Introduction

Earthquakes, and their genesis processes, change the internal state of the Earth, via stress state changes, pore fluid movement, fractures around the fault, and shallow ground damage. The Earth’s interior state affects seismic wave velocity and scatterer distribution, or scattering properties. Therefore, we can understand the temporal evolution of the Earth’s interior state, when associated with earthquakes, better, by monitoring changes in the seismic wave propagation process over time.

Seismic interferometry is a useful method with which to monitor temporal change in the seismic wave propagation process (e.g., Sens-Schönfelder and Wegler 2006). Seismic interferometry is a method to obtain Green’s function between two seismic stations, by the computing cross-correlation functions of either ambient noise or coda waves. Repeating earthquakes and artificial explosions have also been used to detect seismic velocity changes associated with large earthquakes or volcanic activity (e.g., Nishimura et al. 2000; Poupinet et al. 1984). However, since repeating earthquakes do not occur frequently, and artificial explosions are expensive, the temporal and spatial resolution of velocity changes has been low in these studies. Methods using auto- and cross-correlation functions of the continuous ambient noise record (ACFs and CCFs) can estimate temporal changes in the velocity structure with better spatial and temporal resolution.

Several studies have reported temporal changes in the velocity structure associated with large earthquakes, by applying seismic interferometry (e.g., Brenguier et al. 2008; Wegler et al. 2009). Regarding the seismic velocity change which accompanied large earthquakes, damage to the shallow subsurface resulting from strong ground motion has been found to contribute largely to the velocity reduction of the near surface layer (e.g., Hobiger et al. 2016; Nakata and Snieder 2011; Sawazaki and Snieder 2013; Takagi et al. 2012). In addition to the damage in shallow, subsurface layers, deformation and stress relaxation in the deep crust associated with large earthquakes have also been reported to have caused seismic velocity drops—and their recovery—after earthquakes (Brenguier et al. 2008; Chen et al. 2010). Moreover, several studies have reported that seismic velocity changed during earthquake swarm activities and also during slow slip events that did not generate strong ground motion (Maeda et al. 2010; Ueno et al. 2012; Rivet et al. 2011).

Changes in subsurface scatterer distribution, and/or scattering property, can also be monitored with seismic interferometry. While seismic velocity changes cause phase shifts in the ACF and CCF waveforms, scattering property changes cause waveform shape changes, which can be measured through the reduced cross-correlation coefficient between waveforms measured before and after scattering property changes. Obermann et al. (2014) detected decreased correlation values between CCFs from before and after the 2008 Sichuan earthquake and located the area of the change in the scattering property near the fault zone. Chen et al. (2015) have reported changes to the repeating earthquake waveforms after the 1999 Chichi earthquake and attributed the changes to deep fault zone damage.

The Mjma 6.7 Hokkaido Eastern Iburi Earthquake occurred on September 6, 2018; it generated strong ground motion, with the maximum seismic intensity reaching 7, the highest value in the Japan Meteorological Agency (JMA) scale (https://www.jma.go.jp/jma/en/Activities/inttable.html). The JMA estimated the depth of the hypocenters at 37 km, which was deeper than normal for inland earthquakes in Japan. The average depth of the Moho discontinuity in the central part of the northeaster Japan arc is ~ 35 km (e.g., Katsumata 2010). Kita et al. (2010, 2012) have shown that the low-velocity anomaly zone corresponding to the seismic velocity of the crustal rock (Vp < 7.2 km/s and Vs < 4.2 km/s) existed for a depth of 35–80 km under the Hidaka district of Hokkaido. Because of the complicated structure, this earthquake may have occurred at a depth of 37 km. The initial focal mechanism solution determined by the polarization of P-waves showed a strike-slip type fault, with a pressure axis extending from the northeast in a westerly direction to the southwest, whereas the centroid moment tensor solution showed a reverse fault type (National Research Institute for Earth Science and Disaster Resilience 2018)—a discrepancy which suggested a complex fault rupture process.

In the study reported here, we detected temporal change in subsurface structures during the 2018 Hokkaido Eastern Iburi Earthquake, based on ACF analysis, and using ambient noise records. We focused on temporal changes, not only in seismic velocity, but also in scattering property.

