In this paper, we conducted an analysis of distortion tendencies using water tank test data and quantitatively identified differences in distortion magnitude related to instruments, angle dependence, and directional dependence attributed to the sea surface platform. We proposed a new identification algorithm, Acoustic Ambiguity Reduction (AAR) method, using a catalog of distortions for each device, and improved the observational capabilities of the vertical component. [ABSTRACT FROM AUTHOR]

The ocean sound speed changes drastically with time and space. It is almost impossible to achieve centimeter-level-precision Global Navigation Satellite System (GNSS)-Acoustic (GNSS-A) positioning without regarding spatio-temporal variations of sound speed. Inspired by the atmospheric delay estimation, we define zenith acoustic delay (ZAD) as the zenith-direction ranging error sourced by the sound speed variations, and then it is decomposed into one temporal component and two horizontal components for the sound speed variations in time and space, respectively. We propose a network solution with the three ZAD components of each seafloor geodetic point as common parameters to be estimated, and then present a piece-wise estimation to characterize their time-varying nature. To remedy the ray bending effect this study is implemented in the context of the ray tracing algorithm based on a reference sound speed profile (SSP). Experimental tests show that the proposed network solution improves ZAD estimation and results in a better position determination as compared to the single-point positioning (SPP) solution. The proposed network solution for a single campaign can achieve a horizontal positioning precision better than 5 cm (1-sigma) for the seafloor geodetic array centroid. The temporal variation of ZAD is up to one meter while the horizontal variations vary within a few decimeters in the time domain and show an azimuthal asymmetry in space. [ABSTRACT FROM AUTHOR]

Abstract In-field Sound Speed Profile (SSP) measurement is still indispensable for achieving centimeter-level-precision Global Navigation Satellite System (GNSS)-Acoustic (GNSS-A) positioning in current state of the art. However, in-field SSP measurement on the one hand causes a huge cost and on the other hand prevents GNSS-A from global seafloor geodesy especially for real-time applications. We propose an Empirical Sound Speed Profile (ESSP) model with three unknown temperature parameters jointly estimated with the seafloor geodetic station coordinates, which is called the 1st-level optimization. Furthermore, regarding the sound speed variations of ESSP we propose a so-called 2nd-level optimization to achieve the centimeter-level-precision positioning for monitoring the seafloor tectonic movement. Long-term seafloor geodetic data analysis shows that, the proposed two-level optimization approach can achieve almost the same positioning result with that based on the in-field SSP. The influence of substituting the in-field SSP with ESSP on the horizontal coordinates is less than 3 mm, while that on the vertical coordinate is only 2–3 cm in the standard deviation sense.

In-field Sound Speed Profile (SSP) measurement is still indispensable for achieving centimeter-level-precision Global Navigation Satellite System (GNSS)-Acoustic (GNSS-A) positioning in current state of the art. However, in-field SSP measurement on the one hand causes a huge cost and on the other hand prevents GNSS-A from global seafloor geodesy especially for real-time applications. We propose an Empirical Sound Speed Profile (ESSP) model with three unknown temperature parameters jointly estimated with the seafloor geodetic station coordinates, which is called the 1st-level optimization. Furthermore, regarding the sound speed variations of ESSP we propose a so-called 2nd-level optimization to achieve the centimeter-level-precision positioning for monitoring the seafloor tectonic movement. Long-term seafloor geodetic data analysis shows that, the proposed two-level optimization approach can achieve almost the same positioning result with that based on the in-field SSP. The influence of substituting the in-field SSP with ESSP on the horizontal coordinates is less than 3 mm, while that on the vertical coordinate is only 2–3 cm in the standard deviation sense. [ABSTRACT FROM AUTHOR]

A systematic analysis methodology for precise seafloor positioning using the GNSS-A has been constructed and implemented in the open-source software GARPOS. It introduces a linearized perturbation field model for extraction of the 4-dimensional sound speed variation, and solves the perturbation parameters simultaneously with the seafloor position based on the empirical Bayes approach. Although it can provide the solutions stably and almost analytically, it has less expandability when imposing additional nonlinear constraint parameters in the observation equation. Even though such parameters can be optimized by applying some information criteria, information on the details of the joint posterior probability would be lost and only the conditional posterior can be estimated. To overcome the above limitations, we implemented full-Bayes estimation using the Markov-Chain Monte Carlo algorithm. This approach can not only help evaluate the dependency of the existing constraint parameters on the seafloor position, but also let us discuss the effects of the additionally imposed constraints. We imposed a constraint under the assumption that a temporally-variable gradient layer steadily lies at a certain depth in the observation scale (typically < 10 km × 10 km, < 1 day). This models the cases with temperature gradients due to a large-scale structure such as the Kuroshio current or internal waves with long-wavelength. The constraint narrows the posterior of the horizontal position and provides a better solution for many datasets, especially in the Nankai Trough region. For the other datasets, the constraint emphasized bias errors, which can also provide information on the possibility of instrumental and modelling errors. [ABSTRACT FROM AUTHOR]

