Earthquake detection capacity of the Dense Oceanfloor Network system for Earthquakes and Tsunamis (DONET)

We studied the earthquake detection capacity of DONET (Dense Oceanfloor Network system for Earthquakes and Tsunamis) operating in the Nankai Trough, a target region monitored for future megathrust earthquakes. The focus of this paper was to evaluate the impact on this capacity from the malfunction of parts of the network. For this purpose, the completeness magnitude, above which all earthquakes are considered to be detected by a seismic network, was used. Then, a catalog that includes events observed by DONET was used. We found spatiotemporal variability of completeness magnitude, ranging from values below 1 in one of the areas where stations are densely deployed to values above 2 at the periphery and outside of the DONET area. We conducted a simulation computation for cases of malfunction of densely distributed stations. The results showed that completeness estimates in the area near the malfunctioning stations were about 1 magnitude larger. This implies that malfunction repair and/or replacement with new stations would be desirable because they pronouncedly affect earthquake monitoring. We then demonstrated an example of how to use the information of completeness magnitude as prior knowledge to compute the b value of the Gutenberg-Richter distribution. The result indicates the b value as a proxy that can help to image stress heterogeneity when there is a magnitude-6 class slow slip event on the Nankai Trough plate boundary.


Introduction
About 80 years have passed since the last series of Nankai Trough earthquakes occurred, the 1944 Tonankai and the 1946 Nankai earthquakes, both belonging to a magnitude (M) 8 class. The Nankai Trough earthquakes occurred with a return period of about 100-200 years. The possibility of large earthquakes in the Nankai Trough has now increased. The probability of the occurrence of an impending large earthquake along the Nankai Trough is 70-80% in the next 30 years (Headquarters for Earthquake Research Promotion 2023).
In the wake of the 2004 Sumatra earthquake (e.g., Wiseman and Bürgmann 2011), the Japanese government established a seafloor network of cable-linked observatories around the Nankai Trough (e.g., Ariyoshi et al., 2021a). This network is known as the Dense Oceanfloor Network system for Earthquakes and Tsunamis (DONET: Kaneda et al. 2015;Kawaguchi et al. 2015), and is in operation to constantly monitor earthquakes Nakano et al. , 2018a and tsunamis (Maeda et al. 2015) (Figs. 1 and 2). Each station within DONET is equipped with strong-motion seismometers, broadband velocity seismometers, quartz pressure gauges, and differential pressure gauges to detect all types of seafloor movements, from slow movements such as crustal deformation to fast movements such as ground motion generated by earthquakes. DONET was developed and installed by the Japan Agency for Marine-Earth Science and Technology (JAMSTEC), and is currently being transferred to and operated by the National Research Institute for Earth Science and Disaster Resilience (NIED) (Aoi et al. 2020).
Parts of DONET stations started to be used in 2020 to create an earthquake catalog maintained by the Japan Meteorological Agency (JMA) as an open resource to evaluate seismicity, especially along the Nankai Trough, as well as for its use in long-term seismic evaluation and basic research. On the other hand, JAMSTEC, following the installation of DONET, processed waveform data to create an earthquake 5 of 48 catalog for detailed understanding of seismicity along the Nankai Trough (Nakano et al. 2018b;Yamamoto et al. 2022a,b). These are invaluable resources for seismicity-related studies. It is thus vital to establish clear quality benchmarks for the catalog. A common benchmark is the magnitude of completeness, above which all events are assumed to be detected by the seismic network (Gomberg 1991;Kvaerna et al. 2002aKvaerna et al. , 2002bEnescu et al. 2007Enescu et al. , 2009Rydelek and Sack 1989;Wiemer 2001;Cao and Gao 2002;Wiemer andWyss 2000, 2002;Marsan 2003;Woessner and Wiemer 2005;Amorèse 2007;Tinti and Mulargia 1985;Nanjo et al. 2010a). Such quantification of completeness is a necessary input for virtually any study involving the statistical properties of earthquake populations, for example, rate estimates or estimates of the b-value of the Gutenberg-Richter (GR) distribution (Gutenberg and Richter 1994;Ishimoto and Iida 1939). They provide descriptions of completeness for direct use by end users, such as cutting the catalog at a level of completeness to contain only events with magnitudes that are considered to be completely recorded.
We examined earthquake detection probabilities and completeness levels for the catalog created and maintained by JAMSTEC. Among the various existing methods to compute these detection probabilities and completeness levels, we opted to employ the Probability-based Magnitude of Completeness (PMC) method (Schorlemmer and Woessner 2008;Schorlemmer et al. 2010Schorlemmer et al. , 2018Nanjo et al. 2010b;Gentli et al. 2011;El-Hussain et al. 2020;Nanjo 2020). Using this method, for 52 stations (Fig. 2), detection capabilities were derived over time from empirical data only, namely earthquake information, phase data, station information, and network-specific attenuation relations. From the entire phase-data history, we estimated the operational times of each station, then synthesized detection-probability maps for specific magnitudes and completeness maps. These maps could be computed for any time in 2015-2019, a period in which a dataset was available for our study.

