Based on many recent findings such as those for geodetic data from Japan's GEONET nationwide GPS network and geological investigations of a tsunami-inundated Ryujin Lake in Kyushu, we present a revised source rupture model for the great 1707 Hoei earthquake that occurred in the Nankai Trough off southwestern Japan. The source rupture area of the new Hoei earthquake source model extends further, to the Hyuga-nada, more than 70 km beyond the currently accepted location at the westernmost end of Shikoku. Numerical simulation of the tsunami using a new source rupture model for the Hoei earthquake explains the distribution of the very high tsunami observed along the Pacific coast from western Shikoku to Kyushu more consistently. A simulation of the tsunami runup into Ryujin Lake using the onshore tsunami estimated by the new model demonstrates a tsunami inundation process; inflow and outflow speeds affect transport and deposition of sand in the lake and around the channel connecting it to the sea. Tsunamis from the 684 Tenmu, 1361 Shokei, and 1707 Hoei earthquakes deposited sand in Ryujin Lake and around the channel connecting it to the sea, but lesser tsunamis from other earthquakes were unable to reach Ryujin Lake. This irregular behavior suggests that in addition to the regular Nankai Trough earthquake cycle of 100–150 years, there is a hyperearthquake cycle of 300–500 years. These greater earthquakes produce the largest tsunamis from western Shikoku to Kyushu.
 Great interplate earthquakes have occurred at the Nankai Trough at a recurrence interval of approximately 100 to 150 years due to the subduction of the Philippine Sea plate beneath southwestern Japan. The Nankai Trough extends from Suruga Bay to the Hyuga-nada. Its total length is approximately 800 km. The history of Nankai Trough earthquake occurrences can be traced through 11 events, beginning with the Hakuho Nankai earthquake in AD 684 [e.g., Ishibashi, 2004; Ando, 1975]. The earthquake occurrence pattern can be characterized by three fault segments: the Nankai, the Tonankai, and the Tokai, from west to east. The fault rupture pattern is described as either simultaneous or individual ruptures of each earthquake segment.
Figure 1 illustrates the Nankai Trough earthquake occurrence pattern for three recent events, the 1944 Tonankai (M7.9) and 1946 Nankai (M8.0) earthquakes, the 1854 Ansei Nankai (M8.4) and Ansei Tokai (M8.4) earthquakes, and the 1707 Hoei earthquake (M8.4). The spread of the source area of the 1944 Tonankai earthquake was rather short and stopped before the Tokai earthquake fault segment. Thus, a Tokai earthquake has not occurred for more than 150 years since the 1854 Ansei Tokai earthquake. Since more than 60 years have been passed since the former earthquake cycle we expect that next earthquake sequence might occur along the Nankai Trough in the next 30 years.
 In the recorded history of the Nankai Trough earthquakes the 1707 Hoei earthquake (hereafter called the Hoei earthquake) was the largest shock in modern Japanese history. It killed more than 20,000 people due to its strong ground motion and the tsunami associated with the earthquake [Usami, 1996, 2003]. The fault rupture area of the Hoei earthquake has been thought to spread from Suruga Bay to the westernmost end of Shikoku, i.e., the whole extent of the 1854 Ansei Tokai and the 1854 Ansei Nankai earthquake source segments. Therefore, the Hoei earthquake is often referred as a worst case scenario for earthquakes occurring in the Nankai Trough. This source model is often used for assessing earthquake-induced damage expected for future Nankai Trough earthquakes.
 The source rupture histories of the recent 1944 Tonankai and 1946 Nankai earthquakes were examined extensively based on the analysis of modern instrumental data, such as tide gauge records of tsunami waveforms [Aida, 1981; Tanioka, 2001; Tanioka and Satake, 2001; Baba et al., 2002, 2006], seismograms of regional strong ground motions and teleseismic waveforms [Ichinose et al., 2003; Murotani, 2007; Yamanaka, 2004], geodetic data derived from leveling surveys [Fitch and Scholz, 1971; Kanamori, 1972; Ando, 1975; Ishibashi, 1981; Sagiya and Thatcher, 1999], and combinations of these data [Satake, 1993]. Source models of historical events such as the Hoei earthquake, on the other hand, have mostly been deduced from descriptions of earthquake phenomenon in ancient documents such as shaking felt by humans, damage to houses, and visual measurements of tsunami inundation or tsunami runup height. Ando  deduced the source model of the Hoei earthquake using various data sets, including the vertical movements of ground surface associated with the earthquake [Kawasumi, 1950], the distribution pattern of seismic intensities [Omori, 1913], and comparisons between these phenomena and measurements from the recent 1944 Tonankai and 1946 Tokai earthquakes. Aida  deduced a source model for the Hoei earthquake based on tsunami data compiled by Hatori [1966, 1974] and presented a better source model that explains distribution of the tsunami height along the Pacific coast from Shikoku to Suruga Bay. An'naka et al.  modified the source model of Aida  and improved the agreement between tsunami simulations and observed tsunami height distributions.
