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This article was submitted to Solid Earth Geophysics, a section of the journal Frontiers in Earth Science

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Estimating the coseismic slip distribution and interseismic slip-deficit distribution play an important role in understanding the mechanism of massive earthquakes and predicting the resulting damage. It is useful to observe the crustal deformation not only in the land area, but also directly above the seismogenic zone. Therefore, improvements in terms of measurement precision and increase in the number of observation points have been proposed in various forms of seafloor observation. However, there is lack of research on the quantitative evaluation of the estimation accuracy in cases where new crustal deformation observation points are available or when the precision of the observation methods have been improved. On the other hand, the crustal structure models are improving and finite element analysis using these highly detailed crustal structure models is becoming possible. As such, there is the real possibility of performing an inverted slip estimation with high accuracy via numerical experiments. In view of this, in this study, we proposed a method for quantitatively evaluating the improvement in the estimation accuracy of the coseismic slip distribution and the interseismic slip-deficit distribution in cases where new crustal deformation observation points are available or where the precision of the observation methods have been improved. As a demonstration, a quantitative evaluation was performed using an actual crustal structure model and observation point arrangement. For the target area, we selected the Kuril Trench off Tokachi and Nemuro, where M9-class earthquakes have been known to occur in the past and where the next imminent earthquake is anticipated. To appropriately handle the effects of the topography and plate boundary geometry, a highly detailed three-dimensional finite element model was constructed and Green’s functions of crustal deformation were calculated with high accuracy. By performing many inversions via optimization using Green’s functions, we statistically evaluated the effect of increase in the number of observation points of the seafloor crustal deformation measurement and the influence of measurement error, taking into consideration the diversity of measurement errors. As a result, it was demonstrated that the observation of seafloor crustal deformation near the trench axis plays an extremely important role in the estimation performance.

At most of the plate convergent margins, the denser oceanic plates subduct beneath the continental plates and due to the subduction, topographic depressions, trenches or troughs, are created and filled with sea water. Since plate subduction proceeds under the seafloor, the seismogenic zone of a large interplate earthquake would also be located in the offshore region. This type of earthquake may generate a tsunami due to the crustal deformation on the seafloor resulting from the coseismic displacement. In previous M9-class earthquakes (e.g., the Tohoku, Sumatra, Cascadia, and Chile earthquakes), the induced tsunami run-up has stretched as far as several kilometers from the coastline, causing great damage. After the 2011 earthquake that occurred off the Pacific coast of Tohoku (M9, hereafter the 2011 Tohoku-Oki earthquake), the Geospatial Information Authority of Japan (GSI) and Tohoku University jointly developed the real-time analysis system to accurately estimate the moment magnitude of the huge earthquake using real-time Global Navigation Satellite System (GNSS) data (

However, it is difficult to estimate the coseismic slip behavior in the offshore regions simply based on the onshore GNSS data. In fact, the 2011 Tohoku-Oki earthquake highlighted the importance of the seafloor geodetic technique, such as the GNSS-acoustic coupling method (here in after, GNSS-A) and the seafloor pressure sensors, for understanding the slip characteristics close to the trench axis (e.g.,

In recent years, it has been confirmed that the fault slip during an earthquake involves a process of releasing the elastic strain energy stored underground, and the state of energy accumulation can be estimated via analysis of the crustal deformation data (e.g.,

Satellite geodesy based on electromagnetic waves (microwaves) has resulted in significant progress in the field of land-related crustal deformation studies. However, as the microwaves do not penetrate through seawater due to the rapid attenuation, the observation of any geodetic deformation on the seafloor requires using alternative methods such as acoustic ranging. The currently used seafloor-related crustal deformation measurement methods include the vertical crustal deformation measurement using ocean bottom pressure (OBP) sensors, the horizontal and vertical crustal deformation measurement using the GNSS-A acoustic technique (combination of GNSS and acoustic ranging), and strain measurement based on the acoustic distance measurement between different observation sites on seafloor. Here, specific analysis has been performed on the data obtained by these methods after the observation. In recent years, the real-time measurement of OBP data using submarine cable networks (e.g.,

As yet, few studies have sufficiently focused on the quantitative evaluation of the improvement in the accuracy of coseismic slip distribution and interseismic slip-deficit distribution estimations following the incorporation of such observational data. Previous studies that assess the detection ability enhancement through increasing the number of observation points do exist (e.g.,

The purpose of this study is to propose a method that will allow us to quantitatively evaluate the effect of adding offshore geodetic data in view of improving the accuracy of coseismic slip distribution and interseismic slip-deficit distribution estimations near the trench axis. We use a numerical experiment to demonstrate the approach.