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Our focus was to examine a possible use of the PMC method, which is used to assess a network's performance (Schorlemmer and Woessner, 2008;Schorlemmer et al. 2010;Nanjo et al. 2010b, Nanjo 2020. We explored it for cases where stations were virtually removed from the existing DONET. We propose the use of this application to investigate the effect of network failures on completeness. It is of interest to demonstrate the direct use of the completeness obtained in this study as foresight information for seismicity-related studies. We studied the b-values computed by using only complete data to investigate whether they were correlated to a slow slip event (SSE) detected by the oceanfloor geodetic system, which functions independently from DONET.

PMC method and GR distribution
In this section, we first explain the PMC method. This method relies on two sources of data: (1) station data describing the location for each station in the network; (2) earthquake data describing the location, time, and M for each earthquake including data describing which stations were used to detect this earthquake. The method is divided into an analysis section and a synthesis section. We recommend the readers to also appreciate previous applications (Schorlemmer and Woessner 2008;Nanjo et al 2010b;Schorlemmer et al. 2010Schorlemmer et al. , 2018Gentili et al. 2011;El-Hussain et al. 2020;Nanjo 2020).
We then briefly introduce the concept of the GR frequency-magnitude distribution (Gutenberg and Richter, 1944;Ishimoto and Iida, 1939). Based on this GR distribution, we provide an example of using the result of completeness estimates as prior information on seismicity-related studies.
2.2 PMC method: analysis part 7 of 48 In the analysis, data triplets were first compiled for each station. A triplet contains, for each earthquake, (i) information on whether or not this station was used for detecting the event, (ii) the M of the event, and (iii) its distance L from the station. Figure 3a provides an illustrative example to show how to generate data triplets. The top panel of Fig. 3a shows that the station was used to detect events 1, 2, and 4 (green), but not events 3 and 5 (red), where the i-th event is identified by the index in M and L (Mi and Li) (i = 1, 2, …, 5).
Note that events 3 and 5 were recorded by using other stations. The data triplet of event 1 contains (i) the fact that the station was used to detect this event (green), (ii) the magnitude (M1), and (iii) its distance from the station (L1). If a station was used to detect an event, the data triplet of this event was referred to as the "plus triplet" for the station, otherwise as the "minus triplet". Data triplets of events 1, 2, and 4 are plus triplets, and those of events 3 and 5 are minus triplets. These triplets were plotted in a graph of L as a function of M. The same applies for all stations.
The illustrative example (Fig. 3a) is based on the premise of detecting an event with small M. If an event with large M occurs, the detecting algorithm -depending on the network operators' protocol-may abort using distant stations from the event in order to avoid operator overloading. Namely, there is a bias that all of the triplets are minus ones for L larger than a threshold distance and for M larger than a threshold magnitude, both predefined by network operators. Detecting the algorithm at JAMSTEC did not abort it and there was no bias for the ranges of M and L (0£M£3 and 0£L£200 km in Fig. 3b) considered in this study.
Using triplets for each station, the desire was to determine Pst(M, L), the probability that the station was used to detect an earthquake for a given set of M and L. Using data triplets close to a given pair (M, L), Pst (M, L) was computed based on the number of plus triplets, N+ (green plus symbol), divided by the sum of N+ and the number of minus triplets, N-(red minus symbol): Pst(M, L) = N+/(N+ + N-) (Fig. 3b).
Pst(M, L) was smoothed by applying a simple constraint: Pst cannot decrease with a smaller L for the same M. This smoothing accounts for high probabilities at short distances (Fig. 3b). Another constraint was also applied, namely that the smoothed probability cannot increase with decreasing M at the same distance.

