A Single‐Station Method for Seismic Detection of Slow Earthquakes: Applications to Japan and the Mexican Subduction Zone

Slow‐earthquake signals are generally smaller than or comparable to noise levels at almost all seismological frequencies. Comprehensive detection of these events requires continuous waveforms from many stations, but such data are not always available, even in regions with high slow‐earthquake activity. We therefore need a simple and stable detection method that is also applicable to regions with sparse seismic observation networks to truly advance our understanding of slow earthquakes. Here, we utilize the proportionality between the seismic energy rate and seismic moment rate of slow earthquakes to develop a slow‐earthquake detection method using broadband waveforms from a single station. We introduce the method and estimate its performance using continuous waveform data in Japan. The new method only detects events when the tectonic tremors occur near the station, for example, 89.1% of the detections have corresponding tectonic tremor activities within 60 km, which suggests that the false‐positive rate is low. We then apply it to waveform data from the Guerrero, Oaxaca, and Jalisco regions along the Mexican subduction zone. The results for the Guerrero and Oaxaca regions are largely consistent with the geodetic and seismological results from a previous study. We also detect many events in the Jalisco region using a permanent station and provide the first seismological report of long‐term slow‐earthquake activity in this region. Some of the large‐scale slow‐earthquake activity that is detected in this study is consistent with the timings of known slow‐slip events, which implies that other unknown slow‐slip events may have occurred when we detected many events.

Tectonic tremor and VLFEs are strongly related and often regarded as different manifestations of a single process, as these two seismogenic phenomena occur simultaneously at almost the same location and with almost the same focal mechanism (Ide et al., 2007).Previous studies have sought to explain the relationship between these phenomena (e.g., Gomberg et al., 2016;Hawthorne & Bartlow, 2018;Ide, 2008).However, recent observations have suggested that we do not have to consider these phenomena separately.This separation is simply due to the seismological observation limit, which is defined by the large microseism signals that are dominant in the 0.1-1.0Hz band between these two phenomena.In fact, Kaneko et al. (2018) were able to directly observe continuous broadband signals that span the entire 0.01-10 Hz frequency range using a broadband seismometer in a deep ocean-bottom borehole that was located within 10 km of the earthquake sources along the shallow part of the plate interface in the Nankai subduction zone during a period when the microseismic noise was low (Kaneko et al., 2018).In addition to this special direct observation, such continuous signals that span the 0.01-10 Hz frequency range and cannot be observed directly have been obtained indirectly by stacking the LFE signals that radiated from the deeper part of the Cascadia (Ide, 2019) and Nankai (Masuda et al., 2020) subduction zones.