 The source model for the Hoei earthquake deduced by Ando , Aida , and An'naka et al.  determined that the source rupture area of this event extends from Suruga Bay to the westernmost end of Shikoku, i.e., the whole extent of the source area of the 1856 Ansei Tokai and the Ansei Nankai earthquakes. However, it should be kept in mind that objective data, such as shaking intensities and tsunami heights in Kyushu, were rather limited at that time and thus, these data may not well incorporated in their analysis. Thus, further supporting evidence is needed to develop a reliable and detailed source rupture history for the Hoei earthquake.
 Recently, there have been numerous works reporting geological surveys of earthquake-related lacustrine sediment in seashore lakes along the Pacific coast from Shikoku to Kyushu. These studies endeavor to clarify the tsunami history of the historical and prehistorical Nankai Trough earthquakes [e.g., Tsukuda et al., 1999; Okamura et al., 1997, 2000, 2003, 2004; Tsuji et al., 1998, 2002; Nanayama and Shigeno, 2004; Komatsubara and Fujiwara, 2007; Matsuoka and Okamura, 2009]. Ryujin Lake is one such onshore lake that has tsunami-induced oceanic deposits (hereafter called tsunami lakes), located along the coast of the Hyuga-nada in Kyushu. Ryujin Lake has a thick cover of marine deposits, including coarse-grained sea sands and marine sediments containing oceanic plankton carried by Nankai Trough earthquake. It should also be noted that such tsunami-induced onshore deposits have not accrued regularly in Ryujin Lake due to the Nankai earthquakes that occur every 100 to 150 years, but were only deposited in the 1707 Hoei earthquake, the 1361 Shohei earthquake, and the 684 Tenmu earthquake, which are probably associated with larger tsunamis than the other Nankai earthquakes [Matsuoka and Okamura, 2009; Okamura et al., 2004]. Recent findings in the historical documents claim that the height of the tsunami during the Hoei earthquake at the village of Yonouzu, near Ryujin Lake, was more than 10 m, which is very much larger than the tsunamis associated with the 1854 and 1946 events [Chida et al., 2003; Chida and Nakayama, 2006].
 Following these new findings and supporting instrumental data, we will reexamine the source model for the Hoei earthquake. Our belief based on detail tsunami simulation is that the source rupture area of the Hoei earthquake extended an additional 70 km eastward to the Hyuga-nada from the westernmost end of Shikoku. Thus, the Hoei earthquake was not a linkage occurrence of the 1854 Ansei Nankai and the Ansei Tokai earthquakes but a much larger event. Similar discussion on the possible extension of the Hoei earthquake source area was also discussed by Harada and Ishibashi  based on tsunami simulation. Our new source model with the source rupture area extended to the Hyuga-nada explains the large tsunami observed in Kyushu more consistently than previous models. The tsunami inundated Ryujin Lake, acting together with subsidence of the coastline associated with the earthquake is also explained by the new source model very effectively.
 In section 2, we first simulate the tsunami and ground deformation patterns from the Hoei earthquakes to show the applicability and limitations of the current source model of, e.g., An'naka et al. . We compare the simulation results with observed heights of the tsunami along the Pacific coast of the Nankai Trough, especially from western Shikoku to Kyushu [Hatori, 1974, 1985; Murakami et al., 1996]. We then reexamine the source model of the Hoei earthquake based on recent objective data derived by the geological and geodetic investigations mentioned above. Finally, we simulate the tsunami runup and inundation of Ryujin Lake using a high-resolution bathymetric model to demonstrate the effectiveness of our new Hoei model in duplicating observed data due to the earthquake and to understand how the tall tsunami generated by the Hoei earthquake transported oceanic sand into Ryujin Lake.
2. Tsunami Simulation for the 1707 Hoei Earthquake
 We first conducted tsunami simulation for the Hoei earthquake using a source model of An'naka et al.  to examine the effectiveness of the present source model for reproducing observed height of the tsunami along the Pacific coast of the Nankai Trough [Hatori, 1974, 1985; Murakami et al., 1996].
2.1. Deformation of the Ground Surface in the Hoei Earthquake
 The source model of the Hoei earthquake deduced by An'naka et al.  consists of four fault segments (N1 to N4), which extend from Suruga Bay to the westernmost end of Shikoku, a total length of 605 km. The geometry and source parameters of each segment are shown in Table 1.
