We applied a new matched-filter technique that was developed by Kurihara et al. (2021), which uses the product of the mutual information (MI) and correlation coefficient (CC) for earthquake detection (the product is called as “MICC” in below), to the continuous data recorded at a single seismic station (N.SUKH in Fig. 1). We applied a 1–8-Hz bandpass filter, 25-Hz sampling frequency, and 8-s window length to the waveforms prior to the analysis, as outlined in Kurihara et al. (2021). We employed 293 DLF earthquakes from the April 2004–December 2018 period in the JMA catalog as template events.

In the calculation of MICC, we normalize the waveforms within each 8-s time window using its maximum absolute amplitude. We then assigned the normalized velocities of each time step in each time window, \({\overline{v}}_{\mathrm{tp}}\left(t\right)\) and \({\overline{v}}_{\mathrm{tg}}\left(t\right)\), as

$${\overline{v} }_{\mathrm{tp}}\left(t\right)=\frac{{v}_{\mathrm{tp}}(t)}{\underset{t}{\mathrm{max}}\left(\left|{v}_{\mathrm{tp}}\left(t\right)\right|\right)}$$

(1)

and

$${\overline{v} }_{\mathrm{tg}}\left(t\right)=\frac{{v}_{\mathrm{tg}}(t)}{\underset{t}{\mathrm{max}}(\left|{v}_{\mathrm{tg}}\left(t\right)\right|)}.$$

(2)

where the “tg” and “tp” subscripts refer to the velocities of the target and template waveforms, respectively, and the | | notation indicates the absolution value function. We then divide the points in the normalized velocity seismograms into discrete 5 × 5 cells in the x,y domain. Two integers, \({n}_{\mathrm{tp}}\) and \({n}_{\mathrm{tg}}\), which indicate the coordinate value of cells between 1 and 5, are given by

$${n}_{\mathrm{tp}}\left(t\right)=\left\lfloor \left({\overline{v} }_{\mathrm{tp}}\left(t\right)+1.4\right)*2.5\right\rfloor \quad (\mathrm{when }\,{\overline{v} }_{\mathrm{tp}}\left(t\right)<1)$$

(3)

$${n}_{\mathrm{tg}}\left(t\right)=\left\lfloor\left({\overline{v} }_{\mathrm{tg}}\left(t\right)+1.4\right)*2.5 \right\rfloor \quad (\mathrm{when }\,{\overline{v} }_{\mathrm{tg}}\left(t\right)<1)$$

(4)

$${n}_{\mathrm{tp}}\left(t\right)=5 \quad (\mathrm{when}\, {\overline{v} }_{\mathrm{tp}}\left(t\right)=1)$$

(5)

$${n}_{tg}\left(t\right)= 5 \quad \left(\mathrm{When}\, {\overline{v} }_{tg}\left(t\right)=1\right),$$

(6)

where the ⌊ ⌋ notation indicates the floor function.

We then used these integers for the calculation of MI:

$$\mathrm{MI}\left(t\right)=\sum_{{n}_{\mathrm{tp}}=1}^{5}\sum_{{n}_{\mathrm{tg}}=1}^{5}p\left({n}_{\mathrm{tp}},{n}_{\mathrm{tg}}\right)\mathrm{log}\frac{p\left({n}_{\mathrm{tp}},{n}_{\mathrm{tg}}\right)}{p\left({n}_{\mathrm{tp}}\right)p\left({n}_{\mathrm{tg}}\right)}$$

(7)

where \(p\) indicates the probability density function. Here, we defined the function *p*(*n*_{tg},*n*_{tg}) by dividing the number of points corresponding to each time steps in each 5 × 5 cell by the total number of the time steps (200). We defined the information entropies, \({h}_{\mathrm{tp}}\) and \({h}_{\mathrm{tg}}\), as

$${h}_{\mathrm{tp}}=\sum -p\left({n}_{\mathrm{tp}}\right)\mathrm{log}p({n}_{\mathrm{tp}})$$

(8)

and

$${h}_{\mathrm{tg}}=\sum -p\left({n}_{\mathrm{tg}}\right)\mathrm{log}p\left({n}_{\mathrm{tg}}\right),$$

(9)

respectively. We then normalized MI as

$$\overline{\mathrm{MI} }=\frac{2.0*\mathrm{MI}}{{h}_{\mathrm{tp}}+{h}_{\mathrm{tg}}}.$$

(10)

We hereafter simply describe \(\overline{\mathrm{MI} }\) as MI. This value shows the similarity of normalized velocity of the target and template events. MI reflects similarities of waveform portions with amplitudes close to zero, where CC is less sensitive generally.

