We have developed a new automated method for the identification and location of slow slip events (SSEs) during episodic tremor and slip (ETS) in the Nankai subduction zone without any tremor information. SSE models are estimated from continuous tilt data using the Kalman filter algorithm and a grid search, and are eventually identified through statistical evaluations. We applied this method to data recorded for two years in Shikoku, Japan and successfully detected four SSEs coincident with major tremor bursts. Before the onset of SSEs, precursory minor tremor activities usually occur around the fault where SSEs are subsequently detected when tremor migrates into the SSE faults. This suggests that an ETS episode begins with geodetically undetectable small slip around the main fault and grows to a detectable SSE. Such evolution of SSE and tremor activity would reflect the spatial change in the slip property on the plate interface.
 In subduction zones such as Nankai and Cascadia, various types of slow earthquakes have been detected using dense seismic and geodetic observation networks. Nonvolcanic deep low-frequency tremor [Obara, 2002] radiates long lasting waves. Slow slip events (SSEs) generate static crustal deformations [e.g., Dragert et al., 2001]. These seismic and geodetic slow earthquakes, called episodic tremor and slip (ETS), usually occur simultaneously on the plate interface [Rogers and Dragert, 2003; Obara et al., 2004]. In order to reveal the source physics of various interplate slip phenomena, it is important to understand the relationship among members of slow earthquakes [e.g., Peng and Gomberg, 2010; Obara, 2010].
 Whereas Cascadia SSEs during ETS episodes are well detected from GPS data [Dragert et al., 2001; Miller et al., 2002], the magnitude of Nankai SSEs is usually lower than 6.2 [Sekine et al., 2010], which is too small to be detected by the GPS network in Japan. Rather than the GPS, borehole geodetic sensors such as high-sensitivity accelerometers (tiltmeters) installed at Hi-net stations of the National Research Institute for Earth Science and Disaster Prevention enable these SSEs to be detected [Obara et al., 2004; Hirose and Obara, 2005]. In previous studies on Nankai ETS, coherent tilt changes were detected as SSEs by consulting the tremor catalog [e.g., Obara et al., 2004] because local tilt changes due to disturbances such as rainfall prevented automatic signal detection. However, in order to clarify the relationship between geodetic SSEs and seismic tremor, SSEs must be detected objectively and independently of the tremor information.
 In the present paper, we develop a new automated detection method that reverses the order of the traditional methodology of SSE identification and estimation. This method enables 1) the estimation and identification of Nankai SSEs by using tilt data without any tremor information and 2) automated rejection of false-detections due to local tilt changes. We apply this method to the tilt data in Shikoku, southwest Japan, from 2007 to 2008 and then discuss the difference in the onset between the geodetically detected SSE and seismic tremor during the same ETS episode.
2.1. Modeling of Tilt Data
 We model the ground tilt yij(t) of the jth component at the ith station as a function of time t as follows:
where Sij(t), Lij(t), rij(t), and wij(t) represent the deformation due to an SSE, background trend, local random-walk motion, and observation error, respectively. The formulation of equation (1) is almost the same as that of the Network Inversion Filter (NIF) method [Segall and Matthews, 1997], replacing displacement Green's functions with tilt ones.
 Since our main focus is to detect an SSE, we assume the SSE as a simple model: a uniform slip on a rectangular fault with a time-invariant slip-rate. Therefore, Sij(t) represents the tilt changes due to slip on a fault at a position, ξ:
where A, s, n, Σ, T0 and τ represent SSE source parameters, that is the total slip, unit directional vector of slip, unit normal to the fault surface, fault size, onset time, and duration, respectively, and G is Green's function. For p and q (= 1, 2, 3), which represent components of s and n, respectively, summation on repeated indices is implied. In order to simplify the SSE model, parameters for fault location, geometry, size, and slip direction are combined into a single parameter, k (= 1, 2, …, M), where a set of combined parameters, (ξ(k), n(k), Σ(k), s(k)), represents a candidate for the SSE fault.
 In equation (1), Lij(t) represents the background trend, including effects of a steady-state deformation and long-term drift of a sensor, and is modeled as a linear function, Lij(t) = aijt + bij. rij(t) and wij(t) are a random-walk noise, ij(t) ∼ N(0, ρij2), and white noise, wij(t) ∼ N(0, σij2), respectively. The noise strength parameters, ρij and σij, are evaluated before detection (see section 3.1). Therefore, unknown parameters in equation (1) are k, T0, τ, A, aij, and bij.
2.2. Detection of SSE
 An optimum source model of SSEs is identified through the following three steps (Figure 1).