Table 1. Fault Parameters for the 1707 Hoei Earthquake Described by Subfault Segments N1 to N4a
Figure 2 illustrates the calculated vertical ground deformation due to fault rupture of the N1 through N4 fault segments for the Hoei earthquake, derived following Mansinha and Smylie . Large slips over the shallowly dipping N1 through N4 fault planes over the subducting Philippine Sea plate develop coseismic deformations on the Earth's surface with upheaval and subsidence of several tens of centimeters to meters in height extending along the source rupture area. Such deformations of the ground surface associated with large subduction zone earthquakes are known to produce marine terraces by upheaval and onshore lakes by subsidence. Postseismic deformations of the ground surface during interearthquake cycles gradually resolve such earthquake-induced deformation to a normal level over tens of years. Large ground upheavals of up to 2 m have been confirmed above the shallowest end of the source fault segment on the trench side. Such ground surface upheaval occurs mostly at sea but some can be found on land, including at Cape Muroto, Cape Shiono, and along the coast of Suruga Bay. On the other hand, large surface subsidence of as much as 2 m is found widely on land in a narrow belt zone extending from Shizuoka to the westernmost end of Shikoku. Such ground deformations caused by the rupture of the N1 to N4 segments is consistent with the observed ground deformation pattern of the Hoei earthquake compiled by Kawasumi , which includes large vertical upheavals of 2 to 2.5 m at Cape Muroto, 1 m at Omaezaki, and subsidence of 2 m at Kochi.
2.2. Tsunami Simulation
 Using the results of the coseismic ground deformation pattern, we conducted a tsunami simulation for the Hoei earthquake. The area of the tsunami simulation is 540 km by 860 km, which covers the entire Pacific Coast from Honshu to Kyushu where the large tsunami hit during the Hoei earthquake. We used a nested mesh model that connects gradually 30 m, 90 m, and 270 m mesh model to allow efficient simulation of the tsunami in heterogeneous bathymetry (Figure 3). The bathymetric model of each resolution was provided by the Central Disaster Mitigation Council, Cabinet Office, Government of Japan. Subfault segments N1 to N4 of the source model of the Hoei earthquake are divided into small pieces 1 km by 1 km in size. The source rupture is assumed to start in the Kumano Sea off the Kii Peninsula, spreading bilaterally toward Kyushu and Suruga Bay at a rupture speed of Vr = 2.7 km/s. The rupture of each subfault takes 5 s. For simplicity, we assumed that the shape of the initial tsunami on the sea surface is identical to the sea bottom deformation associated with the earthquake. The model of bathymetric and topography model just after the earthquake are modified using resultant vertical ground deformation pattern (Figure 2) due to the earthquake. Then propagation of the tsunami over the sea taking heterogeneous bathymetry into account and tsunami runup on heterogeneous topography are calculated based on a finite difference method (FDM) of a nonlinear, long-wave tsunami model [Goto and Ogawa, 1997], assuming Manning's roughness coefficients of 0.025 m−1/3 s and 0.04 m−1/3 s in the sea and on land, respectively. The computational time step is set at Dt = 0.6 s to satisfy FDM simulation stability conditions.
 Snapshots of tsunami propagation obtained from the simulation of the Hoei earthquake are illustrated in Figure 4 at time T = 1, 5, 10, 20, 40, and 80 min from the time the earthquake started in Animation S1. In Figure 4a (T = 1 min) the development of tsunami above the Hoei earthquake source segment (N1–4) is very striking, with an uplift of the sea surface of approximately 3 m over the Nankai Trough. As time passes, the raised mass of seawater gradually spreads bilaterally as two tsunamis, one propagating toward the seashore and the other to the open ocean at a faster speed. Figure 4b (T = 5.0 min) illustrates two such peaks of elevated sea surface parallel to the trough. Radiation of tsunamis from rectangular fault sources has been confirmed to be very strong in the direction perpendicular to the trough axis, while it is very weak in the direction parallel to the trough. As the tsunami approaches the shore, its speed decreases suddenly and its height increases very drastically. The onshore height of the tsunami, more than 8 m, is several times larger than the height of the initial tsunami above the source area. The later snapshot (Figures 4d and 4e; T = 20 and 40 min) illustrate the arrival of the large tsunami along the Pacific coast from the westernmost end of Shikoku to Hyuga-nada. The tsunami lasts for several tens of minutes after the earthquake. A number of tsunami trains are captured within Tosa Bay (Figure 4f).
Figure 5 illustrates the distribution of maximum simulated tsunami height for An'naka et al.  Hoei earthquake source model. From historical records, tsunami heights of 9 m at Tosa Shimizu and Ashizuri Cape and more than 4 m along the coast from Ashizuri Cape to Hyuga-nada are known to have occurred (shown as circles in Figure 5 [Murakami et al., 1996]). The simulated maximum tsunami height along the Pacific coast from Tosa Bay to Suruga Bay generally agrees well with observed tsunami runup during the Hoei earthquake [e.g., Hatori, 1974, 1985; Murakami et al., 1996]. However, the height of the simulated tsunami from western Shikoku to Hyuga-nada in Kyushu is less than half of the actual height observed. For example, historical archives document that at Yonouzu village, at the northern end of Hyuga-nada, the tsunami was more than 10 m and killed 18 people [Chida et al., 2003; Chida and Nakayama, 2006]. The height of the tsunami during the Hoei earthquake at Yonouzu was several times larger than that experienced during the 1854 Ansei earthquake. Yet the simulated tsunami height at Yonouzu is less than 4 m, which is comparable to the tsunami caused by the 1854 Ansei Nankai earthquake but much shorter than the tsunami experienced with the Hoei earthquake.