Data and methods

We computed ACFs for ambient noise and estimated temporal variations in seismic velocity according to the methods described in Yukutake et al. (2016), and Wegler et al. (2009). We used continuous, vertical-component waveform data, from 11 Hi-net stations managed by the National Research Institute for Earth Science and Disaster Resilience (NIED; National Research Institute for Earth Science and Disaster Resilience 2019b), and one JMA station (Fig. 1). The time period for the data analysis was from March 1 to October 31, 2018.

Fig. 1
figure 1

Locations of seismic stations used in this study, and the seismicity from September 1 to October 31, 2018. The inset map shows the location of the study area

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Calculating ACFs

We computed daily ACFs to detect temporal subsurface variations. Firstly, we divided 1-day records into 1-min time windows, with overlaps of 30 s; then, we applied a bandpass filter between 0.1–0.5 Hz, 1–3 Hz, and 2–8 Hz to the time-windowed data, after removing the linear trend and offset. We then carried out down-sampling from 100 to 20 Hz and one-bit normalization (after, e.g., Campillo and Paul 2003). We then computed ACFs for all time windows, and averaged them to obtain daily ACFs.

The computed daily ACFs in the 0.1–0.5 Hz and 2–8 Hz ranges were unstable, and in the 0.1–0.5 Hz range, temporal phase fluctuations of the ACFs were too large to detect subtle change due to subsurface structural variation, which may have been caused by temporal change in the distribution sources of microseisms. In the 1–3 Hz and 2–8 Hz ranges, some stations showed monotonic behavior, with peak frequencies above 3 Hz. Therefore, we again applied a bandpass filter, between 1 and 2 Hz, to the ACFs in the 1–3 Hz range, and to obtain more stable ACFs, we stacked the ACFs for 1 week before the corresponding dates.

Temporal changes in distribution sources of ambient noise have been reported as causing apparent changes to ACFs and in seismic velocity (Wegler et al. 2009). For detecting temporal changes in subsurface structure after large earthquakes, contamination of aftershocks in observed records may be the main factor changing the source distributions. Thus, we discarded the 1-min time windows containing earthquake signals, based on the standard deviation of the observed amplitude. We set threshold values as five times the median of the standard deviation during the whole observation period, and when standard deviations in a time window exceeded the thresholds, those time windows were not used to compute ACFs.

Stretching method

The stretching method was used to estimate velocity change (e.g., Sens-Schönfelder and Wegler 2006). The stretching method assumes a spatially homogenous velocity change. With this assumption, the time delay after seismic velocity change can be predicted as shown in (1), where dv/v is a velocity change ratio, t is the lag time of the ACF, and dt is the time shift in the ACF at t.

$$dv / v = - dt / t$$
(1)

The ACF waveform is stretched or compressed by the predicted time delay and is then cross-correlated with a reference waveform. We can obtain the optimum value of dv/v by maximizing the cross-correlation coefficient between the stretched and reference ACFs. The reference ACF in this study was calculated from the mean of all ACFs before the mainshock. We performed grid searches for dv/v within the range from − 5 to 5%, with steps of 0.1%. Three lag time windows of 4–15 s, 4–9.5 s, and 9.5–15 s were examined. The dv/v measurement standard deviations were estimated using the following theoretical formula (Eq. (2) from Weaver et al. 2011). In (2), T is the inverse of the frequency band, \(t_{1}\) and \(t_{2}\) are the minimum value and the maximum value of the time window, respectively, \(\omega_{c}\) is the median value of the frequency, and CC is the correlation coefficient between the reference ACF and other ACFs.

$$\sigma_{d} = \frac{{\sqrt {1 - CC^{2} } }}{2CC}\sqrt {\frac{{6\sqrt {\frac{\pi }{2}} T}}{{\omega_{c}^{2} \left( {t_{2}^{3} - t_{1}^{3} } \right)}}}$$
(2)

Detecting waveform distortion

If the earthquake perturbs not only seismic velocity but also scattering property, by crack nucleation and/or fault zone damage, we can observe distortion of the ACF waveforms, in addition to the phase delay caused by velocity change. In order to quantify the waveform distortion, we compared averaged ACFs before and after the mainshock. We stretched or compressed the post-seismic ACF according to Eq. (1) and computed maximum correlation coefficients using moving time windows of 3 s, using 0.5-s steps. Waveform stretching corrects the phase delay due to seismic velocity change and thus enables detection of waveform distortion without phase shift. The moving time window allowed us to examine the relationship between lag time and waveform distortion.