The idea that a single slow earthquake radiates signals in two frequency bands indicates that it should not be surprising that the measured seismic energy rate for tectonic tremor and the measured seismic moment rate for VLFEs are almost always proportional, as reported by Ide et al. (2008).Ide et al. (2008) showed that the seismic moment rate functions of the analyzed VLFEs, which were estimated in the 0.005-0.05Hz band, had a nearly identical shape to the seismic energy rate function, which was approximated by the smoothed squared velocity tremor waveforms in the 2-8 Hz band, using a broadband seismometer at a single station in the Nankai subduction zone.Similar observations have been confirmed in other regions (e.g., S. Baba et al., 2021;Ide & Yabe, 2014;Yabe et al., 2019Yabe et al., , 2021)).These results suggest that the scaled energy (Kanamori & Rivera, 2006), which is the ratio of the seismic energy and seismic moment, is constant.This constant has been estimated to be 10 −10 to 10 −8 (e.g., Ide & Maury, 2018), which is much smaller than the constant used to scale the energy of ordinary, fast earthquakes (10 −5 to 10 −4 ; Ide & Beroza, 2001).The present study utilizes this proportionality between the seismic energy rate and seismic moment rate of slow earthquakes to develop a new method for seismological slow-earthquake detection.
Although most seismological detection methods for slow earthquakes use multiple stations (e.g., Asano et al., 2008;Maeda & Obara, 2009;Obara, 2002;Wech & Creager, 2008), a single station may be sufficient to detect events, thereby making a single-station approach ideal for applications in sparsely instrumented regions.Brudzinski and Allen (2007) analyzed the filtered envelope amplitudes in the 2-6 Hz band and detected peaks that correspond to tectonic tremor activity.Kao et al. (2007) calculated the moving average and scintillation index of each segment of seismic waveforms in the 1.5-5.0Hz band on an hourly basis and used the combination of these statistics to classify each waveform segment as either a regular earthquake, background noise, or tectonic tremor.Sit et al. (2012) compared the envelope amplitudes of three frequency bands (2-5, 10-15, and 0.02-0.1 Hz) that correspond to the tectonic tremor, local earthquake, and surface-wave passbands, respectively.Husker et al. (2019) created spectral templates of tectonic tremor events and compared them with continuous waveforms.However, these above-mentioned methods primarily targeted tremor events and/or their activity and only analyzed waveforms in the 1-10 Hz band or a narrower frequency band within this range, even though it is not easy to distinguish the signals from various noise sources using limited information in a single, narrow frequency band.Therefore, the present study uses signals in both the high-and low-frequency bands at a single station and compares the time functions, as opposed to the spectral amplitudes, based on the idea that slow earthquakes are a broadband phenomenon.
The remainder of this paper is organized as follows.We first describe the data used in the analysis and the new single-station seismic method for slow-earthquake detection in Section 2. We then show the results of the application of the new method using waveform data from the Nankai subduction zone in Section 3, where we confirm that the detected events are consistent with known slow-earthquake activity.We also apply the new method to waveform data from the Mexican subduction zone, where we show that some of the detected events are consistent with previous studies and also discover previously undocumented slow-earthquake events using the new method.In Section 4, we discuss the validity of the parameters in our method and some special cases where the new method is ineffective.Finally, we conclude with a summary of our method and the main findings in Section 5.