Abstract Underwater disturbances are the largest error source in Global Navigation Satellite System ‐ Acoustic ranging combination technique (GNSS‐A) seafloor geodetic observation. In particular, the gradient of sound speed structure (SSS) directly affects the horizontal accuracy and needs to be examined. Previous studies have not investigated its temporal change component. In this paper, we verified the assumption that the underwater gradient structure does not change significantly during GNSS‐A observation for several hours through applying a modified version of an analysis software called GARPOS to actual data of SGO‐A (provided by Japan Coast Guard). Obtained results suggested that this assumption holds at many observation data, and the positioning accuracy becomes better. Some non‐improved observation epochs were speculated to be accompanied by structure changes for which this assumption was not valid. It is suggested that the SSS change during observation will be an important research topic in GNSS‐A.

Abstract The GNSS-A technique is an observation method that can detect seafloor crustal deformations with centimeter-level positioning accuracy. The GNSS-A seafloor geodetic observation array operated by the Japan Coast Guard (SGO-A) has been constructed near the Japanese Islands along the Nankai Trough and the Japan Trench. This observation array has detected several earthquakes’ displacements and episodic slow crustal deformation. To compare the detection results of SGO-A with other observation networks and expand the SGO-A coverage area, it is necessary to correctly understand its detection capability. In this paper, numerical simulations and statistical verifications were used to assess the capabilities of the present GNSS-A system using a manned vessel (observation frequency: 4–6 times/year, positioning accuracy: standard deviation = 1.5 cm) to detect (1) secular deformation only, (2) a transient slip event only and (3) secular deformation and a transient event together. We verified these results with appropriate thresholds and found the following features: When it is known that there is no transient event, the 95% confidence level (CL) for the estimation of secular crustal deformation rate with 4-year observation is about 0.5–0.8 cm/year; when the deformation rate is known, a signal of about 3.0 cm can be detected by observations of about 4 times before and after the transient event. When the deformation rate and the transient event are detected together, to keep the false positive low (about 0.05), the false negative becomes high (about 0.7–0.2 for detecting a signal of 4.5–6.0 cm). The determined rate and event variations are approximately 1.8 cm/year (95%CL) and 1.5 cm (standard deviation), respectively. We also examined the detection capability for higher observation frequency and positioning accuracy, to examine how the detection capability improves by technological advancements in the future. Additionally, we calculated the spatial range of event detectability using the determined values of detection sensitivity. Obtained results show that each seafloor site can detect a slip event of

Abstract Investigations of the co- and postseismic processes of the 2011 Tohoku-oki earthquake provide essential information on the seismic cycle in the Japan Trench. Although almost all of the source region lies beneath the seafloor, recent seafloor geophysical instruments have enabled to detect the near-field signals of both the coseismic rupture and the postseismic stress relaxation phenomena. Annual-scale seafloor geodesy contributed to refining the postseismic deformation models, specifically to the incorporation of viscoelastic effects. However, because of the insufficiency in the spatial coverage and observation period of seafloor geodetic observations, no consensus on crustal deformation models has been reached, especially on the along-strike extent of the main rupture, even for the coseismic process. To decompose the postseismic transient processes in and around the source region, i.e., viscoelastic relaxation and afterslip, long-term postseismic geodetic observations on the seafloor play an essential role. Here, from decadal seafloor geodetic data, we provide empirical evidence for offshore aseismic afterslip on the rupture edges that had almost decayed within 2–3 year. The afterslip regions are considered to have stopped the north–south rupture propagation due to their velocity strengthening frictional properties. In the southern source region (~ 37° N), despite not being resolved by coseismic geodetic data, shallow tsunamigenic slip near the trench is inferred from postseismic seafloor geodesy as a subsequent viscoelastic deformation causing persistent seafloor subsidence at a geodetic site off-Fukushima. After a decade from the earthquake, the long-term viscoelastic relaxation process in the oceanic asthenosphere is currently in progress and is still dominant not only in the rupture area, but also in the off-Fukushima region.

