Introduction

Non-volcanic deep low-frequency tremors and short-term slow slip events (SSEs) are related to stress relaxation at plate boundaries, and it is speculated that their occurrence depends on local physical and chemical conditions. Such events have been observed along subduction zones around the Pacific Rim (e.g., Obara and Kato 2016), including along the Nankai Trough, southwest Japan (e.g., Obara 2002, 2010; Sekine et al. 2010; Itaba and Ando 2011; Kobayashi 2014, 2017; Suito and Ozawa 2009), although they do not occur ubiquitously along the trough. Deep low-frequency tremors and short-term SSEs often occur closely in space and time, but their spatiotemporal distributions do not completely match. A clear gap in tremor occurrence is observed around Ise Bay and in Kii Channel, and although short-term SSEs have not been observed in Kii Channel, they were discovered around Ise Bay in tiltmeter (Obara and Sekine 2009; Obara 2010) and GNSS data (Nishimura et al. 2013).

Unconsolidated sedimentary layers such as the Neogene-Quaternary Tokai Group are thickly deposited around Ise Bay (Makinouchi 2001). Such soft strata are unsuitable for crustal deformation observations via strainmeter or tiltmeter. Furthermore, no strainmeters are deployed around the northern part of Ise Bay, and tiltmeters, although they are in operation around the bay, have rarely been used for short-term SSE analysis (e.g., Obara and Sekine 2009). Small short-term SSEs are difficult to reliably identify because they are characterized by slips too small to be resolved in GNSS data. These limitations in short-term SSE detection around Ise Bay hinder verification of short-term SSE occurrences, leading to uncertainty in estimating the amount of slip during short-term SSE. Thus, it has not been verified whether the slip distribution of short-term SSEs along the Nankai Trough extends to the northern part of Ise Bay.

In areas characterized by hard (e.g., igneous or metamorphic) rocks, such as in continental areas, short-term SSEs can be observed as groundwater pressure changes in closed wells which are strongly related to crustal strain changes (Kitagawa and Koizumi 2013), and groundwater data are used to estimate SSE fault models. Here, we apply these concepts and use the groundwater level at the Hokusei observation site (HKS), located in a soft sedimentary layer of the Tokai Group northwest around Ise Bay (Fig. 1), to estimate the north ends of short-term SSEs occurring around Ise Bay.

Fig. 1
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Locations of the Hokusei (HKS) and ANO observation sites. The Kii and Tokai tremor occurrences (see Fig. 5) were counted within the parallelograms labeled ‘Kii’ and ‘Tokai’, respectively

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The HKS observation site

Groundwater levels have been observed in a 502-m-depth well at HKS since 1998 (Sato et al. 2000). HKS is located along a river near a mountain. The altitude of the ground surface at HKS is 116 m. The well was drilled in unconsolidated sediments of the Tokai Group and does not reach the basement rock. Active faults are present in this area (Ota and Sangawa 1984), and it is presumed that the well crosses the Futamura fault at 170–190 m depth. The well has a double-pipe structure; the inner pipe is used to observe groundwater in the deeper strata, and the outer pipe is used for observations in the shallower strata (Fig. 2). Screens allow groundwater into the inner pipe over the 429–439 m depth interval and into the outer pipe over the 100–269 m depth interval. The geology in the vicinity of the inner pipe’s screen is characterized by alternating layers of clay and fine sand. A gravel layer within the depth interval of the screen seems to be the main supply of groundwater. The hydraulic transmissivity of layers near the screen is presumed to be 2 × 10−6 m2/s, based on pumping tests, and their hydraulic conductivities, determined from soil tests of core samples, range from 1 × 10−8 to 4 × 10−7 m/s (Sato et al. 2000). Because these values are relatively low, the wellbore storage effect greatly influences the behavior of the groundwater level (Hsieh et al. 1987), and the groundwater level at HKS does not quickly respond to short-duration crustal deformations. Therefore, the inner pipe of the observation well (HKSi) was sealed with a packer in May 2016 to improve the groundwater level response to short-duration crustal deformations by reducing the wellbore storage effect (Bredehoeft and Papadopulos 1980; Pickens et al. 1987). The packer was installed with its lower end at about 32 m depth, about 10 m below the natural groundwater level (20 m depth), to avoid joints in the casing. Before sealing, the natural groundwater level was measured using a barometric pressure open-type water level gauge; after sealing, we installed a shield gauge-type water pressure gauge (27XW, Keller America, Inc., pressure reference of 100 kPa) under the packer (at about 33 m depth) that has since been used exclusively. This water pressure gauge has an operational range of 0–300 kPa, and its current output is 4–20 mA. The output is converted to a voltage (0.4–2.0 V) at the ground surface and recorded with a data logger at 2-min intervals. Barometric pressure and rainfall at the site are also measured at 2-min intervals. To convert the output of the water pressure gauge to well water level data (the same standard used before sealing), a shield pressure of 100 kPa is added to the output, the barometric pressure is subtracted, and the measured pressure is converted to the height of the water column.

