Slip distributions of the 1944 Tonankai and 1946 Nankai earthquakes including the horizontal movement effect on tsunami generation Toshitaka Baba Research Program for Plate Dynamics, Institute for Frontier Research on Earth Evolution (IFREE) Introduction The Nankai Trough has a long history of great interplate earthquakes dating back to the 7th century (Ando, 1975). The recurrence interval of great earthquakes appears to be 100-150 years. The latest events were the 1944 Tonankai and 1946 Nankai earthquakes. The source processes of the 1944 and 1946 events have been studied using seismic wave data, geodetic data and tsunami data. Recently, Tanioka and Satake (2001a; 2001b) and Baba et al. (2002) have estimated the slip distributions of the 1944 and 1946 earthquakes by inverting tsunami waveforms. However, those studies have a drawback: The effect of horizontal movement on tsunami generation (Tanioka and Satake, 1996) was not considered in these studies. Generally, tsunami generation by an earthquake is modeled by water surface displacement identical to the vertical deformation of the ocean bottom due to faulting. The horizontal deformation of ocean bottom is usually neglected. A horizontal deformation model is valid only for events that occur on a flat or gently dipping ocean bottom. On a steeply dipping ocean bottom like the deformation front, horizontal displacement can affect tsunami generation. Here we consider whether the horizontal movement effect on tsunami generation affects the slip distributions of the 1944 Tonankai and 1946 Nankai earthquake. Tsunami analysis Initial waveform of tsunami including horizontal movement effect On a steeply dipping ocean bottom such as in an ocean trench, horizontal displacement of the slope can generate a tsunami (Fig. 1). We have therefore included the effect of horizontal movement on tsunami generation (Tanioka and Satake, 1996). The vertical displacement of water due to the horizontal movement of the slope, u h, is calculated as where H is the water depth and u x, u y are the horizontal displacements due to faulting. The vertical and horizontal displacements are calculated with the equations of Okada (1985). Finally, the initial condition of the tsunami is calculated based on total vertical displacement, u h +u z. The initial water surface deformation is usually assumed to be equal to the ocean bottom deformation. However, the wavelength of the ocean bottom deformation including the effect of horizontal movement (1) is not much longer than the ocean depth, which is inconsistent with the long wavelength theory used to calculate the tsunami propagation. Kajiura (1963) showed that this problem can be alleviated by using the following expression to calculate the water surface deformation, h(x,y), due to the ocean bottom deformation, H B (x 0,y 0 ) = [u h +u z ](x 0,y 0 ): where We numerically compute the water surface deformation, h(x,y), using the above equations and use this as the initial water surface condition of the tsunami. Inversion of tsunami waveforms A model for the shape of the Philippine Sea Plate subducting beneath southwest Japan is constructed by combining marine seismic survey results data (Fig 2). We divided the plate boundary on which rupture is assumed to occur into two collections of planar subfaults appropriate to the 1944 and 1946 earthquake slip areas. The depth and dip of each planar subfault used in the inversion analysis is set according to the plate boundary model (Fig. 2, Tables 1, 2). The subfault size is identical to that of Tanioka and Satake (2001a; 2001b), which is 45km by 45km. The strikes and rakes are also identical to those of Tanioka and Satake (2001a, 2001b): The strike is 240 degrees and the rake angle 110 degrees for the 1944 Tonankai earthquake, whereas they are 250 and 120 degrees for the 1946 Nankai earthquake. For the inversions of the 1944 Tonankai and 1946 Nankai earthquakes, we used tsunami waveform data recorded at, respectively, 10 tide gauge stations (Mera, Uchiura, Ito, Matsuzaka, Morozaki, Fukue, Shimotsu, Tosashimizu, Hosojima, Aburatsu) and 