PMC method: synthesis part
In the synthesis part, basic combinatorics were used to obtain the earthquake detection probability PE(M, x) for detecting an earthquake of M at location x, given a specific network configuration (Schorlemmer and Woessner 2008). PE (M, x) for DONET is defined as the probability that three or more stations detect an earthquake of M at x. The minimum number of stations must be adjusted if the DONET condition is based on another number of stations.
If PE is larger than the threshold, this is considered as an indication that an earthquake will not be missed. Previous researchers arbitrarily selected several values below but close to 1 as their threshold (Schorlemmer and Woessner 2008;Nanjo et al 2010b;Schorlemmer et al. 2010Schorlemmer et al. , 2018Gentili et al. 2011;El-Hussain et al. 2020;Nanjo 2020). Given the considerable uncertainty of all phenomena such as tectonic strain/stress accumulation, earthquakes, and others in this study, the threshold needs to be as high as possible to ensure that an earthquake will not be missed. The completeness magnitude Mp(x) is given as M above which earthquakes are detected with PE(M, x)³1-Q, where Q is the complementary probability that events will be missed. The choice of the Q value is arbitrary and should reflect desired accuracy. We assumed a conservative value of Q=10 -6 . This is lower than the values adopted by previous studies, because we desired the highest accuracy.
2.4 GR distribution 9 of 48 GR distribution is given as LogN=a-bM, where N is the number of earthquakes with magnitudes larger than or equal to M, while a and b are constants. a characterizes seismic activity or earthquake productivity of a region and b is used to describe the relative occurrence of large and small events (i.e., a high b value indicates a larger proportion of small earthquakes, and vice versa). Spatial and temporal changes in b are known to reflect the stress state of the Earth's crust (e.g., Smith 1981;Narteau et al. 2009) and are influenced by asperities and frictional properties (Hirose et al. 2002;Yabe 2003;, and by an interface locking along subduction zones (Sobiesiak et al. 2007;Ghosh et al. 2008;Nanjo and Yoshida 2018). In the laboratory, b values are inversely dependent on differential stress (Scholz 1968). If this dependence holds in the Earth's crust (Scholz 2015), then measurements of spatial and temporal changes in b could act as a 'stress meter'. To estimate b values consistently over time and space, information on completeness magnitudes is needed. Below the state of completeness, a fraction of events is missed by the observation network because: (1) they are too small to be recorded by enough stations; (2) network operators decided that events below a certain threshold are not of interest; (3) in the case of an aftershock sequence, because they are too small to be detected within the coda of larger events (Woessner and Wiemer 2005). Thus, an earthquake sample used to compute the b value must be above or equal to the level of completeness. Incorrectly estimated completeness may subsequently lead to wrong results when computing b values, and underestimation of the completeness level would lead to an underestimation of the b value.
Among existing methods to compute b values, the most basic and computationally inexpensive method is the Maximum Curvature (MAXC) method (Wiemer and Wyss 2000;Wiemer 2001 We used the test proposed by Utsu (1992Utsu ( , 1999 to examine whether the difference in b is significant. If logPb, the logarithm of the probability that the b values are not different, is equal to or smaller than -1.3 (logPb≤-1.3), then the difference in b is significant (Schorlemmer et al. 2004). We also introduced bootstrapping errors (Schorlemmer et al. 2003) to show an error bar (one standard deviation) of b and

DONET and earthquakes
DONET, one of the densest oceanfloor networks in Japan (Figs. 1 and 2), was constructed to achieve a real-time monitoring system in the central region of the Nankai Trough (Kaneda et al. 2015;Kawaguchi et al. 2015). Its primary objectives are the early detection of earthquakes and tsunamis. DONET1 and DONET2, subnetworks of DONET, cover the areas from which ruptures of the 1944 Showa Tonankai earthquake and the 1946 Showa Nankai earthquake extended to 120 km east and 120 km west, respectively (Kanamori, 1972). The previous Nankai Trough event, a set of the 1854 Ansei Tokai earthquake and Ansei Nankai earthquake 32 hours later (Ando 1975) had a rupture pattern similar to the 1944/1946 Tonankai/Nankai earthquakes. Thus, the DONET area should be intensively monitored for future mega earthquakes.