Results

We detected changes to the ACFs after the mainshock. Figure 2 shows the calculated ACFs at seismic stations N.AMAH and ATSUMA: At N.AMAH, we found ACF phase delays at lag times 4–6 s after the mainshock, while at ATSUMA, we could also see ACF phase delays at lag times 4–9 s after the mainshock, and further confirmed the tendency of phase delay to increase with lag time. In addition to the phase delays, we found changes in the characteristics of the ACF waveform. The shape of the ACF waveform changed before and after the earthquake around lag times 6, 9, and 12 s, at N.AMAH, and around the lag time 10 s at ATSUMA. Around the lag times, simple homogeneous phase shifts based on Eq. (1) cannot explain the change in the ACF waveform.

Fig. 2
figure 2

Calculated ACFs at a N.AMAH, and b ATSUMA seismic stations. The top panels show the averaged ACFs before (black) and after (red) the mainshock. The bottom panels show the 7-day averages of the ACFs. The red line in the bottom panels indicates the day the mainshock occurred

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The stretching method revealed the temporal changes to the dv/v at each station. Figure 3 shows the result of the stretching method with a time window of 4–15 s. The dv/v for all stations, except for N.KYMH, fluctuated within ± 0.5% of the value recorded before the earthquake. At N.AMAH, which was close to the main shock epicenter, the seismic velocity decreased by about 3% after the main shock. ATSUMA station also showed seismic velocity reduction, in this case by about 2%. Post-seismic dv/v recovery was not clear within the analysis period. Although a dv/v reduction exceeding 1% was not observed at other stations, the average values of the dv/v after the earthquake were smaller than the averages before the earthquake in N.MBWH, N.OIWH, and N.CTSH. In order to obtain the coseismic changes in dv/v, we averaged the dv/v after the mainshock in Fig. 3 using the errors of the individual measurements as a weighting factor. The average values and standard deviations of the average are listed in Table 1, and most of the stations show coseismic velocity decreases.

Fig. 3
figure 3

Estimated temporal changes in dv/v over time, at each station. The color shows cross-correlation coefficients between the reference and individual ACFs. Only dv/v values with cross-correlation coefficients ≥ 0.6 are colored. The red line indicates the day the mainshock occurred

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Table 1 Average values in dv/v and their standard deviations estimated from the three time windows, and computed indexes of strong ground motion, at each station
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Note that the 7-day averages of the ACFs before the corresponding dates were used to estimate the velocity changes. The 7-day moving average causes apparent time delay of the velocity change. In addition, data were missed just after the main shock for 2 days at N.AMAH and a half day at ATSUMA. The aftershock removal in the ACF also may reduce the available data soon after the mainshock. Although the velocity reduction occurred a few days after the main shock at N.AMAH and gradually occurred at ATSUMA, the delayed response can be explained by the aforementioned factors.

The results of the stretching method depended on the time window used. Figure 4a, b shows the results of the stretching method, with the time windows 4–9.5 s and 9.5–15 s, at N.AMAH and ATSUMA, respectively. The magnitude of the dv/v differed when we used different time windows, which suggested that, at these two stations, the ACF changes could not be simply explained by a homogeneous velocity change. In addition, the correlation coefficient after the waveform stretching decreased after the earthquake (Figs. 3 and 4). This decoherence also suggested that not only seismic velocity, but also scattering properties, affected temporal ACF variation.

Fig. 4
figure 4

Estimated temporal changes in dv/v over time, using respective time windows, at a N.AMAH, and b ATSUMA seismic stations

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Figure 5 shows the lag time dependency of the ACF waveform change, based on the correlation coefficient between the reference and post-seismic ACFs. The degradation characteristics of the correlation coefficient varied between seismic stations: It was seen to decrease significantly near the lag time of 10 s, at ATSUMA, and around 6.5 s, 10 s, and 12.5 s, at N.AMAH. The decrease in correlation values could also be confirmed from the ACFs shown in Fig. 2. In general, later lag times may have tended to have low correlation coefficients, due to a decreasing signal-to-noise ratio with increasing lag time. At ATSUMA station however, for example, the correlation coefficient became higher than 0.9, after the drop in the correlation coefficient around 10 s. Thus, the decreased correlation values have reflected changes to the subsurface structure.