3. Revision of the 1707 Hoei Earthquake Source Model
 In order to better explain the size of the Hoei earthquake tsunami from Cape Ashizuri to Hyuga-nada, we revised the present source model of the Hoei earthquake developed by An'naka et al.  by modifying the structure of the subfault segments off Shikoku based on the findings of a number of recent geodetic and geological investigations of the Nankai Trough.
3.1. Recent Geological Investigations and Tsunami Lakes
 Tsunami lakes on the shoreline of the Pacific coast along the Nankai Trough are aligned linearly over the area where large ground subsidence has occurred during Nankai Trough earthquakes (Figure 2). It is thought that ground surface subsidence due to the earthquakes results in particularly deep tsunami inundation on land, which transports sea sand into onshore lakes very effectively. Then, for several tens of years after the earthquake, gradual upheaval of the ground surface occurs and it recovers the subsided ground surface to a normal level and preserves tsunami deposits by protecting from erosion by sea waves or rains for the long periods of time during the interearthquake cycle. The tsunami lakes distributed along the Nankai Trough shoreline lie along a larger zone that subsides during the Nankai Trough earthquakes have developed and preserved in such way. Ryujin Lake, however, recently observed by Okamura et al.  at the Hyuga-nada seashore in Kyushu, is not in a location typical of other tsunami lakes in Shikoku and Honshu where large ground subsidence is considered to have occurred during Nankai Trough earthquakes. The pattern of earthquake ground deformation shows that the area of coseismic ground deformation terminates at the westernmost end of Shikoku, approximately 100 km farther east from Ryujin Lake (Figure 2). This implies that the source rupture area of the Nankai subfault segments might not stop at the westernmost end of Shikoku as most source models assume [Ando, 1975; Aida, 1981; An'naka et al., 2003], but may extend further, to Hyuga-nada.
 We therefore examined other findings supporting our hypothesis of an extended source of the Hoei earthquake. The C14 age determination for the sedimentation of Ryujin Lake revealed that three sheets of sand layers sandwiched between muddy host sediments were developed during the 1707 Hoei, the 1361 Shohei, and the 684 Tenmu earthquakes [Okamura et al., 2003, 2004]. On the other hand tsunami deposits from the other Nankai Trough earthquakes, which have occurred every 100 to 150 years, do not exist in Ryujin Lake. This implies that unusually large earthquakes associated with larger tsunamis than usual have struck there during the 1707 Hoei, the 1361 Shohei, and the 684 Tenmu earthquakes. The maximum water depth of the lake is approximately 3 m in the center, and a narrow channel or waterway southwest of the lake connects it to the sea. Okamura et al. [2003, 2004] noted that the tsunami deposits are very thick at the southwest side of the lake where the channel connects it to the sea and become thinner toward the center of the lake, implying an another important constraint that tsunami height at the Ryujin Lake was not as tall as overlying beach hill of 10 m surrounding the lake.
3.2. Ground Deformation and Interplate Coupling Pattern Derived From GPS Data
 Ten years of data from the nationwide GEONET GPS network illustrates the current pattern of ground deformation (Figure 6). The pattern of vertical ground deformation derived from GEONET data indicates areas where ground upheaval larger than 2 mm/yr has occurred over the past 10 years. A wide upheaval area extends on land from Enshu-nada to Hyuga-nada, roughly covering the area that suffered subsidence due to the Hoei earthquake (Figure 2). Also, sporadic areas of large (>2 mm/yr) ground subsidence appear on land along the shoreline of the Pacific coast such as at Cape Ashizuri, Cape Muroto, Cape Shiono, and Omaezaki. These correspond to ground upheaval areas associated with the Hoei earthquake (Figure 2). This pattern of vertical ground movement is considered to illustrate the process of recovery of ground surface deformation due to the Nankai Trough earthquakes.
 If we assume that gentle ground upheaval has continued in the area around Ryujin Lake at a rate of roughly 2 mm/yr until now, the change in ground elevation is estimated to be 60 cm in the past 300 years since the Hoei earthquake in 1707. Because the water level in Ryujin lake is now at mean sea level, it is reasonable to conclude that a large ground subsidence of roughly 60 cm occurred there due to the Hoei earthquake.
 Following these new findings, we revised the source rupture model for the Hoei earthquake and extended the border of the Hoei earthquake source segments of An'naka et al.  and others from the westernmost end of Shikoku to Hyuga-nada, where strong interplate coupling has been found by studies using the GEONET data. We worked to match the ground deformation pattern due to the Hoei earthquake and the present ground deformation field shown by the GEONET data, assuming that the significant ground deformation associated with the Hoei earthquake is still influencing the present deformation field.
