Distribution of coseismic vertical displacement
Global sea level during the past 5000 years has remained within 0.25 m of the present-day level (Woodroff et al. 2012). This study assumes that sea level has been stable over the past 5000 years.
Both F. albicostatus and H. mutabilis inhabit in intertidal zone from −0.8 to 0.8 m amsl (Okutani 2000; Yamaguchi and Hisatsune 2006). Their fossils occur at 1.5 m amsl at the Kujyuhama coast and at 1.9 m amsl at Tarai Cape, indicating that 1.5 and 1.9 m of relative sea level fall has occurred at the Kujyuhama coast and Tarai Cape, respectively. Figure 2 compares our 14C data with those of Kitamura et al. (2015). The ages and elevations of the specimens at Tarai Cape and the Kujyuhama coast match those of zones B and C at Kisami, respectively. This indicates that their emergence was related to uplifts 2 and 3, respectively, and that there is no significant spatial difference in total uplift in the coastal area between Tarai Cape and Kujyuhama.
As noted above, barnacle individuals have been reported at 1.8–2.2 m amsl along the Koina coast (Fig. 1) (Taguchi 1993), and their elevation corresponds to that of zone B at Kisami. We therefore used the values of total coseismic uplift deduced from the large cave at Kisami to infer the total coseismic uplift in the coastal area between Koina and Kujyuhama.
At the large cave at Kisami, the highest emergent sessile assemblages, dated at 1256–950 BC, occur at 3.40 m amsl and consist of the barnacle Tetraclitella chinensis. Given that this species inhabits the intertidal zone from −0.8 to 0.8 m amsl (Yamaguchi and Hisatsune 2006), we estimate the total uplift at Kisami to be 2.6–4.2 m. The AD 1974 Off-Izu Peninsula earthquake on the Irozaki Fault caused 0.1 m of uplift in the study area (Danbara and Tsuchi 1975). Given that the rate of subsidence during the past 3000 years has been the same as that between 1896 and 1968 (0.6 mm/year; Danbara and Tsuchi 1975), the net uplift is calculated to be 4.3–6.1 m. In each of the four uplift events, the mean coseismic uplift is estimated to have been 1.1–1.5 m (Fig. 6).
Based on previous studies of the sedimentary facies in cored coastal plain deposits of the southeastern Izu Peninsula, reliable constraints on the age and amount of coseismic uplift were obtained at site 7 near Minami Izu (Fig. 1). Here, Kitamura et al. (2013) determined that the uppermost tidal deposits were deposited at 4530–4430 calendar year BP, at −0.7 m amsl. Using the above constraints, the mean coseismic uplift at site 7 is estimated to be 0.3–0.7 m (Fig. 6).
Taguchi (1993) reported that the elevations of emerged notches, which form in the intertidal zone (from −0.8 to 0.8 m amsl), are up to 3.0 m amsl at Shirahama. Given that the rate of subsidence during the past 3000 years has been the same as that between 1896 and 1968 (0 mm/year; Danbara and Tsuchi 1975), the net uplift is calculated to be 2.2–3.8 m. At Shirahama, the mean coseismic uplift is estimated to be 0.6–1.0 m (Fig. 6).
Fault source model
As noted above, there is no significant spatial difference in total uplift in the coastal area between Tarai Cape and Kujyuhama, indicating that the fault is a west-dipping reverse fault and strikes NNE–SSW, parallel to the coastline of the Izu Peninsula. Since emerged coastal landforms are not observed west of Koina (Fig. 6), the western edge of the fault seems to be located off Koina.
We applied a characteristic earthquake model to reconstruct the source fault for the four uplift-inducing earthquakes. Kitamura et al. (2015) suggested that the most recent coseismic uplift event (uplift 4) was caused by a historical earthquake near the southern Izu Peninsula at 1200–1300 hours (local time) on 8 March 1729 (Usami 1975). This earthquake was recorded at Edo (present-day Tokyo), Nikko, Sunpu (present-day Shizuoka), Kyoto, and Nara (Fig. 7) (Usami 1975). This distribution of shaking closely matches that of intensity map for the AD 1974 Off-Izu Peninsula earthquake (M 6.9) (Murai and Kaneko 1974), meaning that the reverse fault located offshore of the southern Izu Peninsula has caused a Mw 7 equivalent earthquake.
Kanamori and Anderson (1975) proposed a typical stress drop value of 10 MPa for intraplate earthquakes. Using this value and a scaling relation between stress drop and fault area (Kanamori and Anderson 1975), we estimate that the fault area of the targeted Mw 7 class earthquake was several hundred square kilometers.
Given these constraints on the fault, and the assumptions described in the methods, we constructed two models for estimating the average coseismic uplift. A submarine fault in model 1 is located 15 km off the coast of Shimoda, based on topographic analysis of the seabed inferred by Kim et al. (2012) (Fig. 1), and is located 5 km south of Mikomotojima. Although there is absence of emergent marine sessile assemblages and landforms at the island, the area is very erosional all around, so that emerged evidences might disappear. A submarine fault in model 2 is located at the base of a steep slope at 1 km off the Suzaki Peninsula (Fig. 6b).
First, we set a rectangular fault for model 1. The eastern corner of the top edge (0 km depth) is located at 34.6979° N, 139.1468° E, and the western corner is at 34.5336° N, 138.9415° E. The fault strike is about 226°. Figure 8a presents the results of a grid search performed by varying the dip angle and the slip amount of the fault. The best-fit case (i.e., that with the minimum sum of squared residuals) indicates a dip angle of 31° and a slip amount of 4.4 m. Based on our assumption that the lower limit of the fault occurs at 10-km depth, the fault width is calculated to be 19 km. The moment magnitude is 7.2 with a rigidity of 30 GPa. The stress drop estimated from the scaling relation (Kanamori and Anderson 1975) is about 13 MPa.
Second, we set another fault for model 2. The eastern corner of the top edge (0 km depth) is at 34.6882° N, 139.1364° E, and the western corner is at 34.6165° N, 138.8905° E. The fault strike is approximately 250°. Figure 8b shows the grid search result. The best-fit case is a dip angle of 52° and a slip amount of 2.7 m. The fault is 25 km long and 13 km wide. The moment magnitude is 6.9 with a rigidity of 30 GPa. The stress drop is approximately 11 MPa.
Then we reconstructed the coseismic vertical deformation at each observation point using the boundary element method with Green’s function (Okada 1992). Figure 9 compares the observed vertical deformation with the calculated deformation from the best-fit cases. In both models (models 1 and 2), the maximum seafloor uplift around the top edge of the fault is below 1.9 m. This value is almost as large as the observed coseismic uplift at the coastal area. This fact implied that the tsunami height at the coastal area was small and explained that there is no document about tsunami associated with the 1729 earthquake.
When comparing two models, model 2 is more realistic than model 1 in the following respects: (1) the sum of squared residuals between the observed and calculated values for model 2 is far smaller than the sum of squared residuals for model 1 (see Fig. 8). (2) The vertical deformation at Mikomotojima (34.5754° N, 138.9416° E) for model 2 is nearly zero, but that for model 1 is over 1.8 m. The slight vertical deformation for model 2 may correspond to the absence of emergent marine sessile assemblages and landforms at Mikomotojima.
In contrast, the dip angle for model 2, 52° (>45°), seems peculiar as a reverse fault in terms of Anderson’s theory. One can consider that the high-angle reverse fault was a reactivated one (Jackson 1980). Or we confirmed that the dip angle for model 2 can be <45° when the eastern corner of the top edge is near the coastline, although this setting leads to a smaller fault and higher stress drop deviating from the scaling relation.