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DONET consists of 51 stations in total (Fig. 2) and each station is equipped with a ground motion sensing system as well as a pressure sensing system. The former system consists of a strong-motion seismometer and a broadband velocity seismometer Nakano et al. , 2018Maeda et al. 2015), while the latter system consists of a quartz pressure gauge and a differential pressure gauge (Araki et al. 2017;Ariyoshi et al. 2021a,b). Burying the ground motion sensing system into the sediment layer reduced the background noise and other environmental effects (Araki et al. 2008;Kaneko et al. 2009). For DONET1 and DONET2, the looped backbone cable that provides the power feed and communications channel to stations is separately connected among science nodes (Fig. 2c). The node is a device that functions as a hub that connects the stations. DONET1 has five science nodes connecting 22 stations while DONET2 has seven science nodes connecting 29 stations, where each node connects 4 or 5 stations at a station interval of 10-20 km and stations are aggregated around each node. All DONET data are transmitted to JAMSTEC, JMA, and NIED in real-time where they are stored. Additionally, one station called KMDB1 (Kopf et al. 2011), which was installed in a borehole, and with a broadband velocity seismometer, was operating during the period of investigation (2015-2019), so we included this station in our analysis (Fig. 2).
As of March 31, 2019 (the most recent time of earthquakes stored in the catalog we used), DONET was operating 41 stations and one borehole station (KMDB1), as shown in Fig. 2a,b. The operation of Node A (4 stations) and Node E (5 stations) of DONET1 was interrupted since 2018 and 2016, respectively, due to a defective connection between these nodes and the backbone cable caused by a malfunction of these nodes.
The operation of station MRF22 connecting Node F of DONET2 was also interrupted since 2018 due to a communication failure between the node and the station.
JAMSTEC is recording seismicity in and around the central Nankai Trough with DONET, including ordinary and very low-frequency earthquakes, and tremors. JAMSTEC created an earthquake catalog that includes ordinary earthquakes since Oct. 2015 to Mar. 2019. It was created by using waveform data of broadband velocity seismometers, while strong-motion seismometers are rarely used. The method of Horiuchi et al. (2010) was used for event detection and automatic arrival time picking. Operators visually revised the results of automatic picking for events that were detected by three or more DONET stations and were located in and around the authoritative region within which JAMSTEC aims to detect earthquakes (134-138°E, 32-34°N). In the operation associated with this visual revision, operators additionally checked waveform data for all stations to conduct manual picking. However, there is an exception for a specific period (Sep. 2016 to Mar. 2017) in which operators did not check them for all stations (see the subsection "Operational times for individual stations").
To define our study region, we used the authoritative region (134-138°E, 32-34°N) to cover the extent of DONET and a depth range of 0-60 km. For this study region, the catalog contains 11,538 ordinary events for M=-0.4 to 5.9 from Oct. 2015 to Mar. 2019 ( Fig. 1). Our interest was the earthquake detection capacity along the Philippine Sea plate. Seismicity in the Philippine Sea plate in the coupling zone is considered to reflect interplate partial locking between the subducting plate and the overriding plate (Matsumura 1997). We considered seismicity both around the plate boundary and within the Philippine Sea plate. We retrieved from the catalog, any earthquakes in the depth range from 5 km above the plate boundary (or the upper surface of the Philippine Sea plate; Nakanishi et al. 2018) to 25 km below the boundary. The shallower limit of the depth range, namely a depth of 5 km above the plate boundary, was used to ensure that a usual depth error was taken into consideration. Since PE and Mp are computed for points in space and time, the depth at which these values are computed needs to be defined.