Study Region
We first develop and verify the new method using slow earthquakes in the Nankai subduction zone, which is one of the most studied regions for slow earthquakes, with frequent episodic activity along both the deep and shallow parts of the plate interface (e.g., Obara, 2020).Here, we focus on the deep part, where the tectonic tremor events are distributed within a belt-like zone that possesses several gaps from the Bungo Channel in the west to the deep part of the Suruga Trough in the east (Figures 1a and 1b).Although LFEs and VLFEs have only been detected in parts of the tectonic tremor distribution, stacking the tectonic tremor waveforms has enabled the extraction of impulsive signals, such as LFEs in the high-frequency band and VLFEs in the low-frequency band, even where only tectonic tremors occur (Ide, 2021;Ide & Yabe, 2014).We therefore assume that the tectonic tremor distribution represents that of slow earthquakes and compare our results with the tectonic tremor catalog compiled by Mizuno and Ide (2019).
The single-station method is more suitable for less-instrumented regions.Here, we select the Mexican subduction zone, a well-studied region with moderate seismological instrumentation where various slow earthquakes have previously been reported (Figure 1c; Kostoglodov et al., 2010;Lowry et al., 2001;Maury et al., 2016Maury et al., , 2018)).The Servicio Sismológico Nacional (SSN) has been operating a nationwide permanent network of broadband seismometers across the region; however, the station density is not uniform.Although tectonic tremor events can be detected using only the SSN network in some regions, a lot of detections were only possible with the help of campaign observations.In the Jalisco region, which lies along the northwestern section of the Mexican subduction zone, tremor activity has been studied using data from the Mapping the Rivera Subduction Zone (MARS) observational campaign (Yang et al., 2009) during the period from January 2006 to June 2007 (e.g., Brudzinski et al., 2016;Ide, 2012;Maury et al., 2018).In the Guerrero region, LFE, Three-letter codes refer to the stations specifically mentioned in the manuscript.The green dots represent the tremor distribution along the Nankai subduction zone (Mizuno & Ide, 2019).Dashed lines and two-letter codes here and in (b) and (c) represent trench lines and plate names.AM, Amur Plate; PS, Philippine Sea Plate; PA, Pacific Plate; OK, Okhotsk Plate; CO, Cocos Plate; RI, Rivera Plate; NA, North America Plate (Bird, 2003).(b) Enlarged map of the Nankai subduction zone in (a).Dotted lines are the isodepth of the top of the subducting plates every 10 km (T.Baba et al., 2002;F. Hirose et al., 2008;Nakajima & Hasegawa, 2007).(c) Map of the Mexican subduction zone, showing the distribution of stations and deep tectonic tremor.The triangles denote the stations used in this study.The green dots represent the deep tectonic tremor distribution along the Mexican subduction zone (Maury et al., 2018).The four-letter codes next to the stations are the station names.Dotted lines are the isodepth of the top of the subducting plates every 10 km (Hayes et al., 2018).
tremor, and VLFE activity has been studied using data from the Meso America Subduction Experiment observational campaign during the period from January 2005 to June 2007 and G-GAP observational campaign during the period from November 2009 to December 2013 (e.g., Farge et al., 2020;Frank et al., 2014;Idehara et al., 2014;Maury et al., 2016Maury et al., , 2018;;Payero et al., 2008).In the Oaxaca region, which is to the southeast of the Guerrero region, tremor and VLFE activity has been studied using data from the G-GAP observational campaign and the local OXNET seismic-global positioning system (GPS) network (e.g., Brudzinski et al., 2010;Fasola et al., 2016;Maury et al., 2018).Maury et al. (2018) successfully detected tremor events and VLFEs in the Oaxaca region using only SSN permanent stations; however, the study region was limited to a part of the western Oaxaca region due to the station coverage.These previous studies highlight that longterm continuous observations of slow earthquakes have not been possible along most sections of the Mexican subduction zone to date.