The target area is the offshore region of Tokachi and Nemuro, the southwestern part of the Kuril Trench where 9M-class earthquakes have been known to occur in the past, and where the next imminent earthquake is anticipated (

Reference spatial distribution of coseismic fault slip is shown as color contour. The direction of the slip was uniform in the 112° clockwise from north direction. The rectangle (solid line) is the target area for estimating the fault slip distribution. The curved thin solid line indicates the trench axis. The GNSS observation points are represented by circles, and the S-net and PG observation points are represented by crosses. The target range of the finite element model is indicated with dotted lines in the inset figure.

Much like with the Japan Trench, the Kuril Trench is an area where the Pacific plate subducts. Based on the distribution of tsunami deposits, it has been proposed that both segments off of Tokachi and Nemuro ruptured in the Seventeenth century (

We use the geometry of the plate interface used in the tsunami hazard scenario from the Cabinet Office (Disaster Management) as announced in 2019 (

Reference spatial distribution of interseismic slip-deficit in one year is shown as color contour. The direction of the slip-deficit was uniform in the 68° counter-clockwise from north direction. The curved thin solid line indicates the trench axis. The position of GNSS observation points, GNSS-A observation points (G21, G22, G23), and the virtual GNSS-A observation points (VG1–VG4) are represented by circles, empty triangles, and filled triangles, respectively.

Since the purpose of this study is to quantitatively investigate the effect of observation error on the estimation of slip distribution, it was necessary to calculate the crustal deformation for the aforementioned reference slip distribution at each observation point, and then to provide a prescribed pseudo error for the observation data. In terms of observation data, we assume the measurement of crustal deformation via onshore GNSS, the measurement of vertical crustal deformation via OBP sensors (S-net, PG1, PG2), and the measurement of horizontal and vertical crustal deformation via GNSS-A. The measurement precision when using crustal deformation observation in terms of both land and seafloor for coseismic (precision available in real-time) and interseismic (precision obtained by post analysis) periods are shown in

Precision of the detection level of the crustal deformation for each sensor in coseismic and interseismic time.

Coseismic (real-time) | Interseismic (post-processed) | |
---|---|---|

OBP (S-net) | V: 20 mm | NA |

OBP (PG1, PG2) | V: 30 mm | NA |

GNSS-A | NA | H: 20 mm/year |

High-precision GNSS-A | NA | H: 5 mm/year |

Onshore GNSS | H: 30 mm, V: 70 mm | H: 4 mm/year, V: 8 mm/year |

H and V indicate horizontal and vertical components, respectively.

We can expect improvement to the accuracy of fault slip distribution estimation when using Green’s functions that reflect the three-dimensional (3D) crust structure with the surface topography (e.g.,

We estimated the fault slip distribution using geodetic data observed at

We estimated the coseismic slip distribution and the interseismic slip-deficit distribution off Tokachi and Nemuro using the proposed inversion method. To verify the effect of the precision of the observation data and the presence of various observation points on the estimation accuracy, a reference solution must be generated for comparison with the estimated solutions. We obtained artificial observation data by applying the FE analysis to the reference slip distribution and adding the assumed noise to it. Using these artificial observation data, we estimated the slip distribution at the fault plane via the developed inversion method. To evaluate the difference in estimation accuracy with/without observation points and with varying observation precision, we introduced a Monte Carlo approach involving the inversion for 4,000 artificial observation datasets with different noise patterns for each case. From each inversion result, we verified the error distribution and the uncertainty in the estimated seismic slip and slip-deficit.

For the crustal structure data, we used the surface topography and the plate boundary set by the Cabinet Office’s disaster prevention division (

Overview and close-up view of the FE model.

The area of the fault plane for which Green’s functions were calculated was −189 km ≤

In the following subsections, we estimate the coseismic slip and the interseimic slip-deficit distributions using the observation points shown in

We conducted estimations using two sets of observation data: 1) land GNSS, and 2) land GNSS and OBP. For the fault slip estimation immediately after the occurrence of an earthquake (within around 5 min), only GNSS results is used. Compared with the reference solution (

Mean, absolute error between mean and reference solution, and standard deviation of coseismic fault slip distribution with 4,000× Monte Carlo inversions using

The above results are the cases where model errors are ignored. If model errors are taken into account, we can imagine that the recovery to the reference model will be worse in any case. However, the important question here is how the effect of addition of offshore observation points changes when model errors are considered. Based on the results in a previous study (

The cable OBP data, which is useful for measuring coseismic seafloor deformation as shown in

Mean, absolute error between mean and reference solution, and standard deviation of interseismic fault slip-deficit distribution with 4,000× Monte Carlo inversions using

To examine the effect of the improvement in observation precision and the addition of observation points in more detail, a pointwise evaluation was performed at the installed GNSS-A observation point G22 and the virtual GNSS-A observation point VG1 (