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To find a meaningful depth, we investigated cross-sectional distributions of earthquakes. Visual inspection of the three selected cross-sections (Fig. 1b) shows that a depth of 10 km below the plate boundary is an appropriate depth to represent seismicity along the Philippine Sea plate. We defined it as the depth for which we computed PE and Mp.
We used only P-phases recorded by DONET stations because of the greater accuracy of P-phase detection relative to S-wave detection. To improve the reliability of locating earthquakes and estimating their magnitudes, JAMSTEC retrieves data from onland stations. The onland stations that are not connected to the detecting algorithm were not included in our analysis. JAMSTEC routinely computes magnitude with the attenuation relation of Watanabe (1971) To compute Pst(M, L), data triplets were used, each having M and L close to a given pair (M, L). Triplets were selected by measuring the distance between each triplet and pair (M, L). To measure such a distance, a metric in the M-L space needs to be defined. Schorlemmer and Woessner (2008) proposed the use of an attenuation equation for earthquakes located in a given local seismic network, and redefined a metric in the transformed magnitude-magnitude space. In this study, we followed this idea and used the attenuation equation of Watanabe (1971). We selected all triplets that obey the criterion of metric£0.4, which is a usual magnitude error (roughly the mean of the standard deviations of magnitudes determined by JAMSTEC).
This approach assumes that single earthquakes occur at different times because multiple earthquakes that had occurred at different locations at the same time were not reported by JAMSTEC during 2015-2019.

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As a basis of the seismicity study, understanding magnitude scales is critical. We examined whether large earthquakes in our catalog were indeed large, as in the JMA catalog, and vice versa. We used earthquakes in the authoritative region (134-138°E, 32-34°N, depth of 0-60 km) for both catalogs. Then, an earthquake in the DONET catalog was paired with that in the JMA catalog if the time difference between them was within two seconds and the epicentral distance between them was less than 30 km, while ignoring one-to-multiple cases. A list of paired earthquakes (Fig. 4a) shows that magnitude of the DONET catalog was positively correlated with magnitude of the JMA catalog (MJMA). A similar correlation was observed in a previous study (Yamamoto et al. 2022). We also found that the slope of the least-square regression line between these magnitudes (black line) was less than one, due to the tendency M>MJMA for small magnitudes (MJMA from 0 to 2~3). To show that this tendency was location-dependent, the study region was divided into a nearshore region (33-34°N) and an offshore region (32-33°N) (Fig. 4b,c). The slope of the regression line for the former region ( Fig. 4b) was larger than that for the latter one (Fig. 4c). This suggests that for the offshore region, the tendency of M>MJMA was more pronounced with decreasing MJMA. The relation between M and MJMA will bedebated in the "Discussion and conclusions" section.
Although sophisticated regressions such as the weighted linear regression (weighted least squares) are available, a simple approach was taken to capture essential aspects of the relation between M and MJMA. That is, we took the ordinary linear regression (ordinary lease squares) and showed the results using the black line in Fig. 4a-c.

SSE
As shown in the "Results" section, information on the resultant completeness is applicable to seismicity analysis. As an example, we will investigate the relation between the spatiotemporal changes in b and Various slow earthquakes, including not only SSEs but also tremors and very low-frequency events, occur along the Nankai Trough (Tamaribuchi et al. 2022;Takemura et al. 2022). The observation of slow earthquakes' analogies and differences has a multidisciplinary value with respect to the physical process of the plate boundary (Yokota and Ishikawa 2020). Our future research aims to conduct comparative studies among various slow earthquakes (SSEs, tremors, and very low-frequency events) and ordinary (fast) earthquakes. As a first attempt, we considered one example in the "Results" section, comparing ordinary (fast) earthquakes based on b values with an SSE.