2.2.1. Step 1: Estimation of the SSE Model
 We assume that an SSE occurs in the analyzed time period, and estimate the optimum source model of the imaginary SSE and likelihood of the model. Nonlinear model parameters, k, T0 and τ, are grid-searched to maximize the likelihood. At each grid point, A, aij, bij, and likelihood are estimated by the linear Kalman filter [e.g., Segall and Matthews, 1997].
2.2.2. Step 2: Identification of Potential SSE
 We determine whether tilt changes modeled in Step 1 are significant through comparison with the model including no SSE response using Akaike's Information Criterion (AIC). The likelihood of the model without an SSE is estimated using the Kalman filter with equation (1) while neglecting Sij(t). The model with an SSE is identified as a potential SSE model when the model is selected.
2.2.3. Step 3: Robustness Test
 In order to avoid false-detections of local anomalous tilt changes due to disturbances, we introduce a robustness test of the potential SSE model. An arbitrary station selected from all available stations is temporarily excluded, and the data at remaining stations are re-processed in the same way as Steps 1 and 2. In this step, the nonlinear parameters k, T0, and τ are fixed to the values initially estimated from all the stations. When the tilt changes are not identified as a potential SSE for the remaining stations, the potential SSE model identified previously from all the stations is regarded as a false-detection due to a local tilt change at the excluded station. Then, we remove the data at the excluded station between estimated T0 and the end of analyzed time period, and return to Step 1 in order to detect another potential SSE. When the potential SSE model passes the robustness tests for all available stations, we identify this model as an SSE. We then subtract the response to the detected SSE, Sij(t), from the observed data and return to Step 1 to detect another SSE.
3. Application to the Data and Results
3.1. Tilt Data and Parameterization
 We applied the automated detection method to tilt data at Hi-net stations around Shikoku (Figure 2a) from 2007 to 2008. The hourly-sampled tilt data was pre-processed by the following standard method [e.g., Obara et al., 2004]. We first subtracted tidal and atmospheric pressure effects using BAYTAP-G [Tamura et al., 1991] with atmospheric pressure data recorded at Japan Meteorological Agency (JMA) observatories (Figure 2a). Then some steps by large earthquakes and drifts by instrument maintenance or heavy rainfall were removed.
 In order to evaluate the noise parameters ρij and σij, tilt data within a 30-day moving time-window incremented at three days was modeled in the same way as the estimation of the model without an SSE in Step 2, and the optimum pair of noise parameters for each time-window was estimated by the maximum likelihood method. The parameters that give the median value of the noise level for τ = 3 days, i.e., , was used as time-invariant noise strengths in the detection. The estimated ρij and σij are ∼10−5μrad/sec1/2 and ∼10−2μrad, respectively.
 As shown in Figure 3a, we placed candidate SSE faults on the plate interface within the source areas of SSEs and tremor estimated in previous studies [Sekine et al., 2010; Obara et al., 2010]. Each candidate fault of 30 km × 30 km in size was located 5 km above the Moho of the subducting Philippine Sea plate (PHS) [Shiomi et al., 2008], and the slip was fixed in the relative plate motion direction [DeMets et al., 1994] with the non-negative slip constraint [Simon and Simon, 2006]. The response of the ground tilt to a unit slip on a candidate fault was calculated using Okada's  analytical expression in a homogeneous elastic half-space.
 The detection was performed within the moving time-window in the same way as the noise parameter estimation. The duration, τ, ranging from three to nine days, and start time, T0, were grid-searched with a one-day interval.
3.2. Detection Capability
 Before detection, we evaluated the capability of detecting SSEs using the estimated noise parameters. The detection limit is defined as the minimum amplitude of slip on each candidate fault that generates synthetic tilt changes larger than the noise level in either component for at least two stations. We calculated the limit of the moment magnitude for each candidate fault with a horizontal interval of 5 km (Figure 2b). In the tremor belt-like zone, western and eastern Shikoku exhibit better detection capabilities (MW ∼ 5.7) than the other areas (MW ∼ 5.9).
3.3. Detected SSEs
Figure 3b shows the spatiotemporal distribution of the detected SSEs and tremor. We detected four SSEs with magnitude ranging from 5.7 to 5.9, and the duration of three days (Table S1). Synthetic tilt changes calculated from the estimated SSE models are consistent with the observations (Figures 4, S1, and S2). All of SSEs are coincident with tremor bursts [Obara et al., 2010], which means that, in Shikoku, detectable large SSEs are always accompanied by tremor bursts.