Data
The data consist of continuous three-component broadband velocity seismograms.For the Nankai analysis, we used the waveform data from 75 station of F-net (National Research Institute for Earth Science and Disaster Resilience, 2019), which is a broadband seismograph network within the nationwide Monitoring of Waves on Land and Seafloor integrated observation network in Japan (Aoi et al., 2020;Figures 1a and 1b).We included all of the available F-net stations (i.e., not just those near the slow-earthquake zone), to verify the applicability of our proposed method.For the Mexican analysis, we used the continuous waveform data from seven stations in the SSN network across Mexico to analyze three regions (Jalisco, Guerrero, and Oaxaca) where slow-earthquake activity has been confirmed (Figure 1c).Each seismogram has been resampled to 20 samples per second.The station list and associated study period for each seismic station in Japan and Mexico are provided in Table S1.

Method
This study utilizes the key characteristics of slow earthquakes, whereby the seismic energy rate and seismic moment rate of slow earthquakes are always proportional (Ide et al., 2008).We compare the seismic energy rate of the observed waveforms in the high-frequency band and the seismic moment rate of the observed waveforms in the low-frequency band and consider the signal to be that of a slow earthquake if the two waveforms are similar.The period with such a similarity between the high-and low-frequency bands is then extracted from the continuous data and considered to be the period when slow-earthquake activity occurs.The proposed method is described in detail below and illustrated in Figure 2.
We first compute a time function, e HF , which is almost proportional to the seismic energy rate function.The original three-component velocity data are band-pass filtered at 2-8 Hz, squared, summed over the three components, and then band-pass filtered at 0.02-0.05Hz as follows: where v i (t) is the velocity signal for component i, and The seismic moment rate is approximately proportional to the observed far-field displacement (Aki & Richards, 1980, 2002).Therefore, we integrate the velocity time series to obtain the associated displacement and apply a 0.02-0.05Hz band-pass filter to obtain a time function, u LF , which is approximately proportional to the moment rate function.Here, we limit the frequency range to minimize the effects of scattering and microseism noise on u LF : where Δt is the sampling interval (=0.05 s) and v U-D (t) is the velocity of the vertical component, which is used because its background noise is the lowest among the three components. 10.1029/2023JB027311 5 of 14 The similarity between e HF and u LF is examined for each time step Δt CC (=10 s) in time window T CC (=300 s) in the correlation coefficient time series.The correlation coefficient between e HF and u LF at time t is calculated as follows: where and N is the number of the sampling points defined as The CC time series often contains spiky false signals due to other factors, such as local regular earthquakes with the corner in 0.02-0.05Hz, equipment failure, or interpolations due to missing data.We therefore take the moving average of CC over time window T MA (=10,000 s) to suppress these false signals and only extract the slow-earthquake signals: where M is the number of the sampling points defined as Figure 3 shows examples of the CC MA histograms for a 1-year period using stations in regions proximal and distal to the slow-earthquake activity.The histogram for station KZK, which is located at least 195 km from the slow-earthquake activity, can be approximated by a normal distribution, with a standard deviation of 0.035 (Figures 3a and 3d).This approximation is correct around 0, and the distribution has short tails because the correlation coefficient values are between −1 and 1 (Figure S1 in Supporting Information S1).Conversely, the histograms for stations KIS and TGA, which are within the band-like slow-earthquake zone, are asymmetric (Figures 3b,3c,3e,and 3f).One side is the same as that for the region with no detected slow-earthquake activity; however, the other side possesses a large tail and deviates from a normal distribution.The periods with such large values are regarded as periods with slow-earthquake activity.The polarity depends on the station and slow-earthquake activity locations because the displacement data can be inverted with respect to the seismic 10.1029/2023JB027311 7 of 14 moment rate, which is influenced by the radiation pattern.The threshold is set to 4 times the standard deviation of CC MA (4σ) for the entire study period at each station, and continuous time steps with CC MA exceeding the threshold are regarded as a detection.The false-positive rate is 0.006% when a normal distribution is assumed, which equates to about 10 hr for the 18-year period of the analyzed F-net waveforms in Japan.
Even after using the moving average, these detections may include false detections.We can reject some of these false detections using the signal amplitude information.We can assume that the signals with very large amplitudes are coming from other sources, such as seismic waves from large earthquakes and anthropogenic sources, since the signals from slow earthquakes along the deeper part of the subduction zone are generally very small in the 0.02-0.05Hz band (e.g., Ito et al., 2007).Therefore, we calculate the root-mean-square amplitude of the velocity data for the horizontal components in the 0.02-0.05Hz band each hour and exclude the period from the detection when it exceeds 1 × 10 −7 m/s.