Operational times for individual stations
To compute operational times of all stations for the entire period of investigation, picks recorded by each station to detect an earthquake were plotted as a function of time (green dots in Fig. 2a For each station, it was necessary to define the time range from which pick information was sampled to compute detection-probability distributions (Fig. 3b), as described in the "Methods" section.
Offtime periods for some stations were short and negligible compared with their entire lifetime, so we decided to use the entire lifetime (grey bars in Fig. 2a,b). There was no triplet for short distances (L<10 km) due to the distances from stations to earthquakes along the subducting Philippine Sea plate (earthquakes with depths equal to or shallower than a depth of 5 km above the plate boundary were not used). Pst>0.8 (green) in M=0.5~2.5 was found for L=0~30 km, highlighting that the dense configuration of stations connecting Node B enhanced the detection capacity of earthquakes for such values of M and L. Detection probabilities decreased with increasing distances while keeping the magnitude fixed. This is in accordance with the expectation that the probabilities should be higher for smaller distances and higher magnitudes. This characteristic was, in principle, recognized for all of the stations. on Jan. 1, 2019 (Fig. 2a,b), where L is the distance from x to a station. The distribution of Pst(M, L) for each station was computed based on data triplets for the period shown in a grey bar in Fig. 2a Fig. 5a. The same applies to M=1.5 and 2.0. As expected, the three maps (Fig. 5a-c) show that PE increased with M. We plotted, in Fig. 5a-c, earthquakes in the depth range from 5 km above the plate boundary to 25 km below the boundary during Oct. 16, 2018-Mar. 31, 2019, where station configuration was unchanged (Fig. 2a,b), including our selected time point, Jan. 1, 2019. These earthquakes were located in areas with predominantly high probabilities, supporting consistency between our synthesis and the observation. Figure 5a shows spatial variability of detection probabilities for M=1.0: a large PE is highlighted in areas near the stations. In particular, PE≥0.9 (green) for M=1.0 was observed in three areas: the DONET1 area, the area near Node A, B, …, and F of DONET2, and the area near Node G of DONET2. Although PE for M=1.5 was generally > 0.9 over almost the entire DONET area (Fig. 5b), we again observed a similar variability and strong decrease towards the outside of the DONET area. PE≥0.9 for M=2.0 (Fig. 5c) was observed over almost the entire study region (i.e., the authoritative region of DONET).

Mapping PE and Mp in and around DONET
We found that Mp for Jan. 1, 2019 (Fig. 6a)   Node E of DONET2. The most likely scenario is a malfunction of this node. When excluding the Node E stations of DONET2, completeness magnitudes were larger than or equal to the completeness magnitude of the stations. In detail, the DMp map in Fig. 7c shows that completeness estimates, excluding Node E stations of DONET2 in the area near this node, were about 1 magnitude larger (orange). This map also shows a general decreasing trend of DMp with increasing distance from this node. Removing another Node D next to the removed Node E, which would imply a further enhanced scenario of node malfunction ( Fig. 7b), was considered next. In detail, completeness estimates, excluding stations of Nodes D and E of DONET2 in the area near these nodes, were about 1.2 magnitudes larger (red) (Fig. 7d). Similar to Fig. 7c, there was a general decreasing trend of DMp with increasing distance from Nodes D and E of DONET2 (Fig. 7d). The spatial extent of the influence was broader.
The area that covers the extent of Nodes D and E is located near the region which straddles the rupture zone of the 1944 Tonankai earthquake and the rupture zone of the 1946 Nankai earthquake. Near this region, the former rupture started to propagate east while the latter one propagated west. Future Nankai Trough earthquakes may have a similar rupture characteristic to the 1944/1946 Tonankai/Nankai earthquakes. Given that the sites near Nodes D and E of DONET2 in Fig. 6a showed the lowest Mp values (<1) in the study region, failure of Nodes D and E affecting earthquake monitoring would be the most pronounced among these nodes' failures. Repairing these nodes or replacing them with new ones when their malfunction occurs would be desirable.
On the other hand, our scenario computation resulted in DMp<0.4 (white in Fig. 7b,d) at almost all sites except for the area that covers the extent of Nodes D and E, where the usual magnitude of error of DONET was 0.4, as described in the "Data" section. This can be interpreted as an indication that the 21 of 48 success of aggregated configuration of stations around the respective nodes enhanced the stability of event detection capacity.