Seafloor transponder coordinates are determined by measurements between a ship-borne GNSS-acoustic transducer and the transponder. Differencing techniques can be applied to eliminate the impact of measurement biases for precise positioning effectively. The problem is that the correlations between differenced measurements must be adequately considered in the covariance matrix, which might cause a great number of calculations. This paper presents a set of conversion formulae to derive the differenced solution from the undifferenced model without nuisance parameters, and then we propose a dimension-reduction algorithm to fast solve the Gauss–Markov model augmented with nuisance parameters. The equivalence of the differenced and undifferenced solution is discussed within a wider range. It shows that: (1) the undifferenced solution can be converted into the differenced solution with only a few additional calculations; (2) there are a class of differencing schemes which are completely equivalent to each other having unique differencing equivalence weight (DEW) matrix; (3) the proposed algorithm is more efficient and has a good numerical stability relative to the blocking–stacking algorithm and the one-by-one elimination. The simulation and the real trial performed in a 3000-m depth sea area verified the proposed results. [ABSTRACT FROM AUTHOR]

Abstract Using Global Navigation Satellite System–Acoustic (GNSS-A) technique, we have been developing observation system on a moored buoy for continuous monitoring of seafloor crustal deformation. The sound speed structure near a warm current has heterogeneity, which is the main cause of a seafloor positioning error. Assuming a sloping structure, previous studies proposed sound speed model to reduce positioning error. We examined the validity of the model by comparing the estimated structure with the actual structure measured at multiple points around our observation site. The result shows that the gradient parameter estimated from GNSS-A data acquired by vessel is appropriate. The numerical examination indicates that modeling error caused by the misinterpretation of the depth of gradient layer occurs, and it can be suppressed by performing acoustic ranging at the point near the centroid of units. From the calculation of estimation error of sound speed variation, the predicted acoustic ranging error observed using the moored buoy staying near the centroid is 9.0 cm or below. Therefore, seafloor displacement can be detected with centimeter class via moored buoy in the basin of a warm current.

The GNSS-A technique is an observation method that can detect seafloor crustal deformations with centimeter-level positioning accuracy. The GNSS-A seafloor geodetic observation array operated by the Japan Coast Guard (SGO-A) has been constructed near the Japanese Islands along the Nankai Trough and the Japan Trench. This observation array has detected several earthquakes' displacements and episodic slow crustal deformation. To compare the detection results of SGO-A with other observation networks and expand the SGO-A coverage area, it is necessary to correctly understand its detection capability. In this paper, numerical simulations and statistical verifications were used to assess the capabilities of the present GNSS-A system using a manned vessel (observation frequency: 4–6 times/year, positioning accuracy: standard deviation = 1.5 cm) to detect (1) secular deformation only, (2) a transient slip event only and (3) secular deformation and a transient event together. We verified these results with appropriate thresholds and found the following features: When it is known that there is no transient event, the 95% confidence level (CL) for the estimation of secular crustal deformation rate with 4-year observation is about 0.5–0.8 cm/year; when the deformation rate is known, a signal of about 3.0 cm can be detected by observations of about 4 times before and after the transient event. When the deformation rate and the transient event are detected together, to keep the false positive low (about 0.05), the false negative becomes high (about 0.7–0.2 for detecting a signal of 4.5–6.0 cm). The determined rate and event variations are approximately 1.8 cm/year (95%CL) and 1.5 cm (standard deviation), respectively. We also examined the detection capability for higher observation frequency and positioning accuracy, to examine how the detection capability improves by technological advancements in the future. Additionally, we calculated the spatial range of event detectability using the determined values of detection sensitivity. Obtained results show that each seafloor site can detect a slip event of < 1.0 m scale within about 30 km radius, and approximately one-third of the subseafloor slip event over 100 km from land along the Nankai Trough can only be detected by SGO-A. [ABSTRACT FROM AUTHOR]