Application to Slow-Earthquake Detection in Japan
We applied the new method to the F-net continuous seismograms.Figure 4 shows an example of the time series of the moving-average correlation coefficient, CC MA (Equation 7), at station KIS.CC MA usually stays around 0, as expected based on Figures 3b and 3e, with occasional high values obtained.These high values denote the timing of slow-earthquake detections.We compared these detections with the tectonic tremor activity with the information of distance between the station and events, using the tectonic tremor catalog of Mizuno and Ide (2019).We confirmed the occurrence of tectonic tremor activity near the station for most of the detections (Figure 4b).
In this example, CC MA exceeds the threshold when numerous tremors occur within 30 km of the station.However, CC MA remains under the threshold for the cases where only a few tremors occur more than 30 km from the station.The same observation is true for a longer period (Figure 4a).Here, 80.0% of the detections at station KIS had tremors that occurred within 30 km of the station during the detection period.
We then applied the method to all 75 F-net stations and the 18-year observational period.Figure 5 shows the distribution of the total detection times for each station in Japan.Eight stations have more than 20 hr of slow-earthquake detections per year, and the distribution of these stations is generally consistent with the known spatial distribution of slow earthquakes, as all of these stations are located within 20 km of the tremor zone.Conversely, all of the stations that are distal to the slow earthquakes only recorded short total detection times.Therefore, we can confirm the general applicability of our method for detecting slow earthquakes in the Nankai subduction zone.
We investigated the statistics of the whole detections at eight stations detecting slow earthquakes, which have more than 20 hr of detections per year (warm colors in Figure 5), based on the distance from the station and timing difference.No tectonic tremors occurred within 30, 60, and 100 km of the epicentral distance from the station during the 12-hr periods before and after the timing of detection for 42.8%, 10.9%, and 3.7% of the detection times, respectively (Table 1).These ratios correspond to a false-positive rate of tremor detection.Note that the upper limit of the detectable epicentral distance varies from station to station.It is about 30 km at station KIS, whereas it is about 40 km at station TSA.Based on this, the distance threshold of 60 km is the value that ensures as much as possible the correct detections and excludes as many combinations of detections and tremor events that should not be related as possible among the three threshold values, and a typical false-positive value is considered to be ∼10%.Furthermore, this limitation of the detectable distance constrains the location of detected slow-earthquake activity, even though the detections via this method are obtained using only time information.Conversely, 38.3%, 62.8%, and 75.3% of the tectonic tremor activity with more than 10 events that occurred within 30, 60, and 100 km of the epicentral distance from the station, respectively, was not detected (Table 1).These ratios correspond to the false-negative rate of tremor detection.
We can summarize the applicability of this method based on the F-net observations as follows.The completeness of the detection is not high due to the high (nonnegligible) false-negative rates.Nevertheless, the small false-positive rates suggest that most of the detections are real, which indicates that some slow-earthquake activity occurred somewhere within 100 km of the station.We note that seismic stations are not always as well constructed as the F-net stations, which are all enclosed in vaults to reduce the temperature changes and environmental noise, such that the observation conditions may be different at each station.Therefore, we consider the F-net conditions to be the best case for slow-earthquake detection using the new method.

Application to Slow-Earthquake Detection in Mexico