Applied example by using the result of Mp
Many papers that employed a completeness study argued that for virtually any statistical analysis of earthquake catalogs, the knowledge of completeness of the catalog is crucial (e.g., Wiemer 2001;Wiemer andWyss 2000, 2002;Woessner and Wiemer 2005;Schorlemmer and Woessner 2008;Nanjo et al. 2010a,b). In this paper, we included an applied example by using the resultant Mp as foresight information on seismicity-related studies. We present a comparison between the spatiotemporal changes in b and the M6.6 SSE whose fault model is shown in Fig. 1a. Crustal deformation due to this SSE, which grew over time during 2017-2018, caused stress perturbation in nearby regions. The overriding continental plate slipped with respect to the subducting Philippine Sea plate during the occurrence of the SSE, causing stress to accumulate in a down-dip volume of the Philippine Sea plate, while stress relaxed in an up-dip volume of the same plate. It remains uncertain whether the changes in b in space and time, reflecting the state of stress (Scholz 1968(Scholz , 2015Smith 1981;Narteau et al. 2009), is applicable to assist image stress transferred by the slow slip of an SSE. The M6.6 SSE allows us to address this idea.
In creating Fig. 8a, which shows a time-series of b values for up-dip and down-dip volumes (blue and red regions in Fig. 1a), we used earthquakes in a depth range from the plate boundary to a depth of 25 km below the plate boundary ( Supplementary Fig. S1). We then employed a moving window approach, whereby the window covers 80 earthquakes. The MAXC method (Wiemer and Wyss 2000;Wiemer 2001) was applied to 80 earthquakes covered by the window for computing Mc(MAXC). Then, for computing b, the maximum-likelihood method was applied to earthquakes with M³Mc(MAXC)+Mcorr (Woessner and Wiemer 22 of 48 2005). From our study (Fig. 6a-c), the completeness level in the source area of the M6.6 SSE was Mp~2, irrespective of time in 2015-2019. We used this as prior information. We decided to select Mcorr=0.5 in order for the b value to be computed based on earthquakes with M~2 or higher. Fig. 8b confirms that Mc(MAXC)+Mcorr was around 2 throughout the entire investigation period. Note that a recommended value Mcorr=0.2 (Woessner and Wiemer 2005) was not used for our case. Figure 8a, which shows a time-series of b values computed using samples with M³Mc(MAXC)+Mcorr with Mcorr=0.5, is a product that considers Mp.
The b values for the up-dip and down-dip regions (red and blue regions in Fig. 1a) were mostly around 1.5 before the start of the SSE, after which the b values for the former region (thick red curve in Fig. 8a) showed an increase over time, to values around 2. In contrast, for the latter region, b values showed a decrease over time, to values around 1 (thick blue curve in Fig. 8a). The difference in b between these regions was significant on 2017.5 [decimal year] or later, taking the error bars of b values into consideration.
The result is not induced by sampling bias (thin blue and red curves in Fig. 8a,b). We changed the sampling criterion slightly: sampling earthquakes at a depth range from 5 km above the plate boundary to a depth of 25 km below the plate boundary, in order to take a usual depth error (5 km) into consideration for earthquakes near the plate boundary ( Supplementary Fig. S2). We applied the same plotting procedure as before. The data for both sampling cases (thick and thin curves in Fig. 8a,b) show the decreasing and increasing trends in b during the SSE for the down-dip side (blue curves) and the up-dip side (red curves), respectively. Moreover, the same analysis was conducted for a longer window covering 100 earthquakes ( Supplementary Fig. S3), resulting in a similar result as that in Fig. 8a,b. Figure 8c, which indicates the frequency-magnitude distribution of earthquakes after the start of SSE from the down-dip volume (blue) and 23 of 48 the up-dip volume (red), shows a significant difference in b between them. Our overall results support that the changes in b reflect the changes in stress state caused by crustal deformation due to the SSE.
The same analysis as Fig. 8 was performed for using the JMA catalog. Supplementary Fig. 4 shows similar (but insignificant) outcome to Fig. 8. In creating Supplementary Fig. 4

Discussion and conclusions
The ability of DONET to detect an earthquake was evaluated in this study. We used a currently available catalog that includes earthquakes with M=-0.4~5.9 from Oct. 1, 2015 to Mar. 31, 2019 in and around the authoritative region of DONET (Fig. 1). From this catalog, earthquakes along the Philippine Sea plate were selected. The PMC method was applied to these earthquakes, and adjusted to the evaluation of DONET's performance. The PMC method is not based on sampling earthquakes over time and space, and Mp is not the completeness of a volume from which a sample is drawn. Instead, the PMC method is based on a station's characteristic, namely Pst (Fig. 3b), and Mp is the completeness defined at any location and time point in a given study region and investigation period. We considered the authoritative region of DONET (black rectangle in Fig. 1) as the study region, and used 0.05° × 0.05° grids as location points where Mp was computed. The entire period of earthquakes included in the earthquake catalog (Oct. 1, 2015 to Mar. 31, 2019) was considered as the investigation period, and time points when Mp was computed were selected: Jan. 1 for 2016, 2018, and 2019 (Fig. 6).