 We first set a 70 km by 120 km subfault segment, N5, on the west of the N4 subfault segment and extended the source rupture area of the Hoei earthquake to Hyuga-nada (Figure 7). Other source parameters, including strike, dip, rake and slip were assumed to be the same as for the N4 subfault segment (Table 2). Figure 8a shows the pattern of ground deformation derived from the new Hoei earthquake source model with subfault segments N1 to N5, demonstrating the extension of the ground subsidence area to Kyushu with maximum ground subsidence of 2 m in a narrow belt from Shikoku to Hyuga-nada. Ryujin Lake is now locating over an area of large (150 cm) ground subsidence. However, the level of ground subsidence in the area around Ryujin Lake derived by the new model is several times larger than we expected (60 cm). Moreover the simulated uplift of 100 cm at Cape Ashizuri is far larger than the uplift observed by Kawasumi .
Table 2. Fault Parameters for the N5, N4′, and N5′ Subfaults of the 1707 Hoei Earthquake
Fault Location (Latitude (°N)/Longitude (°E))
 We then modified the geometry of the N5 subfault segment and narrowed it in the direction perpendicular to the trench axis. Also we slightly modified the length of the N4 subfault segment in the direction parallel to the trench axis in order to improve the fitness between synthesized and observed ground deformation pattern reported by Kawasumi . We designated these segments as N4′ and N5′ (Table 2 and Figure 7b). This geometry follows studies on the slow slip events along the Nankai Trough [Hirose and Obara, 2005]. An observation of repeatable slow slip events associated with deep tremor activity around the Bungo Channel noted by Hirose and Obara  may mean that accumulation of strain energy above the plate boundary is not as strong as would be expected based only on the large plate coupling rate deduced from the GEONET data analysis.
 The ground surface deformation pattern derived using subfaults N1 to N5′ is shown in Figure 7b. It agrees well with our expectation of gentle (40 cm) ground subsidence in the area around Ryujin Lake and some subsidence of the ground surface at Cape Ashizuri as noted by Kawasumi . It also corresponds well to the present ground elevation field derived from the GEONET data (Figure 6).
4. Tsunami Simulation Using the New Hoei Earthquake Model
 We then conducted a tsunami simulation for the earthquake using the revised source model of the Hoei earthquake (Figure 7b) to see the contribution of the N5′ subfault segment in increasing simulated tsunami height along the coast from Shikoku to Kyushu and in producing tsunami inundation of Ryujin Lake.
 Snapshots of tsunami propagation derived by the simulation for the new Hoei earthquake source model with subfault segments N1 to N5′ and the former Hoei earthquake model without segment N5′ are compared in Figure 8 and in Animation S2. Figure 9 shows the maximum simulated tsunami heights for the new model along the Pacific coast of Japan in Shikoku and Kyushu. We will highlight the propagation of the tsunami from Shikoku to Kyushu in order to more clearly examine changes in the tsunami wavefield produced by introducing the new N5′ subfault segment. The comparison clearly demonstrates the development of a larger tsunami with heights of 5 m to over 10 m over a wide area along the Pacific coast from the westernmost end of Shikoku to Hyuga-nada due to the N5′ subfault (Figure 8a). The tsunami radiates very strongly in the direction perpendicular to the Nankai Trough trench axis (Figure 8a; T = 5 min). The height of the tsunami due to the N5′ fault is very strong to spread large tsunami wavefront from Cape Ashizuri to Hyuga-nada (Figure 8a; T = 15 min). As a result, the incremental change in tsunami height due to the N5′ subfault is very significant along the coast from the westernmost end of Shikoku to Hyuga-nada.
 In a later snapshot the larger tsunami is radiating into the Bungo Channel and propagating into the Inland Sea of Japan (Figure 8a; T = 30 min), which enhances the height of the tsunami in the Inland Sea. On the other hand, the radiation of the tsunami from the N5′ subfault is very weak in the direction parallel to the trench axis (i.e., southwest to northeast). Thus, the effect of adding the N5′ subfault is only a very minor amplification of the tsunami along the coast from east of Shikoku to Honshu, confirmed by comparing snapshots of Figures 8a and 8b in later time frames (T = 15 and 30 min).
 Our tsunami simulation for the new Hoei earthquake model produces a very tall tsunami, 5 to 8 m high at Yonouzu, located approximately 5 km away from Ryujin Lake in Kyushu where the height from the former Hoei earthquake model was less than 2 m (Figure 9). This explains the description in ancient documents of an exceptionally large tsunami approximately 10 m high occurring during the Hoei earthquake [Chida et al., 2003]. The modeled height is much larger than the maximum height of the tsunamis associated with the 1856 Ansei Nankai and 1946 Nankai earthquakes, which were less than 4 m at Yonouzu [Chida et al., 2003; Chida and Nakayama, 2006].