Fig. 5
figure 5

The relationship between cross-correlation coefficients and lag times for each station

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Discussion

The reduction of dv/v after the mainshock

Immediately after the mainshock on September 6, the dv/v was recorded to decrease by 2–3%, at two seismic stations close to the mainshock. Previous studies reported similar coseismic reductions, of dv/v by a few percent, at the focal region of large earthquakes (e.g., Hobiger et al. 2016). The frequency dependence of dv/v, and comparisons with vertical seismic array analyses, have indicated that such velocity reductions appear to concentrate in the shallow subsurface area, up to a few hundred meters deep (Hobiger et al. 2014; Takagi et al. 2012). Larger velocity decreases in the time window of 4.0–9.5 s than that of 9.5–15.0 s also imply that velocity decrease is mainly located in the shallow subsurface (Table 1). Thus, the dv/v decreases in the ACF estimated by the present study may be due to the shallow ground damage caused by strong ground motions.

We compared the observed seismic velocity change with indexes of strong ground motion. Table 1 shows \(V_{s30}\) at each station, peak ground acceleration (PGA), peak ground velocity (PGV), and peak dynamic strain (PDS), caused by the strong motion of the mainshock. \(V_{s30}\) is the average S-wave velocity from the ground surface to 30 m and is defined as shown by Eq. (3), where \(d_{i}\) is the thickness of a layer and \(v_{{s_{i} }}\) is its S-wave velocity.

$$V_{s30} = \frac{{30\, \left[ {\text{m}} \right]}}{{ \mathop \sum \nolimits_{i} (d_{i} /v_{{s_{i} }} )}}$$
(3)

We estimated PGA and PGV using strong motion records on the ground surface from KiK-net stations collocated with Hi-net stations (National Research Institute for Earth Science and Disaster Resilience 2019a). PDS is the maximum value of a dynamic strain change due to strong ground motion, which is estimated by dividing PGV by \(V_{s30}\) (Takagi and Okada 2012; Sawazaki and Snieder 2013). The station with the maximum PGA and PGV, N.OIWA, showed a dv/v decrease of 0.17%. N.AMAH, on the other hand, had smaller PGA and PGV than those of N.OIWH, with the PDS a maximum at N.AMAH. The maximum coseismic decrease in dv/v was 2.61% among these stations and observed at N.AMAH, indicating that there may be a better relationship between dv/v and PDS, as opposed to PGA and PGV. Moreover, the velocity drop with a similar magnitude to previous works, and correlation with PDS, implied that damage in the shallow layers due to strong ground motion was the main cause of the velocity drop.

Hobiger et al. (2016) measured seismic velocity changes accompanying multiple, large earthquakes in Japan, and compared these with several indexes of strong motion. The data shown in Table 1 were consistent with the relationship trend between the seismic velocity changes and strong motion indexes that they estimated. However, since there is no simple linear relationship between PDS and the rate of dv/v, it is difficult to explain velocity changes using only PDS. For example, as suggested by the data from N.MBWH, N.CTSH, N.YUBH, N.OIWH, N.HOBH stations, although PDS values differed by almost one order of magnitude, their dv/v was the same degree, which suggested that susceptibility to velocity change varied with the ground and geological structure (Brenguier et al. 2014).

Degradation of waveform correlation

We examined the relationship between the lag times and correlation coefficients and found decreased waveform correlations before and after the mainshock. Such decorrelation of the ACF waveforms could be attributed to the changed subsurface scattering property.

Another possible cause of the ACF waveform decorrelation is spatially inhomogeneous or localized velocity changes. Because we assumed spatially homogeneous velocity changes and thus homogeneous phase sifts of the ACFs in 3-s time windows, inhomogeneous phase shifts caused by inhomogeneous or localized velocity changes may result in the decorrelation of the ACF waveforms. For example, the ACFs of N.AMAH station show the phase delays in 4–6 s and phase advances in 7–9 s, the latter of which may be interpreted as localized velocity increase. Although such localized velocity changes may partly explain the observed decorrelation, the shapes and amplitudes of the ACFs around 10 s at ATSUMA, and around 9 s and later lag times at N.AMAH do not appear to be explained by inhomogeneous phase shifts. Thus, hereafter, we attribute the decorrelation to the scattering property changes and discuss the location of the changes.

In order to locate the area showing scattering property change, we needed to distinguish the dominant ACF wave type. Obermann et al. (2013) showed that the body wave component dominated the surface wave in the latter part of CCF. Generally, it has been suggested that surface waves and body waves were included in the ambient noise of 1 Hz or more (Bonnefoy-Claudet et al. 2006). Takagi (2014) showed that the power spectral ratio of Rayleigh waves and P-waves approached 1, in the ACF of 1–2 Hz, vertical component, ambient noise. Roux et al. (2005) also showed that Rayleigh waves and P-waves were extracted from the CCF of ambient noise vertical components and that P-waves were dominant at 0.7 Hz and above.