Fig. 2
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Schematic representation of the double-pipe observation well at HKS. The screen depths and the installation depth of the packer and water pressure gauge (sensor) are shown

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Observational results

Figure 3 shows groundwater level variations in HKSi before and after it was sealed by the packer in May 2016. After sealing, the groundwater level clearly showed a response to tidal fluctuations, barometric pressure, and rainfall (Fig. 4). The crustal volumetric strain sensitivity of groundwater level is estimated by dividing the tidal component of the observed groundwater level by tidal component of the theoretical volumetric strain. The tidal components of groundwater level are calculated based on the tidal potential of the solid earth tide by the tidal analysis program BAYTAP-G (Tamura et al. 1991). The theoretical volumetric strain was estimated from solid earth tide and ocean tide loading effect by the modified GOTIC 2 (Matsumoto et al. 2001; Matsumoto et al. 2010). The phase is based on the decrease in groundwater level with respect to dilatation in crustal volumetric strain of solid earth tide. At that time, the phase shift of the crustal strain sensitivity is defined as 0° when the groundwater level decreases during dilatation in crustal volumetric strain. As a result, the sensitivity of the well to crustal volumetric strain after sealing improved to about ten times that before sealing and the phase delay almost disappeared (Table 1). Although the crustal volumetric strain sensitivity achieved after sealing is about 5 mm per 1e−8 strain units (about 0.5e+6 m per unit strain), because the aquifer comprises soft sedimentary strata, this sensitivity is a fraction of that in wells installed in hard rock areas (e.g., Kitagawa et al. 2011).

Fig. 3
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Observation results at HKS in 2016. Observed groundwater level changes, barometric pressure, and rainfall (bars in top plot) are shown. The inner pipe was sealed in May 2016. Barometric pressure and rainfall are refer to left and right scales, respectively

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Fig. 4
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Observational data and correction of groundwater levels at HKSi from December 2016 to May 2017. Barometric pressure, rainfall (bars in top plot), and groundwater levels were observed at HKS, and the tidal, barometric, and rainfall components of the groundwater level response were identified and removed using BAYTAP-G (Tamura et al. 1991) and the regression of Matsumoto (1992) to produce the final corrected groundwater level trend. Barometric pressure and rainfall are refer to left and right scales, respectively

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Table 1 Tidal components and the associated crustal strain sensitivities of groundwater level fluctuations at HKSi
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Using BAYTAP-G and the regression of Matsumoto (1992), we succeeded in estimating and removing the tidal, barometric, and rainfall components of the groundwater level data (Fig. 4). The corrected groundwater level data show generally smooth and continuous changes except during periods of strong forcings, such as during heavy rain. Although because of an equipment malfunction, the corrected groundwater level data were affected by the room temperature in the observatory during July to September 2016, standard deviation of the 24-h variation of the corrected data was 2.91 mm during December 2016 to May 2017.

Short-term SSE fault model estimation from groundwater level fluctuations

Six episodes of deep low-frequency tremors occurred around Ise Bay during May 2016 to December 2018, and we investigated associated changes in the corrected groundwater level trends at HKSi during those periods (Fig. 5, Table 2). Groundwater level changes during each episode were calculated from the time series data after removal of the linear background trend estimated from the data preceding each episode. The groundwater level changes, shown in Fig. 5, are also compared to changes observed in two wells at site ANO (west of Ise Bay, Fig. 1). ANO1 and ANO2 wells were sealed and the groundwater pressures are observed. The screens of ANO1 and ANO2 are 499–514 m depth and 196–209 m depth, respectively (Kitagawa et al. 2011). The geology at site ANO is mainly granodiorite. The National Research Institute for Earth Science and Disaster Resilience (NIED) catalog was used for hypocenters of deep low-frequency tremors (Maeda and Obara 2009; National Research Institute for Earth Science and Disaster Resilience 2019; Obara et al. 2010).