We confirm the applicability of the new method using waveforms from the same stations in Mexico where Husker et al. (2019) applied the template matching method in the frequency domain.These three stations are station ARIG in the Guerrero region and stations YOIG and TXIG in the Oaxaca region (Figure 1c). Figure 6a shows the cumulative detection at station ARIG.The detection rate increases during the periods of three SSEs that were identified by Husker et al. (2019), which suggests that slow earthquakes mainly occur during SSEs.However, a comparison with the detections in  Note.The percentage calculations are based on the tectonic tremor catalog of Mizuno and Ide (2019).The activity in this calculation is defined as a set of tectonic tremor events that contains 10 or more events and has an event interval of 12 hr or less.The epicentral distance is defined as the distance of the closest event that is included in the activity.Figure 6b shows the cumulative detection at station YOIG.Compared with the results at station ARIG, the correspondence between the increase in slow-earthquake detection and the SSEs that were identified by Husker et al. ( 2019) is unclear.Nevertheless, we do observe an increase in the detection rate during the SSE periods, particularly during the 2015-2016 SSE.Husker et al. (2019) defined the termination of the 2017-2018 SSE as 16 February 2018, when the Mw 7.2 Pinotepa earthquake occurred.However, crustal deformation continued after the earthquake.This postearthquake deformation can be interpreted as afterslip, such that the increase in detection may correspond to slow earthquakes driven by aseismic slip.However, station TXIG does not show a clear increase in detection compared with station YOIG, except for the 2015-2016 SSE (Figure 6c).Note that the correlation between the SSEs and tremor activity at station TXIG is also unclear compared with that at station YOIG in Husker et al. (2019).
We also applied our method to the stations in the Oaxaca region that were not used by Husker et al. (2019).The number of detections at these stations did not increase during the SSEs, except for the 2015-2016 SSE (Figures S2-S4 in Supporting Information S1).This mismatch may reflect the locations of the large SSEs in the Oaxaca region relative to the seismic stations, as they mainly occur to the southeast of the study region (Figure 1c; Graham et al., 2016;Rousset et al., 2016), such that station YOIG is the only station that is proximal to these SSEs.Nevertheless, the increase in detection is confirmed at multiple stations in the Oaxaca region after the Pinotepa earthquake and may be due to the expansion of the aseismic slip region after the Pinotepa earthquake to the northwest (Cruz-Atienza et al., 2021).
It is important to highlight that different frequency bands were analyzed in this study and Husker et al. (2019).Husker et al. (2019) used the 2-10 Hz band, while this study used both the 2-8 and 0.02-0.05Hz bands.Therefore, it is possible that Husker et al. ( 2019) also detected small-scale slow-earthquake activity that lacks a low-frequency signal, which this study cannot detect.The detection rate during the period between the 2010 and 2014 SSEs at station ARIG is smaller in this study compared with that of Husker et al. (2019), even though they are normalized by the final cumulative detection (Figure 6).This suggests that slow-earthquake activity without the radiation of low-frequency seismic waves occurred during this period.Furthermore, the steady increases in the detection rate during the period between the 2014 and 2017 SSEs at station ARIG and during the inter-SSE periods at station YOIG indicate the occurrence of slow-earthquake activity with sufficient low-frequency components, even though there was no corresponding significant change in the global navigation satellite system (GNSS) data.
We then applied the new method to the Jalisco region, where the long-term tremor activity had not been evaluated since the MARS observation period (January 2006 to June 2007).Figure 7 shows the cumulative detection at station CJIG for the period from November 2007 to December 2022.This is the first long-term slow-earthquake catalog using a permanent station in this region.We compared this result with the SSEs detected by Brudzinski et al. (2016) using GNSS data spanning 2006-2015 and observed that the detection rate increased during the geodetically detected SSEs.Furthermore, we detected two periods of significant increases in the detection rate after the study period of Brudzinski et al. (2016), from September 2016 to May 2017 and from June 2020 to at least December 2022.These periods are more clearly confirmed by detrending the cumulative detection curve by 35.9 hr/year, which is the trend of the detections measured during the period from 24 September 2011 to 1 August 2013 (Figure 7).These two significant detection periods may correspond to previously unknown SSEs in the region.