 The maximum tsunami height along the coast near Ryujin Lake as calculated by the present simulation is 6 m, while it is a maximum of 2 m for the former Hoei earthquake source model without the N5′ subfault segment (Figure 9). Thus, tsunami runup into Ryujin Lake might occur when the Nankai Trough fault rupture extends to Hyuga-nada, but not during events like the 1854 Ansei Nankai and 1946 Showa Nankai earthquakes, in which the fault rupture did not extend past the westernmost end of Shikoku. Our newly simulated tsunami height of approximately 6 m at Ryujin Lake also confirms the interpretation of Okamura et al.  that tsunami inundation carrying sea deposits occurs via a narrow channel connecting the sea and lake rather than by overtopping of beach hills that are 10 m high.
5. Simulated Tsunami Inundation of Ryujin Lake
 Finally, we conducted a tsunami inundation simulation in order to understand the process whereby the tsunami carried sea sand into Ryujin Lake during the Hoei earthquake, using the tsunami simulation results from the new Hoei earthquake model described in section 4.
Figure 10 shows the location and topography of the area surrounding Ryujin Lake. Ryujin Lake is surrounded by hills 50 m to 100 m high on the east and south and there is a short beach hill of approximately 10 m on the southwest. There is no river to supply water directly into the lake and inflow and outflow of seawater occur between the lake and the sea during high and low tide, respectively, through a narrow channel connecting it to sea.
 The tsunami inundation simulation covers a 200 m by 300 m area around Ryujin Lake. A high-density digital elevation map was constructed on a basis of recent geographical surveys conducted by the Yonouzu Promotion Office, Oita Prefecture. We modified the model to reconstruct the original shoreline structure by removing recent artificial constructions, such as concrete breakwaters and wharfs created by recent shoreline protection projects. The tsunami inundation simulation was conducted using a fine nested mesh model that connects gradually different mesh resolution of 30 m, 10 m, and 3.3 m.
 Results from a former large-mesh tsunami simulation, in which height and flux of the tsunami in two horizontal directions at the coast near Ryujin Lake were calculated using the larger (30 m) mesh, were used as inputs in the present tsunami inundation simulation. Before starting the simulation, we subsided the altitude of the simulation model at −60 cm in consideration of the results of the ground deformation simulation shown in Figure 7b.
 The results of the tsunami inundation simulation for the new Hoei earthquake model are shown in Animation S3 and in Figure 11 as a sequence of snapshots of the water surface of the Ryujin Lake after T = 14, 19, 24, 29, 34, and 39 min from the start of the earthquake, illustrating the way in which a tsunami with a large flux can inundate Ryujin Lake. In Figure 11b (T = 19 min), the height of the sea surface began to falls as the tsunami wavefront approached. Figure 11c (T = 24 min) shows the seawater gradually inundating the lake through the channel on the right-hand side of the lake. The speed of the seawater at each point is illustrated by red arrows superimposed on the snapshots. These show that the inflow speed from the sea into the lake is a maximum of approximately 6 m/s in the middle of the channel. As the height of the sea surface increases with passing time, the width of the channel grows very dramatically (Figures 11c and 11d; T = 24 and 29 min). This leads to an acceleration of the transmission of seawater into the lake. At this time, the flux of seawater is approximately 1 to 2 m/s at the entrance of the lake and as fast as 5 m/s at the center of the channel. Even though the inflow speed is very large in the channel it should be noted that the speed drops dramatically as it leaves the channel side. This explains the observation of Okamura et al. [2003, 2004] that tsunami deposits are very thick at the southwest side of the lake where the channel connects it to the sea and become thinner toward the center of the lake.
 At 29 min from the time the earthquake started and about 10 min after the beginning of the lake inundation, flow into the lake almost stops (Figure 11d; T = 29 min). Then the water surface in the lake gradually recedes to mean sea level as the water flows back to the sea through the channel (Figure 11e; T = 34 min). Note that the outflow tsunami current in the channel is very weak, less than 1/5 of the peak tsunami inflow speed (Figure 11e). This implies that the large inflow flux of the tsunami through the channel can carry large masses of sea sand into the lake very effectively, but leaves most of the sand in the lake near the channel when the tsunami goes back to sea.
Figure 12 shows changes of the water height in Ryujin Lake and the flow speed of water in the entrance of the lake connecting to the channel. Just after the earthquake occurs, the height of the surface of Ryujin Lake subsides to 30 cm below mean sea level and then gradually decreases to 40 cm below mean sea level due to the dilatational wave of the tsunami. Then the height of water surface suddenly rises after 20 min from the time of the earthquake, and at 25 min the height of water surface is at its maximum level of approximately 5 m above mean sea level. At this time, a very large (>5 m/s) flux of seawater flows through the center of the channel. It can carry sea sand into the lake very effectively (Figure 12a). A set of tsunami trains with large water fluxes might transport sea sand into the lake very effectively and the relatively slow return current from the lake would leave those sea deposits in the lake.