Fig. 5
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Groundwater level observations at HKSi before and after each of the six analyzed episodes. Barometric pressure, rainfall (bars in top plots), corrected groundwater levels after the removing of the linear trends for 8 days just before the episodes at HKSi, ANO1, and ANO2, room temperature at HKS, and tremor occurrences in Kii and Tokai (see Fig. 1) are shown. However, in the case of f, removing of the linear trend from September 17 to 25 is used because data from September 26 to 28 noon are changed by short-term SSE around ANO. Barometric pressure and rainfall are refer to left and right scales, respectively. The six episodes occurred in a July 2016, b December 2016, c May 2017, d November 2017, e April 2018, and f September 2018. Red squares indicate the duration of the episodes. Because the groundwater level data in a were affected by room temperature fluctuations, the estimated groundwater level change during the episode is indicated by horizontal blue lines

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Table 2 Observational results at HKSi and predictions from the fault models
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The first episode (Fig. 5a) occurred in late July 2016; although the HKSi groundwater level data were affected by room temperature fluctuations during that time (see previous section), the groundwater level seems to have increased. The second episode (Fig. 5b) occurred in mid-December 2016 and is observed as a small groundwater level increase at HKSi and a larger increase at ANO. The third episode (Fig. 5c) occurred in early May 2017, during which time the groundwater level decreased at HKSi, but increased at ANO. The fourth event (Fig. 5d) occurred in late November 2017, and is observed as a small groundwater level increase at HKSi and a larger increase at ANO. The fifth event (Fig. 5e) occurred in mid-April 2018, during which time a slight groundwater level increase was observed at HKSi and a larger increase at ANO. The sixth event (Fig. 5f) occurred in late September 2018; the observed groundwater level increases at HKSi and ANO were small, although it seems that the response to heavy typhoon rains during that time was not been completely removed from the groundwater level data.

Strain, tilt, and groundwater level changes during each episode were observed at other observation sites, and are considered to have been generated by short-term SSEs in the Ise Bay area. We estimated fault models for the short-term SSEs using the groundwater level data at HKSi and strain, tilt, and groundwater level changes at other observation sites of the National Institute of Advanced Industrial Science and Technology (AIST), Japan Meteorological Agency (JMA), and NIED. We corrected the strain and tilt data for tidal, barometric, and white noise components using BAYTAP-G, and groundwater level data at ANO1 and ANO2 were corrected following the same protocol used at HKSi. To estimate the fault models, we used a grid-search method (Itaba et al. 2012; Itaba and Ando 2011) to select the position, size, and slip amount of the fault plane that minimizes the difference between the observed changes including HKSi and the calculated changes predicted by the fault model (Figs. 6, 7, 8, 9, 10, 11, Table 2). We detail analysis methods in Appendix A. We estimated fault models for each episode both including and excluding the data at HKSi.

Fig. 6
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Estimated fault model of the short-term SSE in July 2016. Black, dark blue, and green circles indicate AIST, NIED Hi-net, and JMA observation sites, respectively. Small blue circles indicate hypocenters of deep low-frequency tremor estimated by NIED. a The initial fault model estimate. The fault plane was fixed as 20 km × 20 km, and the slip amount on each fault patch was estimated by minimizing the sum of residuals after comparison with the observed strain, tilt and groundwater pressure distribution. The gray color scale shows the distribution of the residuals, and the red rectangle indicates the portion of the fault with the lowest residual. b The refined fault model. The red rectangle shows the length and width of the estimated fault model. Observed and calculated tilt changes are shown by red and blue arrows, respectively. c Observed and calculated principal strain changes. d Observed and calculated volumetric strain changes. At ANO1, ANO2, and HKSi, observed groundwater pressure changes were converted to volumetric strain changes. At Taharafukue and Gamagoriseida, volumetric strain changes were directly observed

