slip distributions of the 1944 tonankai and 1946 nankai ... satake’s (2001b) result. the 1946...

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FRONTIER RESEARCH ON EARTH EVOLUTION, VOL. 1

Introduction

The Nankai Trough has a long history of great interplateearthquakes dating back to the 7th century (Ando, 1975). Therecurrence interval of great earthquakes appears to be 100-150years. The latest events were the 1944 Tonankai and 1946Nankai earthquakes. The source processes of the 1944 and1946 events have been studied using seismic wave data, geo-detic data and tsunami data. Recently, Tanioka and Satake(2001a; 2001b) and Baba et al. (2002) have estimated the slipdistributions of the 1944 and 1946 earthquakes by invertingtsunami waveforms. However, those studies have a drawback:The effect of horizontal movement on tsunami generation(Tanioka and Satake, 1996) was not considered in these stud-ies. Generally, tsunami generation by an earthquake is mod-eled by water surface displacement identical to the verticaldeformation of the ocean bottom due to faulting. The horizon-tal deformation of ocean bottom is usually neglected. A hori-zontal deformation model is valid only for events that occuron a flat or gently dipping ocean bottom. On a steeply dippingocean bottom like the deformation front, horizontal displace-ment can affect tsunami generation. Here we consider whetherthe horizontal movement effect on tsunami generation affectsthe slip distributions of the 1944 Tonankai and 1946 Nankaiearthquake.

Tsunami analysis

Initial waveform of tsunami including horizontalmovement effect

On a steeply dipping ocean bottom such as in an oceantrench, horizontal displacement of the slope can generate atsunami (Fig. 1). We have therefore included the effect of hor-izontal movement on tsunami generation (Tanioka and Satake,1996). The vertical displacement of water due to the horizon-tal movement of the slope, uh, is calculated as

(1)

where H is the water depth and ux, uy are the horizontal dis-placements due to faulting. The vertical and horizontal dis-placements are calculated with the equations of Okada (1985).Finally, the initial condition of the tsunami is calculated basedon total vertical displacement, uh+uz. The initial water surfacedeformation is usually assumed to be equal to the ocean bot-tom deformation. However, the wavelength of the ocean bot-tom deformation including the effect of horizontal movement

is not much longer than the ocean depth, which is inconsistentwith the long wavelength theory used to calculate the tsunamipropagation. Kajiura (1963) showed that this problem can bealleviated by using the following expression to calculate thewater surface deformation, h(x,y), due to the ocean bottomdeformation, HB(x0,y0) = [uh+uz](x0,y0):

(2)

where

(3)

We numerically compute the water surface deformation,h(x,y), using the above equations and use this as the initialwater surface condition of the tsunami.

Inversion of tsunami waveforms

A model for the shape of the Philippine Sea Plate subduct-ing beneath southwest Japan is constructed by combiningmarine seismic survey results data (Fig 2). We divided theplate boundary on which rupture is assumed to occur into twocollections of planar subfaults appropriate to the 1944 and1946 earthquake slip areas. The depth and dip of each planarsubfault used in the inversion analysis is set according to theplate boundary model (Fig. 2, Tables 1, 2). The subfault size isidentical to that of Tanioka and Satake (2001a; 2001b), whichis 45km by 45km. The strikes and rakes are also identical tothose of Tanioka and Satake (2001a, 2001b): The strike is 240degrees and the rake angle 110 degrees for the 1944 Tonankaiearthquake, whereas they are 250 and 120 degrees for the1946 Nankai earthquake.

For the inversions of the 1944 Tonankai and 1946 Nankaiearthquakes, we used tsunami waveform data recorded at,respectively, 10 tide gauge stations (Mera, Uchiura, Ito, Mat-suzaka, Morozaki, Fukue, Shimotsu, Tosashimizu, Hosojima,Aburatsu) and 7 tide gauge stations (Hosojima, Uwajima,Sakai, Fiukue, Uchiura, Ito, Morozaki) (Fig. 3). In the inver-sion analysis, the ocean bottom deformation on each subfaultis calculated using the equations of Okada (1985) with a unitamount of slip. The vertical displacement of the ocean bottomis calculated using equation (1), which includes the effect ofhorizontal displacement of the ocean bottom due to faulting.The initial condition of the sea surface is calculated by usingKajiura’s (1963) method (equations 2, 3) to filter the verticalocean bottom displacement. We followed Tanioka and Satake

Slip distributions of the 1944 Tonankai and 1946 Nankai earthquakes including the horizontal movement effect ontsunami generation

Toshitaka Baba

Research Program for Plate Dynamics, Institute for Frontier Research on Earth Evolution (IFREE)

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(2001a) in assuming that the rise time for sea surface displace-ment over each subfault was 60 sec, since this is a typical risetime for a magnitude 8 earthquake. The tsunami Green’s func-tions for inversion are computed using linear long wave equa-tion. A variable grid system was used near the tide gauge sta-tions to incorporate detailed topography around the stations.The grid size is basically 20 sec (about 600m), although finergrids of 4 sec were used near the tide gauge stations. The com-putation uses a time step of 1.5 seconds in order to satisfy thestability condition of the finite difference algorithm. We usednon-negative least squares (Lawson and Hanson, 1974) tosolve for the set of positive subfault slips which most closelymatches the data. For error analysis, the jackknife technique(Tichelaar and Ruff, 1989) was applied.