Discussion
Conventional seismological slow-earthquake detections recognize pulse-like signals in the 1-10 Hz band, signals with durations of several tens of seconds in the 1-10 Hz band, and pulse-like signals in the 0.01-0.1 Hz band as LFE, tectonic tremor, and VLFE events, respectively.The 300-s time window for the correlation coefficient corresponds to the time constant of a signal for such a conventional event.Conversely, the 10,000-s time window for the moving average of the time series of the correlation coefficient corresponds to the shortest time scale of the characteristic that LFE, tremor, and VLFE events occur in bursts over periods that span several hours to several days (e.g., Obara, 2010).Therefore, this study detects the swarm activity associated with these conventional slow-earthquake events, as opposed to the actual events themselves.
The correlation coefficient before the moving average, CC (Equation 3), fluctuates temporally with a period of several hundred seconds (Figure 2).The moving average reduces this fluctuation, and its time window length determines the temporal resolution limit of slow-earthquake detection, although the time window for the correlation coefficient has little effect on the moving-average correlation coefficient, CC MA (Equation 7; Figure S5 in Supporting Information S1).Therefore, one may think that this window length should be sufficiently short to detect a shorter-duration event or that detection without the moving average may be the preferable approach.However, the correlation coefficient without the moving average is distributed between −1 and 1, even during the periods without slow earthquakes, such that we cannot set a threshold to effectively perform the slow-earthquake detection (Figure S1a in Supporting Information S1).The standard deviation of CC MA decreases as the window length increases, and a threshold at a relatively small CC MA value is applicable (Figure S1 in Supporting Information S1).The CC MA of a real signal, if present, is simultaneously smeared out by the moving average with a long window length, and the true, but short, signals fall below the detection threshold.This is the classic problem of the trade-off between detection error and resolution.In fact, we analyzed the false rates for KIS station when changing both the time windows of the correlation coefficient and the moving average and found that shorter time windows of the correlation coefficient and longer time windows of the moving-average time make the false-positive rate smaller, on the other hand, shorter time windows of the moving-average time make the false-negative rate smaller (Figure S6 in Supporting Information S1).The combination of 300 and 10,000 s at KIS station is one of the combinations that gives a better false-negative rate with a sufficiently small false-positive value (less than 1%).The optimal value of the time window length should be determined for each station based on the characteristics of the station noise and the signal from regional slow-earthquake activity.We therefore calculated the standard deviation and maximum value of CC MA for real signals at stations with many detections to determine the optimal time window length.Figure 8 shows the ratio between the maximum and standard deviation of CC MA for different time window lengths.Though the maximum CC MA normalized by the standard deviation of TGA and TGW increases at roughly constant rate until the time window is 30,000 and 44,000 s, respectively, that of other stations increase until the time window from 8,000 to 10,000 s, after which it remains approximately constant or decreases.S1 for station locations.
Therefore, the common setting of 10,000 s is not the optimal value for each station, however, it is not a value that significantly degrades the detection.
Slow-earthquake detection from seismic data is directly affected by the noise level.Some previous studies have limited the study period to the nighttime hours, when the noise level in the high-frequency band is low, to suppress false detections (e.g., Brudzinski & Allen, 2007;Sit et al., 2012).The percentage of detections during daytime hours (05:00-17:00) is 43.9% ± 3.5%.Regardless, the influence of cultural noise in the high-frequency band cannot be completely ignored, even though our method also uses the low-frequency band.Furthermore, while some previous studies used templates that were based on detections that were constrained via visual inspection (e.g., Husker et al., 2019;Shelly et al., 2007), our method does not depend on such a subjective detection.
We observe significant differences in detectability at various stations.For example, station NAA has almost no slow-earthquake detections, even though slow-earthquake activity occurred sufficiently close to the station.One key factor that affects the detectability at a given station is the noise level.We calculated the median value of the hourly root-mean-square amplitudes in the high-and low-frequency bands for each station to compare the noise levels, however, station NAA is not particularly noisy (Figure S7 in Supporting Information S1).At station NAA, slow-earthquake signals can be observed at 2-8 Hz but not at 0.02-0.05Hz, which was also confirmed by the synthetic waveform (see Text S1 in Supporting Information S1), suggesting that this low detectability is probably due to the positional relationship between the source and station.