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Fig. 7
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Estimated fault model of the short-term SSE in December 2016. See caption of Fig. 6

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Fig. 8
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Estimated fault model of the short-term SSE in May 2017. See caption of Fig. 6

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Fig. 9
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Estimated fault model of the short-term SSE in November 2017. See caption of Fig. 6

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Fig. 10
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Estimated fault model of the short-term SSE in April 2018. See caption of Fig. 6. The gray rectangle in b is the fault model estimated by excluding HKSi data

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Fig. 11
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Estimated fault model of the short-term SSE in September 2018. See caption of Fig. 6

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The extent of the fault model estimated for the July 2016 episode includes site HKS (Fig. 6). The volumetric strain change calculated from the observed groundwater level change and that calculated by the fault model roughly match, indicating that fault slip occurred in the northern part of Ise Bay, although tremor activity was not detected there.

The fault model of the December 2016 episode is located to the south of HKS (Fig. 7). The volumetric strain change predicted by the fault model is much smaller than that calculated from the observed groundwater level change at HKS. This difference may suggest that the actual fault slip extended farther north than the modeled slip. However, because the observed groundwater level change was of similar magnitude to the background noise during this episode, we consider it more likely that the groundwater level change was overestimated.

The fault model of the May 2017 episode is located farther south from HKS than that of the December 2016 episode (Fig. 8). The estimated moment magnitude is small, and the volumetric strain change at HKSi predicted by the fault model is almost zero. Thus, we speculate that crustal deformation due to this short-term SSE had almost no influence at site HKS. Unlike the other five events, the groundwater level decreased during this episode, likely unrelated to the short-term SSE.

The extents of the fault models of the November 2017 (Fig. 9) and April 2018 episodes (Fig. 10) included and were near site HKS, respectively. The volumetric strain changes calculated from the observed groundwater level changes and those predicted by the fault models roughly matched in both cases. These results indicate that fault slip during each episode again extended to the northern part of Ise Bay, although little to no tremor activity was detected. In November 2017 episode, the fault slip was estimated to spread north from Ise Bay.

A small fault model in Ise Bay was estimated for the September 2018 episode (Fig. 11). Heavy typhoon rains seem to have affected not only the groundwater level data but also strain and tilt data during this episode. Because tremor activity was detected along the western side of Ise Bay, we expect that the actual fault plane was larger than estimated. However, it is not clear whether fault slip extended to the northern part of Ise Bay during this short-term SSE.

In the above analysis, five of the six fault models estimated using data from HKSi matched those calculated excluding data from HKSi. The only case in which the fault models differ is the April 2018 episode. For this episode, the fault model calculated by excluding data from HKSi (gray rectangle in Fig. 10b) results in a volumetric strain change at HKS of about 0.5e−8, which is very small compared to the observed groundwater level change. In this case, the model improvement achieved by the inclusion of HKSi data clearly indicates that the fault slip of the short-term SSE extended inland beyond the northern part of Ise Bay.

Although tremors rarely occur in the northern part of Ise Bay, it is presumed that slip of short-term SSEs occurs repeatedly, unlike in other areas along the Nankai Trough. Indeed, Nishimura et al. (2013) estimated from GNSS data that the total slip around Ise Bay is relatively large, consistent with our results at HKS.

Conclusions

By sealing the inner well at site HKS, we greatly improved the crustal strain sensitivity of the groundwater level, confirming that the wellbore storage effect can be greatly reduced by sealing wells with a packer. As a result, we were able to detect slow slip occurring along the plate boundary using groundwater pressure changes. Groundwater level fluctuations at HKSi in July 2016 and November 2017 indicated that slip due to short-term SSEs extended to the northern part of Ise Bay. Furthermore, groundwater level fluctuations at HKSi in April 2018 greatly improved short-term SSE fault models of that event, confirming fault slip in the northern part of Ise Bay. Our results show that groundwater pressure observations at HKSi can be used to estimate fault models for short-term SSEs near the northern part of Ise Bay, and thus to verify whether fault slip extends into this area. Importantly, we have demonstrated that groundwater level/pressure fluctuations are an effective means of observing crustal deformation in areas characterized by soft sedimentary layers that are not suitable for strainmeter or tiltmeter observations.