 In order to evaluate the ability of the water flow in the narrow waterway to transport sea sand into the lake through the channel, we calculated the Shields number [e.g., Takahashi et al., 1993], which is an index to specify strength of transporting capability due to water currents [e.g., Takahashi et al., 1993]. We calculated the Shields number at the middle point of the channel at 2 m deep assuming a Manning's roughness coefficient of n = 0.025 m−1/3 s, a sea sand density of r = 1.65 g/cm3, and median particle diameter for the sea sand of d50 = 0.4 mm. These physical constants are assumed from the geology and sedimentation properties of the Ryujin Lake demonstrated by Okamura et al. . The resultant large Shields number, (s > 11), associated with the tsunami's inflow 25 min from the start of the earthquake (Figure 11c), promises that tsunami could efficiently transport sea sand into the lake with very large Shields number of tsunami due to the rupture on the N5′ subfault [see, e.g., Takahashi et al., 1993].
 On the other hand, the water flux in the center of the channel obtained from the former Hoei earthquake model is less than 1 m/s, which is approximately 1/6 of the maximum inflow and almost same as the outflow current speed for the new Hoei earthquake model. Such a slow inflow speed (<1 m/s) and the resultant small Shields number (s < 1) indicate that such a tsunami could not transport sea sand into the lake as compare with large Shields number (s > 11) of former simulation with the N5′ subfault segment. Therefore, the large tsunami generated by the rupture of the N5′ subfault segment and the swift current it produces in the channel is the only agent that can explain the transport of sea sand into the lake.
 The results of tsunami inundation simulation indicate that tsunami-related deposits observed in Ryujin Lake do not occur regularly during Nankai Trough earthquakes but occur during unusually large earthquakes when the fault rupture extends beyond westernmost Shikoku to Hyuga-nada. The Hoei earthquake in 1707 was one such unusually large event, as were the 1361 Shohei and 684 Tenmu earthquakes, evidenced by their ability to deposit tsunami-borne sand in Ryujin Lake [Matsuoka and Okamura, 2009; Okamura et al., 2004].
6. Discussion and Conclusion
 Of the series of repeating megathrust earthquakes in the Nankai Trough that recur every 100 to 150 years, the Hoei earthquake is considered to be the most damaging, with its linkage of Tokai, Tonankai and the Nankai earthquakes, and fault ruptures extending from Suruga Bay to the westernmost end of Shikoku, about 600 km in length [An'naka et al., 2003].
 However, the recent discovery of the tsunami lakes in Kyushu (Ryujin Lake) with their thick cover of tsunami-induced deposits caused by the Hoei earthquake has overturned our understanding. The existence of the tsunami lakes in Kyushu was not well explained by the expected ground deformation pattern produced by the former Hoei earthquake source model where the fault rupture stopped at the westernmost end of Shikoku, not extending to Hyuga-nada. The source model also failed to explain the larger tsunami experienced during the Hoei earthquake from Cape Ashizuri to Hyuga-nada as compared with the tsunami associated with the 1854 Ansei Nankai earthquake.
 Actually, the source model of An'naka et al.  which is described by four (N1–N4) panels of subfaults might be too simple to demonstrate complicated source rupture history of the Nankai Trough earthquake which should be described by rupture above the subducting Philippine Sea plate and landward dipping splay branch from the plate interface. Such splay faults along the Nankai Trough have recently been imaged with multichannel seismic experiments [e.g., Moore et al., 2007; Strasser et al., 2009], and it is considered to be contributing develop additional tsunami and localized ground deformation above the splay faults during the earthquakes [e.g., Cummins and Kaneda, 2000; Cummins et al., 2001]. However, these effects on amplifying tsunami subsides ground surface at Ryujin Lake in Kyushu would be very minor due to larger distances, and most tsunami developed by the splay fault propagates toward rectangular direction of the Trough axis but not to Kyushu. In order to improve tsunami height and ground subsidence in Kyushu, we have to modify source model more drastically.
 An inferred property of the present crustal deformation pattern illustrated by the GEONET GPS measurements and a number of studies on interplate coupling along the Nankai Trough subduction zone based on the GPS data [Hashimoto et al., 2009; Ichitani et al., 2010; Nishimura et al., 1999] indicate that Hyuga-nada may also be in the area of the Nankai Trough earthquake nucleation zone. Following these new geological and geodetic findings, we revised the source model of the Hoei earthquake which had described by four subfault segments (N1 to N4) by introducing a new N5′ subfault segment on the western side of Nankai earthquake segment (N4). We succeeded in explaining development of the large tsunami from Cape Ashizuri to Hyuga-nada with maximum tsunami heights of 5 to 10 m that attack along the Pacific coast from the westernmost end of Shikoku to Hyuga-nada. This agrees with the heights of tsunamis observed along the Pacific coast from Cape Ashizuri to Hyuga-nada during the Hoei earthquake [Hatori, 1974, 1985; Murakami et al., 1996] very consistently. The tsunami runup into Ryujin Lake estimated by the tsunami inundation simulation using a high-resolution bathymetry model demonstrates the process whereby a large flow of seawater with a large difference in inflow and outflow speeds can transport and deposit sea sand into the lake near the inflow channel very effectively.