We calculated the CC of component *j* at seismic station *i* for time *t* as

$${\mathrm{CC}}_{ij}\left(t\right)= \frac{\sum_{\tau }\left({v}_{ij}^{\mathrm{tp}}({t}_{\mathrm{tp}}+{\Delta t}_{i}+\tau ){v}_{ij}^{\mathrm{tg}}(t+{\Delta t}_{i}+\tau )\right)}{\sqrt{\sum_{\tau }{\left({v}_{ij}^{\mathrm{tp}} ({t}_{\mathrm{tp}}+{\Delta t}_{i}+\tau )\right)}^{2}}\sqrt{\sum_{\tau }{\left({v}_{ij}^{\mathrm{tg}}(t+{\Delta t}_{i}+\tau )\right)}^{2}}},$$

(11)

where Δ*t*_{i} is the time delay from the origin time of the template earthquakes to S-wave arrival time at station *i* and *τ* means the time steps in the time window. Here, we define the MICC index, which is the product of MI and CC, as

$$\mathrm{MICC}\left(t\right)=\mathrm{MI}\left(t\right)\mathrm{CC}\left(t\right).$$

(12)

MICC combines two characteristics of MI, which can evaluate the similarity of waveforms in the small amplitude portion, and CC, which is generally sensitive to the large amplitude portion of the waveforms (cf. Kurihara et al. 2021).

We then employed the MICC index for our DLF earthquake detection. We set the MICC threshold at 0.35 for our DLF earthquake detection, following Kurihara et al. (2021). We avoided multiple detections by only including the detection with the highest MICC in a given 10-s time window. Furthermore, we removed any misdetections from surface waves of teleseismic events based on the average amplitudes of the 0–10-s and 10–20-s time windows after the S-wave arrival time, with the potential mis-detections automatically removed when the average amplitude in the 10–20-s window was larger than that in the 0–10-s window. The magnitude of each detected event was calculated based on the average root-mean-square velocities between the detected event and the template event among all of the channels:

$${\text{Mj}}_{\mathrm{detect}}={\text{Mj}}_{\mathrm{temp}}+\frac{1}{0.85}\mathrm{log}\left(\frac{{V}_{\mathrm{detect}}}{{V}_{\mathrm{temp}}}\right),$$

(13)

where \({\text{Mj}}_{\mathrm{detect}}\) and \({\text{Mj}}_{\mathrm{temp}}\) are the JMA magnitudes of the detected and template events, respectively, and \({V}_{\mathrm{detect}}\) and \({V}_{\mathrm{temp}}\) are the root-mean-square velocities of the detected and template events in the 8-s time window, respectively.

We recognized that misdetections from surface waves of teleseismic events and near-surface harmonic tremors (e.g., Natsume et al. 2019) were included in the detections after applying the MICC-based matched-filter method to single station data (Additional file 1: Figs. S1 and S2), even though we automatically removed some misdetections. In particular, many near-surface harmonic tremors were detected on the days of the eruptions; i.e., 6 and 7 March 2018. We visually inspected waveforms for all of the detected events from the 2010–2011 and 2017–2018 periods that were recorded by multiple stations around the Kirishima volcanic complex (Hi-net stations operated by NIED and a seismic station operated by JMA; Fig. 1). We then carefully selected the most robust events by focusing on the event duration, the amplitude ratio between horizontal and vertical components, the arrival time at each station, and the waveform amplitude. Finally, we constructed more precise catalogs of the 2010–2011 and 2017–2018 DLF earthquakes than the automatically constructed catalog.