7 tide gauge stations (Hosojima, Uwajima, Sakai, Fiukue, Uchiura, Ito, Morozaki) (Fig. 3). In the inversion analysis, the ocean bottom deformation on each subfault is calculated using the equations of Okada (1985) with a unit amount of slip. The vertical displacement of the ocean bottom is calculated using equation (1), which includes the effect of horizontal displacement of the ocean bottom due to faulting. The initial condition of the sea surface is calculated by using Kajiura s (1963) method (equations 2, 3) to filter the vertical ocean bottom displacement. We followed Tanioka and Satake (2) (3) 213
(2001a) in assuming that the rise time for sea surface displacement over each subfault was 60 sec, since this is a typical rise time for a magnitude 8 earthquake. The tsunami Green s functions for inversion are computed using linear long wave equation. A variable grid system was used near the tide gauge stations to incorporate detailed topography around the stations. The grid size is basically 20 sec (about 600m), although finer grids of 4 sec were used near the tide gauge stations. The computation uses a time step of 1.5 seconds in order to satisfy the stability condition of the finite difference algorithm. We used non-negative least squares (Lawson and Hanson, 1974) to solve for the set of positive subfault slips which most closely matches the data. For error analysis, the jackknife technique (Tichelaar and Ruff, 1989) was applied. Slip distributions including the horizontal movement effect on tsunami generation The slip distributions obtained from tsunami inversion are shown in Fig. 3 and Tables 1 and 2. A comparison of the observed and computed tsunami waveforms is shown in Fig. 4. The largest slip in the 1944 Tonankai earthquake is 3.40m on subfault T4B, and large slips (>2.0m) also appear on subfaults T3B and T4C. There is considerable slip around the eastern edge of Kii Peninsula. On the other hand, eastern subfaults near the trench (T4A, T5A, T6A, T5B and T6B) have almost zero slip. The epicenter is located off Kii Peninsula (Kanamori, 1972), and the rupture likely propagates to a deeper point in the east. This result also shows that the expected Tokai earthquake area (subfaults T7B and T7C) was not ruptured in the 1944 Tonankai earthquake. The slip pattern is almost identical to that of Tanioka and Satake (2001b). The seismic moment is calculated as 1.9 10 21 Nm, assuming that the rigidity is 5 10 10 N/m 2. Next, we briefly explain the slip distribution of the 1946 Nankai earthquake. We can see two asperities, one near Cape Shiono located on Kii Peninsula (subfault N7B) and the other near Tosa Bay (subfault N3C). The slip amount of subfault N7B is about 3.37m, and it decreases gradually from this subfault. The subfault N3C has the largest slip (4.65m) among all subfaults, and subfaults near N3C (N2C, N4C, N5C and N3D) also have large slips. The slip zone off Kii Peninsula extends from just beneath the coast to near the Nankai trough axis, but, in the western half of the rupture area, there is almost zero slip near the axis of the Nankai trough (subfaults N1A-N4A, N1B- N4B). The seismic moment is calculated as 4.2 10 21 Nm, assuming that the rigidity is 5 10 10 N/m 2. Comparison to previous work Here, we compare our findings with those of previous studies, focusing on the effect horizontal movement of the ocean bottom has on tsunami generation. The slip distributions of the 1944 Tonankai and 1946 Nankai earthquakes have been estimated using various data sets. Yabuki and Matsu ura (1992) and Sagiya and Thatcher (1999) estimated slip distributions using geodetic data. Ando (1975), Kato and Ando (1997), Tanioka and Satake (2001a, b) and Baba et al. (2002) used tsunami data. Satake (1993) inverted tsunami and leveling data to estimate the slip distributions of the 1944 and 1946 earthquakes. Seismic wave data have also been used for the 1944 Tonankai earthquake (Kikuchi et al., 2002). The 1944 Tonankai earthquake A common feature of the slip distribution of the 1944 Tonankai earthquake in these studies is an asperity (large slip) off Shima Peninsula. In this study, this asperity has a slip of about 3.40m (subfault T4B). The slip amount calculated by Tanioka and Sakake (2001b) is about 3.3m, which is consistent with our result. The asperities calculated by Kato and Ando (1997) and by Satake (1993) have smaller slips than our result, about 2.5 and 1.5m, respectively. The horizontal movement effect of the ocean bottom due to faulting is considered in this study. Tanioka and Satake (2001b) did not include this effect. A model that includes the horizontal movement effect can generate a larger tsunami with the same slip amounts as a model that does not include the effect. In other words, a tsunami of the same amplitude can be caused by a smaller slip when the horizontal movement effect is included. The effect should be significant near the trench since the seafloor has a steeply slope. But the estimated slip amounts of subfaults TA1-TA3 near the trench by our inversion are almost identical to those of Tanioka and Satake (2001b). There are also the differences in the models that are the depths and dips of subfaults, which in this study are defined on the basis of a new plate model obtained by compiling seismic survey results. The subfaults TA1-TA3, TB1-TB3, and TC1-TC3 have gentler slopes than those of Tanioka and Satake s (2001b) model. There is a significant difference of about 5 deg in dip on subfaults TA1-TA3. Since the fault plane has a gentler slope, it should require a larger slip than that of Tanioka and Satake s (2001b) model to generate a tsunami of the same amplitude (through vertical deformation of the ocean bottom). Thus, for this case these effects, gentler dip and horizontal movement effect tend to cancel out, so that the slip amounts of TA1-TA3 are almost identical to Tanioka and Satake s (2001b) result. The 1946 Nankai earthquake Baba et al. (2002) estimated the slip distribution of the 1946 Nankai earthquake using a method similar to ours. The significant difference in analysis between this study and Baba et al. (2002) is that ours included the horizontal displacement effect whereas Baba et al. (2002) did not. By including the effect of horizontal displacement on tsunami generation, the slip distribution obtained using our model should be more accurate than that obtained in Baba et al. (2002). Subfaults N5A, N6A and N7A on the 1946 Nankai earthquake of Baba et al. (2002) have 3.6, 3.2 and 3.0m slips, respectively. These slip amounts are larger than those obtained in the present study (N5A: 2.21m, N6A: 2.36m, N7A: 2.71m). This difference can be attributed to the effect of horizontal displacement on tsunami generation. This effect can be significant in an area of steeply dipping seafloor topography, such as an ocean trench, and its neglect likely led Baba et al. (2002) to overestimate the slip amount. The asperity of the Kii Peninsula (N7B: 3.37m) is now much more clearly defined due to the small slip along the trench. The asperity coincides with the location of a large 214
subevent detected by seismic wave analysis (Hashimoto and Kikuchi, 1999; Cummins et al., 2002). We conclude that the rupture of the 1946 Nankai earthquake started off Kii Peninsula and propagated deep along the plate boundary, with the main rupture occurring near Cape Shiono. Conclusions The coseismic slip distributions on the plate boundaries during the 1944 Tonankai and 1946 Nankai earthquakes were estimated from inversions of tsunami waveforms. Although the inversion method was almost identical to that of Tanioka and Satake (2001a, b), two improvements were made. (1) We used a more reliable plate model, which was constructed by combining 15 seismic survey results. (2) We included the effect of horizontal displacement of ocean bottom topography. In the 1946 Nankai earthquake, slip amounts near the trench off Kii Peninsula decreased to about 2m due to horizontal displacement effect. As a consequence, an asperity off the Kii Peninsula was resolved. This asperity coincides with the location of the largest subevent detected by previous seismic wave studies. On