We find significant spatial variations in background seismicity rate \(\mu\) and aftershock productivity \(K\) (Fig. 2a, b, respectively). However, one may argue that the intensive seismicity associated with the Yamagata-Oki earthquake gives a bias for the spatial variations in aftershock productivity (especially large \(K\)-value in the source region of Yamagata-Oki earthquake). To verify the effect of Yamagata-Oki earthquake sequence, we estimate HIST-ETAS parameter using only earthquake catalog before the onset of the Yamagata-Oki earthquake (from January 1, 1998 to June 17, 2019). The spatial distributions of the seismicity parameters and their uncertainties are shown in Additional file 1: Figs. S5 and S6, respectively. The spatial variations in \(\mu\) and \(K\) shown in Additional file 1: Fig. S5 are quite similar to those shown in Fig. 2, although absolute value of \(K\) is different owing to the trade-off between the parameters \(K\) and \(q\). Therefore, we conclude spatial variations in \(\mu\) and \(K\) are stable regardless of the occurrence of the 2019 Yamagata-Oki earthquake sequence.
In addition, we perform two kinds of synthetic tests to verify reliability of the spatial variations of the estimated parameters. A synthetic catalog is created based on the simulation algorithm proposed by Ogata (1998) by giving a spatial distribution of seismicity parameters. We use the same sequence of magnitudes and the same precursory occurrence history as the real earthquake catalog. Subsequently, the synthetic data are inverted applying the HIST-ETAS model. We then evaluate how much the estimated parameters are recovered, comparing with the initially given values.
First, we generate the synthetic catalog #1 using the seismicity parameters estimated from the real catalog (Fig. 2). Comparing the parameters inverted using the synthetic catalog #1 (Additional file 1: Fig. S7) with the initially given values (Fig. 2), the spatial variations of \(\mu\) and \(K\) are well recovered, although absolute value of \(K\) is shifted owing to the trade-off between the parameters \(K\) and \(q\).
Second, we created the synthetic catalog #2 assuming each parameter to be spatially uniform (reference parameters of our result). This aims to test whether the current method causes apparent spatial variation of each parameter during the inversion. From the distribution of the parameters inverted using the synthetic catalog #2, we recognize that the apparent variation in \(K\) is smaller than deduced from the real catalog (Fig. 2b). Based on the above two kinds of the synthetic tests, we conclude that the spatial variations in \(\mu\) and \(K\) obtained from the present study is indeed reliable.
Previous studies have discussed the physical processes that control the background seismicity rate (e.g., Ide 2013; Zeng et al. 2018; Ben-Zion and Zaliapin 2019). Zeng et al. (2018) revealed that the maximum shear strain rate along the San Andreas Fault and Eastern California Shear Zone correlated with the distribution of the background seismicity rate in the shallow-crustal environment. Ide (2013) suggested that subduction zones around the world exhibit an approximately linear increase in the background seismicity rate with the relative convergence rate at each plate boundary. These previous studies suggest that the background seismicity rate can provide clues to understanding the evolution of deformation in the seismogenic zone. Therefore, we compared the spatial variations in background seismicity rate obtained by the current study with the spatial variations in geodetic E–W strain rate obtained by Meneses-Gutierrez and Sagiya (2016); the areas with high background seismicity rates correlate well with those possessing high E–W strain rates (contraction) (Fig. 3). The correlation coefficient between the E–W strain rate and the logarithm of the background seismicity rate is calculated to be − 0.49 (Fig. 3c; the correlation coefficient between the E–W strain rate and the logarithm of the medium of \(\mu\) (black dots in Fig. 3c) is calculated to be − 0.91).
The high E–W contraction area was a northern extension of the Niigata Kobe Tectonic Zone, stretching from Kobe to Niigata District, proposed by Sagiya et al. (2000). The source regions of both the Yamagata-Oki and Niigata earthquakes are located around and in the zone characterized by a high background seismicity rate and high E–W strain rate (Fig. 3). Nishimura (2017) suggested that the large shallow-crustal earthquakes in the Japanese Archipelago (Mj ≥ 6) tend to occur in and around the areas with a high shear strain rate. Ogata (2017) suggested that many large earthquakes in California occurred in areas with high background seismic activities. Our results are consistent with these papers and imply that large shallow-crustal earthquakes are likely to occur in areas with high background seismicity rates. Therefore, capturing spatial variations in the background seismicity rate may assist in evaluating seismic hazard across the Japanese Archipelago. The background seismicity rate is especially effective in areas where a geodetic network has not been densely deployed, such as marine settings and some inland areas, to monitor the secular accumulation of elastic strain.