3.4. Start of SSE and Tremor Activity
 One of the advantages of our method is that the onset of an SSE can be estimated using the tilt data without tremor information. Therefore, we can objectively compare the start of geodetic SSEs with seismic tremor activities. In each ETS episode, minor tremor activity precedes the detected SSE by one to four days (Figures 4, S1, and S2). The average daily number of tremor sources before clustering process [Obara et al., 2010] during the detected SSEs is 99.3, whereas that of precursory tremor is 26.6. In SSE4, precursory tremor occurs beneath Bungo channel and migrates eastward along the strike of the subducting PHS and an SSE is detected when the tremor reaches the SSE fault (Figure S6). In the other episodes, precursory tremor begins in the deep portion, and SSEs are detected as the tremor migrates to the up-dip portion (Figures S3–S5).
 The automated method proposed herein enables us to detect Nankai SSEs using tilt data without any tremor information. In Cascadia, anomalous displacements are identified automatically from individual GPS time-series data, and SSE models are then estimated [e.g., Szeliga et al., 2008]. In contrast, the crustal deformations caused by Nankai SSEs are too small to be identified from individual tilt data. The newly developed method detects coherent SSE signals, whose pattern is consistent with that predicted from a candidate SSE fault, within a group of tilt data. Moreover, by modeling the local random-walk motion in tilt data and through robustness tests, local tilt changes are accounted for or auto-removed, which was performed by hand in previous studies [e.g., Sekine et al., 2010]. In the detection process described in section 3, the total number of local deformations rejected by the robustness test is approximately 400. This means that not only Step 2 but also Step 3 work well to distinguish SSEs from local deformations.
 As demonstrated in section 3.4, the comparison of spatiotemporal distributions between tremor and geodetically detected SSEs clarifies that minor tremor activity precedes the onset of the detected SSE [e.g., Obara and Hirose, 2006]. Moreover, the precursory tremor is located around the SSE fault that is detected later (Figures S3–S6). If the number of tremor can be used as a proxy for the SSE [Obara, 2010], it is possible that an ETS episode begins with the undetectable small SSE and minor tremor activity, and that the magnitude of the SSE becomes large enough to be detected geodetically according to the migration to the estimated fault area with an increasing number of tremor. This discrepancy in location between the detected SSE and precursory tremor would be caused by a spatial change in the slip property on the plate interface.
 Although tremor locates from Bungo channel to eastern Shikoku (Figure 2a), we detected SSEs only in western Shikoku (Figure 3b). This is thought to be a result of the detection capability and size of SSEs. In Bungo channel and central Shikoku, the detection of SSEs is difficult, even if the size is comparable to that in western Shikoku (Figure 2b). On the contrary, in eastern Shikoku, even though the detection capability is comparable to that in western Shikoku, no SSEs were detected. In addition, Sekine et al.  detected only two SSEs there from 2001 to 2008, which are much fewer than in western Shikoku. Because of the small number of tremor during each episode in eastern Shikoku [Obara, 2010], the characteristic moment release of SSEs in eastern Shikoku is expected to be smaller than that in western Shikoku.
 In the target period, three more SSEs were detected manually in Shikoku by consulting the tremor catalog [Sekine et al., 2010]. During the SSE at the end of August 2007, the tilt changes at only two stations slightly exceeded the evaluated noise levels, and they were too small to be identified without tremor information. For the other SSEs in December 2007 and February 2008, some anomalous changes due to uncorrected non-tectonic effects remained before and after SSE signals within 30-day time-windows which are longer than those of Sekine et al. . Therefore, the SSE signals were removed with preceding local deformation parts in Step 3 and/or the background trend, Lij(t), could not be estimated well in Step 1. More valid corrections of non-tectonic effects through the data pre-processing will be needed to detect these SSEs. The locations, magnitudes and periods of SSEs estimated in this study are basically consistent with Sekine et al.  for SSE1–3 and Hirose and Obara  for SSE1. Only for SSE1, the seismic moment is estimated to be twice larger than that of Sekine et al.  because Sekine et al.  estimated the fault depth to be 10 km above the plate interface.
 We have proposed a new detection method for SSEs and have applied the method to tilt data in Shikoku. This method estimating simple SSE models is very useful as a pre-process for detail modeling using the NIF method [e.g., Hirose and Obara, 2010] because the location, period of the SSE and detrended data are obtained objectively. Moreover, the routine application of this method will enable quasi-realtime monitoring of SSEs and may provide a key to understanding the physics of slow earthquakes.
 The authors would like to thank two anonymous reviewers for their variable comments and kind suggestions. Meteorological data were provided by the JMA. The GMT software [Wessel and Smith, 1998] was used to draw figures.