Horizontal displacement distribution at observation points G22 and VG1 (see

Vertical displacement distribution at observation points G22 and VG1 (see

Conventionally, the measurement of the horizontal position was the main purpose of GNSS-A; however, in recent years, methods for realizing high-precision measurement in the vertical direction have been developed. Thus, it is meaningful to consider how much precision is required in the vertical displacement measurement to improve interseismic slip-deficit estimations. For a low-angle fault, the vertical displacement is smaller than the horizontal displacement, which means the difference and variance between the true value and the predicted value becomes smaller. Therefore, if the results of this study as shown in

The purpose of this manuscript is to quantify the effectiveness of the offshore data for the slip estimation especially near the trench axis. Our results demonstrate the effectiveness of the observation of seafloor crustal deformation near the trench axis, as well as the advancement in the modeling, including in terms of topography and plate geometry. For the coseismic slip, the heterogeneous distribution near the trench axis can be reproduced when we include the cable OBP data, which cover whole the offshore source area. Furthermore, it was demonstrated that the interseismic slip-deficit distribution in the shallow part of the subducting plate interface can be reproduced with high accuracy by improving the precision of the seafloor crustal deformation observations (i.e., increasing the observation frequency of GNSS-A). It was also demonstrated that the estimated resolution of the slip-deficit in the strike direction in this area can be improved and the estimation error becomes less than 10% for the whole offshore area by adding four GNSS-A observation points off Tokachi to the currently installed off Nemuro with about 70 km interval. However, the cost of increasing the number of observation points will involve not only the installment costs but also the additional costs for conducting the measurements on each occasion. Thus, obtaining the maximum effect with the minimum number of additional observation points is crucial, and the proposed method applying various combinations of possible distributions of slip-deficit and additional observation points is expected to be useful for this purpose. Meanwhile, it was shown that higher observation precision than that for the horizontal components is required for the vertical components of the observations to become useful for the improvement of the estimation of slip-deficit distribution. However, it is highly possible that this finding was due to the use of exact Green’s functions, and it is thus necessary to conduct additional research by extending the proposed method for the consideration of model error and to conduct appropriately extended evaluations. In addition, a numerical experiment was conducted with assuming a slip-deficit distribution that would suit a preparation process for a large 9M-class earthquake. However, seismic events at a plate interface can occur on a smaller scale (e.g.,

The original contributions presented in the study are included in the article/Supplementary Material, further inquiries can be directed to the corresponding author.

SM, TI, TH, and YO formulated the investigation. SM, TI, and KF developed the finite-element method, SM and TI developed the inversion method, and SM conducted the numerical experiments. TH and YO provided information and discussion related to the observation methods. All authors contributed to the article.

This work was supported by the Ministry of Education, Culture, Sports, Science and Technology of Japan (MEXT) as “Program for Promoting Researches on the Supercomputer Fugaku” (Large-scale numerical simulation of earthquake generation, wave propagation and soil amplification: hp200126) and by JSPS KAKENHI (JP18H05239).

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

We thank the two anonymous reviewers for constructive comments. Digital data of surface topography, plate boundary and coseismic slip distribution are given by Cabinet Office, Disaster Management. This work was supported by the Ministry of Education, Culture, Sports, Science and Technology of Japan (MEXT) as “Program for Promoting Researches on the Supercomputer Fugaku” (Large-scale numerical simulation of earthquake generation, wave propagation and soil amplification: hp200126) and by JSPS KAKENHI (JP18H05239). This work was partly supported by MEXT, under its Earthquake and Volcano Hazards Observation and Research Program.

Here, we explain the characteristics of each observation method and the estimation of observation precision used in this study.

OBP systems present observation sensors that allow us to continuously measure vertical crustal displacements and tsunami heights through measuring the pressure of the water column with a water pressure gauge installed on the seafloor. In recent years, cable OBP observations have been deployed mainly for the purpose of the immediate prediction of tsunamis in Japan. The obtained OBP data contain not only the crustal deformation but also the other contributions, including those of the tidal component, the non-tidal component, and the sensor-specific drift component. However, it is particularly difficult to remove the sensor-specific drift component, which means it is currently difficult to capture the slow crustal deformation in the interseismic period using OBP data. This form of data was thus not used for the interseismic slip-deficit estimation in this study. Meanwhile, the observation of coseismic crustal deformation, postseismic crustal deformation, and unsteady crustal deformation, which are phenomena with shorter time scales, has been carried out by numerous researchers (e.g.,

GNSS-A presents a technology that estimates the relative position of the reference station installed on the seafloor according to the acoustic distance measurement from the sea surface platform, with the position of the sea surface platform obtained via GNSS. The seafloor crustal deformation is then measured by combining these results. Here, we considered the precision of estimating the displacement in the interseismic period via GNSS-A.

In recent years, many attempts have been made to immediately estimate the magnitude of a large earthquake using real-time GNSS data (e.g.,

Next, we considered the precision of interseismic displacement measurement using land-based GNSS.