The relationship between the seismicity parameters that describe aftershock generation and the geophysical features in the seismogenic zone has been explored by previous studies (e.g., Mogi 1967; Ogata 2004; Marsan and Helmstetter 2017; Nandan et al. 2017; Zakharova et al. 2017; Hainzl et al. 2019). For example, Ogata (2004) suggested that aftershock productivity (\(K\)) is high on the boundary of each source region that hosts \({{M}}\) 7-class earthquakes along the subduction zone, offshore NE Japan. The \(K\)-value in the source region of the Yamagata-Oki earthquake is larger than that in the source region of the Niigata earthquake, as shown in Fig. 2b. Here, we focus on spatial variations in the seismic-wave velocity and b-value to investigate the relationship between \(K\) and the observed geophysical features (Fig. 4). Figure 4a, b shows the compressional-wave (P-wave) velocity structures at depths of 10 km and 15 km (the depth layer close to the mainshock hypocenter depth, ~ 14 km) from a regional seismic tomography study (Matsubara et al. 2020). The P-wave velocity in the source region of the Yamagata-Oki earthquake is lower than that in the source region of the Niigata earthquake. It is noted that the shear-wave velocity structure at 15 km depth follows a similar trend to the P-wave velocity structure. But, the contrast of shear-wave velocity between the two source regions becomes weak at 10 km depth. This E–W seismic velocity contrast is also observed in the velocity model estimated by Zhao et al. (2015). We define two zones based on the seismic velocity structure: a low-velocity zone that includes the rupture area of the Yamagata-Oki earthquake (black rectangular region in Fig. 4a, b) and a high-velocity zone that includes the rupture area of the Niigata earthquake (blue rectangular region in Fig. 4a, b). We calculate the \(b\)-value in each region during the 1998–2019 periods (Fig. 4c) using the formula of binned magnitude (Tinti and Mulargia, 1987; Marzocchi and Sandri, 2003).We defined M1.9 as the cutoff magnitude considering the goodness of fit proposed by Wiemer and Wyss (2000), in addition to the temporary deficiency of immediate aftershocks following the 2019 Yamagata-Oki earthquake (Additional file 1: Fig. S1b). We evaluate the uncertainty of \(b\)-value using the bootstrapping method (1000 resampling). Figure 4c shows that the \(b\)-value in the low-velocity zone is lower than that in the high-velocity zone but given the uncertainty the difference in \(b\)-values is not so significant. It is quite difficult to compare \(b\)-value with P-wave velocity in higher spatial resolution, because the number of available earthquakes is not sufficient to obtain reliable \(b\)-value (high goodness of fit > 90%).
The source region of the Yamagata-Oki earthquake has a higher K-value and lower P-wave velocity than that of the Niigata earthquake (Fig. 5). Assuming that \(b\)-value in the source region of the Yamagata-Oki earthquake is lower than that of the Niigata earthquake, we could interpret the low-velocity zone of the Yamagata-Oki earthquake to be a well-developed damaged rock that contains many fractures and cracks over multiple scales. Laboratory experiments and numerical simulations of rock deformation have implied that the progressive damage associated with an increase in shear stress results in both a reduction in the \(b\)-value and an increase in aftershock productivity within a broad volume (e.g., Amitrano 2003). Furthermore, progressive damage makes the rock more ductile at the macroscopic scale because diffuse inelastic deformation is more dominant than localized deformation. Diffuse deformation provides a large spatial correlation dimension for damage, leading to a low \(b\)-value and high productivity of brittle fractures within a broad volume (Amitrano et al. 1999; Amitrano 2003).
The ductility in the source region of the Yamagata-Oki earthquake is therefore considered to be higher than that of the Niigata earthquake. The relative increase in ductility may act as a barrier against the propagation of dynamic rupture during the Niigata earthquake. This is consistent with the case where the ductile flow of thick sediments may have arrested the southwestward propagation of the dynamic rupture of the 2004 Niigata Chuetsu earthquake (Kato et al. 2009, 2010). The crustal structure along the eastern margin of the Sea of Japan is quite complex owing to the evolution of a fold-and-thrust belt system under a W20°N–E20°S horizontal compressive stress regime (Okamura et al. 2007; Kato et al. 2009). It is therefore plausible that lateral heterogeneities in the crustal structure impacted the spatiotemporal pattern of the aftershock sequences.
The results presented suggest that different deformation styles play a key role in controlling seismicity characteristics. A systematic investigation of the spatial variations in seismicity characteristics and related geophysical features could provide new insights into the physics of earthquake generation.