the other hand, for the 1944 Tonankai earthquake, gentler dip of plate configuration and horizontal movement effect tend to cancel out, so that the slip amounts near the trench are almost identical to Tanioka and Satake s (2001b) result. Tanioka, Y., and K. Satake, Tsunami generation by horizontal displacement of ocean bottom, Geophys. Res. Lett., 23, 861-864, 1996. Tanioka, Y., and K. Satake, Coseismic slip distribution of the 1946 Nankai earthquake and aseismic slips caused by the earthquake, Earth Planets Space, 53, 235-241, 2001a. Tanioka, Y., and K. Satake, Detailed coseimic slip distribution of the 1944 Tonankai earthquake estimated from tsunami waveforms, Geophys. Res. Lett., 28, 1075-1078, 2001b. Tichelaar, B. W., and L. J. Ruff, How good are our best models? Jackknifing, bootstrapping, and earthquake depth, EOS, 70, 593, 605-606, 1989. Yabuki, T., and M. Matsu ura, Geodetic data inversion using a Bayesian information criterion for spatial distribution of fault slip, Geophys. J. Int., 109, 363-375, 1992. Acknowledgments. We thank Y. Tanioka (MRI) for providing us with his tsunami analysis tools and waveforms for the 1944 Tonankai and 1946 Nankai earthquakes. References Ando, M., Source mechanisms and tectonic significance of historical earthquake along the Nankai tough, Japan, Tectonophysics, 27, 119-140, 1975, Baba, T., Y. Tanioka, P. R. Cummins, and K. Uhira, The slip distribution of the 1946 Nankai earthquake estimated from tsunami inversion using a new plate model, Phys. Earth Planet. Inter., 132, 59-73, 2002. Cummins, P. R., T. Baba, S. Kodaira, and Y. Kaneda, The 1946 Nankaido earthquake and segmentation of the Nankai Trough, Phys. Earth Planet. Inter., 132, 75-87, 2002. Hashimoto, T., and M. Kikuchi, Source process of the 1946 Nankai earthquake from seismogram (in Japanese), Monthly Chikyu, 24, 16-20, 1999. Kanamori, H., Tectonic implications of the 1944 Tonankai and the 1946 Nakaido earthquake, Phys. Earth Planet Inter., 5, 129-139, 1972. Kato, T., and M. Ando, Source mechanisms of the 1944 Tonankai and 1946 Nankaido earthquakes: Spatial heterogeneity of rise times, Geophys. Res. Lett., 24, 2055-2058, 1997. Kajiura, K., The leading wave of a tsunami, Bull. Earthq. Res. Inst., 41, 535-571, 1963. Kikuchi, M., M. Nakamura, and K. Yoshikawa, Fault Asperity of Large Earthquakes in Japan inferred from Low-gain Historical Seismograms, EPS, submitted, 2002. Lawson, C. L., and R. J. Hanson, Solving least squares problems, pp.340, Prentice-hall series in automatic computation, 1974. Okada, Y., Surface deformation due to shear and tensile faults in a half-space, Bull. Seismol. Soc. Am., 75, 1135-1154, 1985. Sagiya, T., and W. Thatcher, Coseismic slip resolution along a plate boundary magathrust: The Nankai Trough, southwest Japan, J. Geophys. Res., 104, 1111-1129, 1999. Satake, K., Depth distribution of coseismic slip along the Nankai Trough, Japan, from joint inversion of geodetic and tsunami data, J. Geophys. Res., 98, 4553-4565, 1993. 215
Table 1. Subfaults & slip distribution of the 1944 Tonankai earthquake Table 2. Subfaults & slip distribution of the 1946 Nankai earthquake Figure 1. A schematic illustration of tsunami initial conditions for underthrust-type earthquakes. Vertical displacement due to faulting is shown in (a). Horizontal movement of slope is shown in (b). Solid lines show fault planes, arrows on fault planes show fault motions. Arrows on dashed lines show vertical and horizontal motions of slopes due to faulting. Modified from Tanioka and Satake (1996). 216
Figure 2. The area of tsunami computation, locations of subfaults (rectangles), and tide gauges (solid triangles). Dashed lines show the upper surfaces of subducting slabs. Figure 3. Slip distributions of the 1944 Tonankai (upper) and 1946 Nankai (lower) earthquakes. Black and open stars show the locations of the epicenter (Kanamori, 1972) and the subevents (Cummins et al., 2002), respectively. 217
Figure 4. Comparison of the observed (solid) and calculated (dashed) tsunami waveforms at tide gauges. Time 0 indicates the earthquake origin time. 218