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Regions of high probabilities (PE³0.9) in Fig. 5a that DONET detected an earthquake of M=1 for Jan.
1, 2019 covered almost all areas of DONET. PE³0.9 for M=2 (Fig. 5c)  The probability PE=0.999999 was based on two assumptions: first, that future seismicity would replicate past seismic activity, and second, that earthquakes are independent, identically distributed events (e.g., Schorlemmer and Woessner, 2008;Nanjo et al., 2010b). In reality, however, there are many confounding factors such as depth, focal mechanism, aftershock sequences, and other spatiotemporal changes, that can significantly modify the probability of being able to detect an earthquake. Moreover, external causes such as meteorological and oceanographical events can also strongly affect the complementary probability Q. Thus, even if contour lines of PE=0.999999 convey useful information, to avoid any misunderstanding, it is better to keep in mind that such factors and causes were not considered in this study. Only one issue among them was addressed in this study, namely external causes that were taken into account, using the network failure of DONET. We assumed that operation of stations connecting Nodes A and E of DONET1, which were interrupted since 2018 and 2016, respectively (Figs. 2a and 6a-c), had restarted. The area that covers the extent of these nodes corresponds to a deep part of the rupture region of the 1944 Tonankai earthquake, and is associated with a transition between strong and weak plate-coupling zones. The transition zone may be the area at which initiation of future megathrust rupture is likely. Restarting the operation allowed us to intensively monitor seismicity around one of the target areas for future Nankai Trough events.
Second, we used PMC as a scenario computation tool to infer network performance for the virtual removal of stations. Two cases that correspond to a failure of Node E of DONET2 and a failure of another Node D next to the failed Node E showed max DMp~1.0 (Fig. 7c) and 1.2 (Fig. 7d). Given that the earthquake detection capacity at sites near Nodes D and E was the highest in the study region (Fig. 6a) and that rupture initiation of the previous Nankai Trough events (the Tonankai/Nankai earthquakes in 1940's) occurred at sites near Nodes D and E, failure of Node E or both Nodes D and E would be the most pronounced among nodes' failures. Repairing these nodes or replacing them with new ones if they malfunctioned, would be desired.
Even with the failure in operation of one or two nodes, no significant increase in Mp (no significant lowering of earthquake detection capacity) occurs in surroundings of the areas that covered the extent of the failed nodes (Fig. 7c,d). This indicates that the strategy of aggregated configuration of stations around the respective nodes was successful, implying that this configuration minimizes the impact of node malfunction.
An example of how to use Mp information as prior knowledge to seismicity-related studies was demonstrated (Fig. 8). We discuss the reason for these difference based on the comparison between M and MJMA in Fig. 4c for the offshore region, which includes the SSE source area. Since the tendency of M>MJMA was more pronounced with decreasing M (Fig. 4c), the data in the GR distribution for DONET were systematically shifted toward larger magnitudes, and this shift was larger for small M than for large M. The shift in magnitude increased the slope of the GR distribution, suggesting this as a reason for the larger b value for DONET than for JMA.
The main factor impacting the shift in magnitude is the difference between the equation to define magnitude employed by JAMSTEC (equation provided by Watanabe, 1971) and that by JMA (equation values. Another possible factor is increased uncertainties in magnitude determination and event location for the JMA catalog due to distant monitoring of offshore events from onland networks. This was likely the cause of insignificant outcome shown in Supplementary Fig. 4. Further possible factors include difference in network operating procedures between JAMSTEC and JMA, and interaction of one or more of the above-described factors.
The focus of our future research is two-fold: 1. The reader may note that it is not straightforward for the current study to assess the robustness of the temporal change in the b value associated with SSE because the data used for the evaluation is only three years (Fig. 8). JAMSTEC is updating a catalog to include recent events into it. A longer duration of the b value timeseries is required to validate our hypothesis.
2. Our future work will be directed at showing spatiotemporal variability of the completeness magnitude and the monitoring capability in a real-time fashion through a website. That is because the Nankai Trough is one of the areas where seismicity should be monitored intensively.

Acknowledgments
The authors thank JAMSTEC for the earthquake catalog.