 In the Hyuga-nada region a relatively large (M6.5–7.5) interplate earthquakes have occurred frequently at interval approximately 20–30 years. For example, recent events are in 1939 (M6.5), 1941 (M7.5), 1961 (M7.0), 1968 (M7.5), and in 1987 (M6.6). The source rupture areas of these events were almost concentrated in the south half part of Hyuga-nada [e.g., Yagi and Kikuchi, 2003; Yoshioka, 2007], and there was no overlap with the area of our N5′ subfault segment which extends to north half part of Hyuga-nada. Thus, the area of the N5′ subfault is now a seismic gap since the Hoei earthquake in 1707. It is expecting that the rupture of the N5′ subfault segment sometimes occurs by linkage of the N4 Nankai earthquake segment but it does not occurs independently.
 The extension of the source rupture area from westernmost Shikoku to Hyuga-nada would produce increased shaking in Kyushu. Exactly what the intensity was in Kyushu in 1707 is unclear; we are unaware of any historical documents that permit a meaningful comparison of intensities of the 1707 and 1856 earthquakes. Further effort is needed to establish the shaking intensity in Kyushu in 1707.In the present paper, we have focused mainly on the significance of the elongation of the Hoei earthquake source rupture to Hyuga-nada in terms of the strengthening of tsunami height and onshore tsunami runup. However, further studies evaluating shaking intensity such as, e.g., based on the FDM simulation of ground motion is needed to completely understand earthquake-related disasters associated with the Nankai Trough earthquakes. We hope recent investigation of high-resolution geological and geophysical experiments will provide high-density reliable subsurface structure model as well as heterogeneous source rupture model. Steadily improving high-performance computing technologies together with high-resolution earthquake model will enable us for simulating strong ground motion near future.
 The Hoei earthquake, extending as it did from Suruga Bay to Hyuga-nada, approximately 700 km, broke five fault segments (N1–N5′), each with a different geometry. The linkage process between different subfaults in Nankai Trough earthquakes may contribute significantly to the severity of the disaster, especially the tsunamis. Some researchers have claimed that delayed rupture between subfaults amplifies tsunami height over a wide area due to overlap of individual tsunamis from different fault segments [Kawata et al., 2003; Imai et al., 2010]. Moreover, an unusual earthquake with very slow fault rupture speed (e.g., Vr < 0.2 km/s) which is almost comparable to the tsunami propagation speed in deep (e.g., h > 4000 m) sea might amplify tsunami along the direction of fault rupture propagation due to the rupture directivity effect. Such earthquakes with very slow rupture speeds may not produce strong ground motions or large shaking intensity to feel peoples. The contrast of larger tsunami relative to weaker ground shaking raises the potential for a significant tsunami disaster similar to that of the tsunami earthquakes [e.g., Kanamori, 1972; Satake and Tanioka, 1999].
Baba et al.  revealed from tsunami data that the area of large tsunami generation on the fault plane extended along the entire source rupture area in of the 1946 Nankai earthquake. Sagiya and Thatcher  also obtained similar source rupture pattern using the geodetic data. This area roughly corresponds to the N3 and N4 segments of An'naka et al. . However, another source model for this event based on strong ground motion and teleseismic waveform data shows a large fault slip only in the eastern part (N3) of the Nankai earthquake fault segment [Murotani, 2007]. A possible explanation is that slow rupture over the N4 subfault segment generated large coseismic ground deformation and therefore a large tsunami, but did not produce strong ground motion. Existing seismic data would appear to be inadequate to confirm or deny this conjecture, but the possibility of different rupture characteristics on the different subfaults is intriguing. We should be prepared for a diversity of rupture processes during future earthquakes along the Nankai Trough. Finally, this study suggests that earthquake rupture extent along the Nankai Trough may not be as limited as previously described: as combinations of subfaults to produce Nankai, Tonankai, or Tokai earthquakes, or as a grand combination of subfaults N1–N4 to produce a larger earthquake. The Hoei earthquake was a larger event in which rupture spread as far as Hyuga-nada, incorporating the fifth subfault, N5. Such larger events do not occur during the regular Nankai Trough earthquake cycle of 100–150 years, but may occur in a hyperearthquake cycle of 300 to 500 years. The tsunami deposits at Ryujin Lake in Kyushu left by large tsunamis from the 684 Tenmu, 1361 Shohei, and 1707 Hoei earthquakes, attest to such a hyperearthquake cycle.
 We thank two anonymous reviewers and an associate editor for their constructive comments for improving manuscript. This study was supported by the Research Project “Improvements in strong ground motion and tsunami simulation accuracy for application to realistic disaster prevention of Nankai Trough megathrust earthquakes” of the Ministry of Education, Culture, Sports and Technology of Japan. We thank the Central Disaster Mitigation Council, Cabinet Office, government of Japan, and Yonouzu Promotion Office, Oita Prefecture, Japan, for providing bathymetry map data.