Investigations of the co- and postseismic processes of the 2011 Tohoku-oki earthquake provide essential information on the seismic cycle in the Japan Trench. Although almost all of the source region lies beneath the seafloor, recent seafloor geophysical instruments have enabled to detect the near-field signals of both the coseismic rupture and the postseismic stress relaxation phenomena. Annual-scale seafloor geodesy contributed to refining the postseismic deformation models, specifically to the incorporation of viscoelastic effects. However, because of the insufficiency in the spatial coverage and observation period of seafloor geodetic observations, no consensus on crustal deformation models has been reached, especially on the along-strike extent of the main rupture, even for the coseismic process. To decompose the postseismic transient processes in and around the source region, i.e., viscoelastic relaxation and afterslip, long-term postseismic geodetic observations on the seafloor play an essential role. Here, from decadal seafloor geodetic data, we provide empirical evidence for offshore aseismic afterslip on the rupture edges that had almost decayed within 2–3 year. The afterslip regions are considered to have stopped the north–south rupture propagation due to their velocity strengthening frictional properties. In the southern source region (~ 37° N), despite not being resolved by coseismic geodetic data, shallow tsunamigenic slip near the trench is inferred from postseismic seafloor geodesy as a subsequent viscoelastic deformation causing persistent seafloor subsidence at a geodetic site off-Fukushima. After a decade from the earthquake, the long-term viscoelastic relaxation process in the oceanic asthenosphere is currently in progress and is still dominant not only in the rupture area, but also in the off-Fukushima region. [ABSTRACT FROM AUTHOR]

The Global Navigation Satellite System-Acoustic ranging combination technique (GNSS-A) has enabled us to measure seafloor crustal deformation in the precision of centimeters, leading to numerous discoveries of subseafloor tectonic phenomena. The moving observation conducted by our research group allows us to measure both the horizontal and vertical absolute positions of a reference point on the seafloor. However, the observation frequency of our GNSS-A observation system is still insufficient to observe short-term phenomena. This paper focused on the possibility to reduce the observation time per a seafloor site by shrinking the seafloor transponder array size and the survey line radius, which were empirically defined to be equal to the seafloor site depth in the early research. We evaluated the effects of changing these sizes on the GNSS-A positioning accuracy by conducting a series of numerical experiments. The results of the numerical experiments indicated that for a seafloor site with a depth of 3,000 m, the positioning accuracy is rapidly degraded as the transponder array size and the survey line radius are reduced to less than 3,000 m. Additional experiments done for transponder array sizes and survey line radii around 2,000–4,000 m revealed that shrinking the survey line radius has a dominant effect on the decrease in positioning accuracy. Thus, shrinking the transponder array size and the survey line radius is not a suitable option for reducing observation time, and the empirically defined observation configurations are concluded to be quite optimal when regarding both the positioning accuracy and the observation time.

Global Navigation Satellite System–Acoustic ranging combined seafloor geodetic technique (GNSS-A) has extended the geodetic observation network into the ocean. The key issue for analyzing the GNSS-A data is how to correct the effect of sound speed variation in the seawater. We constructed a generalized observation equation and developed a method to directly extract the gradient sound speed structure by introducing appropriate statistical properties in the observation equation, especially the data correlation term. In the proposed scheme, we calculate the posterior probability based on the empirical Bayes approach using the Akaike’s Bayesian Information Criterion for model selection. This approach enabled us to suppress the overfitting of sound speed variables and thus to extract simpler sound speed field and stable seafloor positions from the GNSS-A dataset. The proposed procedure is implemented in the Python-based software “GARPOS” (GNSS-Acoustic Ranging combined POsitioning Solver).

The Global Navigation Satellite System-Acoustic ranging combination technique (GNSS-A) is a recently developed technology to precisely detect seafloor crustal deformation. This method can also estimate km-scale underwater sound speed structure (SSS) as a by-product of monitoring seafloor crustal deformation. This paper evaluates the validity of the spatial gradient and its temporal variation of the SSS estimated by GNSS-A observations off the Kii channel before and after Kuroshio meandering. According to the comparison of the JCOPE2M reanalysis data and the in situ observation data, the GNSS-A estimated SSS has local structures that are not reproduced in this reanalysis but were detected by in situ data. In addition, we investigate the effect of observation time on the stability of SSS estimation. The results suggest that the sufficient time required for stable estimation depends on the spatial coverage of observation data, which depends on the depth of the site. As a result, the time resolution was derived to be about one hour at a site whose depth is 1500 m.