Conclusions
We developed a method to detect slow-earthquake activity using seismic waveform data from a single station based on the characteristic that the seismic energy rate and seismic moment rate are proportional.We first applied this method to F-net waveforms from the Nankai subduction zone in Japan and confirmed that our detection method is spatiotemporally consistent with the existing deep tectonic tremor catalog.The detected slow-earthquake activity is limited to the vicinity of the station, which can be a constraint on the detection and location capability of a given station.We then applied this method to waveforms from the Mexico subduction zone, whereby we increased the number of useable stations in our analysis compared with a previous study in the Guerrero and Oaxaca regions, and successfully detected the first long-term seismological slow-earthquake activity in the Jalisco region.The first two of the four detected large seismic SSEs in the Jalisco region are consistent with a previous GNSS study, and the latter two are newly identified SSEs.The method developed in this study can be used to monitor slow-earthquake activity in a region that possesses a sparse seismic observation network and serves as a preliminary analysis to select a region for a more detailed analysis and/or campaign observations.

Figure 1 .
Figure 1.(a) Map of Japan, showing the F-net station coverage and distribution of deep tectonic tremor.The triangles represent the F-net stations used in this study.Three-letter codes refer to the stations specifically mentioned in the manuscript.The green dots represent the tremor distribution along the Nankai subduction zone(Mizuno & Ide, 2019).Dashed lines and two-letter codes here and in (b) and (c) represent trench lines and plate names.AM, Amur Plate; PS, Philippine Sea Plate; PA, Pacific Plate; OK, Okhotsk Plate; CO, Cocos Plate; RI, Rivera Plate; NA, North America Plate(Bird, 2003).(b) Enlarged map of the Nankai subduction zone in (a).Dotted lines are the isodepth of the top of the subducting plates every 10 km (T.Baba et al., 2002;F. Hirose et al., 2008;Nakajima & Hasegawa, 2007).(c) Map of the Mexican subduction zone, showing the distribution of stations and deep tectonic tremor.The triangles denote the stations used in this study.The green dots represent the deep tectonic tremor distribution along the Mexican subduction zone(Maury et al., 2018).The four-letter codes next to the stations are the station names.Dotted lines are the isodepth of the top of the subducting plates every 10 km(Hayes et al., 2018).

Figure 2 .
Figure 2. Schematic diagram of the proposed method.Here, vel.and disp.represent the velocity and displacement data, respectively.U-D, N-S, and E-W represent the up-down, north-south, and east-west components, respectively.See the text for the details of the CC and CC MA calculations.Note that the CC and CC MA time series have different time scales compared with the upper waveforms.The solid and dashed gray lines represent the time windows of the correlation coefficient (CC) and moving-average correlation coefficient (CC MA ), respectively (i.e., 300 and 10,000 s, respectively).

Figure 3 .
Figure 3. Histograms of the 1-year time series of the moving-average correlation coefficient, CC MA , for 2007.(a, d) Station KZK (37.2977°N, 138.5143°E), which is distal to the slow-earthquake activity.(b, e) Station KIS (33.8652°N, 135.8907°E) and (c, f) station TGA (35.1847°N, 136.3383°E), which are within the region of slow-earthquake activity.The bin width is 0.005, and the vertical axes are linear (a-c) and logarithmic (d-f).The vertical line represents the threshold, which is set at 4σ; the polarity is determined for each station based on the number of values exceeding the CC MA threshold.

Figure 4 .
Figure 4. Time series of the slow-earthquake detection at station KIS.(a) Four-year time series of slow-earthquake detection for 2005-2008.The vertical gray bars indicate the detection periods (when CC MA exceeds the threshold).The blue circles are the deep tectonic tremors that were detected by Mizuno and Ide (2019), which are plotted based on their epicentral distance from the station (right axis).(b) One-month time series for July 2007.The black line is the time series of the moving-average correlation coefficient, CC MA , and the horizontal dashed line represents the correlation threshold (left axis), and the blue circles and vertical gray bars are as in (a).

Figure 5 .
Figure 5. Distribution of the cumulative detection time of slow earthquake in Japan.The triangles represent the stations, which are color coded by their annual cumulative detection time, with warmer colors indicating longer detection times.The green dots represent the distribution of deep tectonic tremor (Mizuno & Ide, 2019).

Figure 6 .
Figure 6.(a) Cumulative detection at station ARIG in the Guerrero region.The blue and red lines are the results of this study (left axis) and Husker et al. (2019) (right axis), respectively.The gray vertical bars indicate the slow-slip events (SSEs) identified by Husker et al. (2019).(b) As for (a), but for the station YOIG in the Oaxaca region.(c) As for (a), but for station TXIG in the Oaxaca region.
Husker et al. (2019) highlights that the duration of total detections is much shorter and the detections during the period between the 2009-2010 and 2014 SSEs are less frequent in this study.

Figure 7 .
Figure 7. Cumulative detection at station CJIG in the Jalisco region.The blue and green lines are the raw (left axis) and detrended (right axis) cumulative detections, respectively, and the black arrow indicates the period used to calculate the trend.The dark-gray and light-gray vertical bars indicate the slow-slip events (SSEs) identified by Brudzinski et al. (2016) and those when the detection rate increased after the study period of Brudzinski et al. (2016), respectively.

Figure 8 .
Figure 8. Maximum value of the moving-average correlation coefficient normalized by the standard deviation for each time window of the moving average.Each line corresponds to the results for a given station.See TableS1for station locations.