Since the possibility of the contribution of the surface wave cannot be completely excluded, by virtue of this research alone, it will be necessary to clarify the ACF wave field, by using, for example, dense array observations near the station where the change was detected. However, according to the previous studies noted above, it may be reasonable to assume that degradation of the waveform correlation was due to P-waves.

In order to locate the area that corresponded with the waveform correlation degradation, we carried out the following analysis. First, we divided the target area into 0.5-km side cubic blocks and computed the two-way travel times from the seismic stations to cubic blocks. A one-dimensional (1D) JMA velocity structure was used for ray tracing (Ueno et al. 2002)—and note that we used the same 1D velocity structure as was used for hypocenter location by the JMA. Then, assuming that the ACFs comprised single backscattered P-waves, and thus regarding the lag times of the ACFs as the two-way travel times, we assigned the decorrelation values (1 − CC) of the corresponding lag times to the cubic blocks. We obtained spatial distribution of the decorrelation values by summing the contributions from all station used in this study. The larger the value of decorrelation, the more significant the influence on the waveform change.

We found three areas with large decorrelation values, as shown in Fig. 6a, which were therefore the candidate regions for scattering property changes. Two areas were located near the northern edge of the aftershock distribution. The depths of the maximum values were 15 and 20 km, although they spread in the depth direction. The other area with large decorrelation value was located at 30 km depth, just west of the central part of the aftershock distribution. Since the average P-wave velocity was approximately 6.0 km/s, the large decorrelation area reflected correlation reductions of about 10 s, at N.AMAH and ATSUMA.

Fig. 6
figure 6

a Analysis results of waveform decorrelation and distribution of seismicity at each depth. The blue color indicates decorrelation values within the blocks. Values of half of the maximum decorrelation value from this study, or more, are colored. Seismicity is plotted from September 6 to September 16, 2018. Each plot size indicates earthquake magnitude, and color indicates when the earthquake occurred. The triangles show locations of stations used in this study. b Figure reproduced from Japan Meteorological Agency (2018). The legends of the star and color scale in the original figure were translated into English from Japanese. The color contour shows the coseismic slip distribution estimated from near-field strong motion records. The black dots show the relocated hypocenters by using the double-difference method

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Figure 6b shows the coseismic slip distribution estimated from strong motion records and hypocenters relocated by applying the double-difference method (Japan Meteorological Agency 2018). The aftershocks were distributed in two, separated depth ranges of the fault plane: 10–15 km and 30–40 km. The coseismic slips were estimated between the two aftershock clusters. The maximum slip was located at 30 km, just above the central part of the deeper aftershock cluster. Geodetic data also suggested that the coseismic fault was modeled at 15–30 km (Geospatial Information Authority of Japan 2018). We found that the large decorrelation areas were located at the depth of 15–30 km. It is noteworthy that one large decorrelation areas, at 30 km, was close to the location of the maximum slip area. The spatial correlation suggested that the decreased ACF waveform correlation in this study was related to coseismic slip on the fault. One interpretation is that the coseismic fault rupture generated cracks within or around the fault zone and that this changed the scattering property, or scatterer distribution.

Conclusion

In the focal region of the 2018 Hokkaido Eastern Iburi Earthquake, we detected temporal changes in seismic velocity and scattering property, based on autocorrelation analysis of ambient seismic noise. The stretching method, with the lag time window of 4.0–9.5 s, estimated seismic velocity reductions of 2–3% at two stations close to the epicenter. Coseismic velocity drops of similar magnitude (a few percent) have been previously reported in the shallow subsurface, down to a few hundred meters. Based on the relation between the values of PGA, PGV, and PDS, and the dv/v, we showed that the velocity change was more closely related to PDS, than to PGA or PGV. The amplitude of the velocity drop, and correlation with PDS, implied that damage in the shallow layer due to strong ground motion was the main cause of the velocity drop.

We also detected waveform distortion of ACFs, before and after the mainshock. If the ACFs were composed of single, backscattered P-waves, the change in scattering property could be estimated where the maximum slip was estimated. This suggested that the coseismic fault rupture generated cracks around the fault, which changed the scattering property in and around the fault zone.