The Global Navigation Satellite System-Acoustic ranging combination technique (GNSS-A) is a seafloor geodetic technique that enables precise global seafloor positioning to detect subseafloor geophysical phenomena. The technique requires a sea surface observation platform that combines GNSS positioning and acoustic ranging. Currently, a survey vessel is used as the platform, which entails substantial financial and human resources costs, which makes increasing observation frequency difficult. It is possible to detect long-term average seafloor movement at the centimeter level, but it is difficult to detect short-term variation due to the insufficiency of observation frequency. The terrestrial GNSS observation network has detected temporal changes in crustal deformation fields. These precise observations provide useful information on the megathrust seismogenic zone. To detect such phenomena on the seafloor, the temporal resolution of the GNSS-A observation needs to be improved. Advances in vessel equipment technology are crucial for increasing observation frequency. In this paper, we review the historical development of the Japan Coast Guard’s GNSS-A observation system, focusing on technological developments of on-board equipment installed on a sea surface platform, and explain how such improvements have increased observation frequency over time. In the present, ranging frequency has improved from 40–60 s to 15–20 s by the introduction of the multiple ranging system, resulting in more frequent observations up to five times per year for an individual site.

Using Global Navigation Satellite System–Acoustic (GNSS-A) technique, we have been developing observation system on a moored buoy for continuous monitoring of seafloor crustal deformation. The sound speed structure near a warm current has heterogeneity, which is the main cause of a seafloor positioning error. Assuming a sloping structure, previous studies proposed sound speed model to reduce positioning error. We examined the validity of the model by comparing the estimated structure with the actual structure measured at multiple points around our observation site. The result shows that the gradient parameter estimated from GNSS-A data acquired by vessel is appropriate. The numerical examination indicates that modeling error caused by the misinterpretation of the depth of gradient layer occurs, and it can be suppressed by performing acoustic ranging at the point near the centroid of units. From the calculation of estimation error of sound speed variation, the predicted acoustic ranging error observed using the moored buoy staying near the centroid is 9.0 cm or below. Therefore, seafloor displacement can be detected with centimeter class via moored buoy in the basin of a warm current. [ABSTRACT FROM AUTHOR]

After the twenty-first century, the Global Navigation Satellite System-Acoustic ranging (GNSS-A) technique detected geodetic events such as co- and postseismic effects following the 2011 Tohoku-oki earthquake and slip-deficit rate distributions along the Nankai Trough subduction zone. Although these are extremely important discoveries in geodesy and seismology, more accurate observation that can capture temporal and spatial changes are required for future earthquake disaster prevention. In order to upgrade the accuracy of the GNSS-A technique, it is necessary to understand disturbances in undersea sound speed structures, which are major error sources. In particular, detailed temporal and spatial variations are difficult to observe accurately, and their effect was not sufficiently extracted in previous studies. In the present paper, we reconstruct an inversion scheme for extracting the effect from GNSS-A data and experimentally apply this scheme to the seafloor sites around the Kuroshio. The extracted gradient effects are believed to represent not only a broad sound speed structure but also a more detailed structure generated in the unsteady disturbance. The accuracy of the seafloor positioning was also improved by this new method. The obtained results demonstrate the feasibility of using the GNSS-A technique to detect a seafloor crustal deformation for oceanography research. [ABSTRACT FROM AUTHOR]

Global Navigation Satellite System—Acoustic (GNSS-A) positioning is the main technique for seafloor geodetic positioning. A transceiver lever arm offset and sound velocity bias in seawater are the main systematic errors of the GNSS-A positioning technique. Based on data from a sea trial in shallow water, this paper studies the functional model of GNSS-A positioning. The impact of the two systematic errors on seafloor positioning is analysed and corresponding processing methods are proposed. The results show that the offset in the lever arm measurement should be parameterised in the observation equation. Given the high correlation between the vertical lever arm offset and the vertical coordinate of the seafloor station, a sample search method was introduced to fix the vertical offset correction. If the calibration of the sound velocity profiler cannot be ensured, the correction parameter of the sound velocity bias should be solved. According to the refined functional model and corrections, the position of a seafloor station in shallow water can be determined with a precision of better than 1 cm.

Global Navigation Satellite System—Acoustic (GNSS-A) positioning is the main technique for seafloor geodetic positioning. A transceiver lever arm offset and sound velocity bias in seawater are the main systematic errors of the GNSS-A positioning technique. Based on data from a sea trial in shallow water, this paper studies the functional model of GNSS-A positioning. The impact of the two systematic errors on seafloor positioning is analysed and corresponding processing methods are proposed. The results show that the offset in the lever arm measurement should be parameterised in the observation equation. Given the high correlation between the vertical lever arm offset and the vertical coordinate of the seafloor station, a sample search method was introduced to fix the vertical offset correction. If the calibration of the sound velocity profiler cannot be ensured, the correction parameter of the sound velocity bias should be solved. According to the refined functional model and corrections, the position of a seafloor station in shallow water can be determined with a precision of better than 1 cm. [ABSTRACT FROM AUTHOR]