Slip distributions including the horizontal movementeffect on tsunami generation

The slip distributions obtained from tsunami inversion areshown in Fig. 3 and Tables 1 and 2. A comparison of theobserved and computed tsunami waveforms is shown in Fig.4. The largest slip in the 1944 Tonankai earthquake is 3.40mon subfault T4B, and large slips (>2.0m) also appear on sub-faults T3B and T4C. There is considerable slip around theeastern edge of Kii Peninsula. On the other hand, eastern sub-faults near the trench (T4A, T5A, T6A, T5B and T6B) havealmost zero slip. The epicenter is located off Kii Peninsula(Kanamori, 1972), and the rupture likely propagates to a deep-er point in the east. This result also shows that the expectedTokai earthquake area (subfaults T7B and T7C) was not rup-tured in the 1944 Tonankai earthquake. The slip pattern isalmost identical to that of Tanioka and Satake (2001b). Theseismic moment is calculated as 1.9×1021Nm, assuming thatthe rigidity is 5×1010N/m2.

Next, we briefly explain the slip distribution of the 1946Nankai earthquake. We can see two asperities, one near CapeShiono located on Kii Peninsula (subfault N7B) and the othernear Tosa Bay (subfault N3C). The slip amount of subfaultN7B is about 3.37m, and it decreases gradually from this sub-fault. The subfault N3C has the largest slip (4.65m) among allsubfaults, and subfaults near N3C (N2C, N4C, N5C and N3D)also have large slips. The slip zone off Kii Peninsula extendsfrom just beneath the coast to near the Nankai trough axis, but,in the western half of the rupture area, there is almost zero slipnear the axis of the Nankai trough (subfaults N1A-N4A, N1B-N4B). The seismic moment is calculated as 4.2×1021Nm,assuming that the rigidity is 5×1010N/m2.

Comparison to previous work

Here, we compare our findings with those of previous stud-ies, focusing on the effect horizontal movement of the oceanbottom has on tsunami generation. The slip distributions of the1944 Tonankai and 1946 Nankai earthquakes have been esti-mated using various data sets. Yabuki and Matsu’ura (1992)and Sagiya and Thatcher (1999) estimated slip distributionsusing geodetic data. Ando (1975), Kato and Ando (1997),Tanioka and Satake (2001a, b) and Baba et al. (2002) usedtsunami data. Satake (1993) inverted tsunami and leveling datato estimate the slip distributions of the 1944 and 1946 earth-

quakes. Seismic wave data have also been used for the 1944Tonankai earthquake (Kikuchi et al., 2002).

The 1944 Tonankai earthquake

A common feature of the slip distribution of the 1944Tonankai earthquake in these studies is an asperity (large slip)off Shima Peninsula. In this study, this asperity has a slip ofabout 3.40m (subfault T4B). The slip amount calculated byTanioka and Sakake (2001b) is about 3.3m, which is consis-tent with our result. The asperities calculated by Kato andAndo (1997) and by Satake (1993) have smaller slips than ourresult, about 2.5 and 1.5m, respectively.

The horizontal movement effect of the ocean bottom due tofaulting is considered in this study. Tanioka and Satake(2001b) did not include this effect. A model that includes thehorizontal movement effect can generate a larger tsunami withthe same slip amounts as a model that does not include theeffect. In other words, a tsunami of the same amplitude can becaused by a smaller slip when the horizontal movement effectis included. The effect should be significant near the trenchsince the seafloor has a steeply slope. But the estimated slipamounts of subfaults TA1-TA3 near the trench by our inver-sion are almost identical to those of Tanioka and Satake(2001b). There are also the differences in the models that arethe depths and dips of subfaults, which in this study aredefined on the basis of a new plate model obtained by compil-ing seismic survey results. The subfaults TA1-TA3, TB1-TB3,and TC1-TC3 have gentler slopes than those of Tanioka andSatake’s (2001b) model. There is a significant difference ofabout 5 deg in dip on subfaults TA1-TA3. Since the faultplane has a gentler slope, it should require a larger slip thanthat of Tanioka and Satake’s (2001b) model to generate atsunami of the same amplitude (through vertical deformationof the ocean bottom). Thus, for this case these effects, gentlerdip and horizontal movement effect tend to cancel out, so thatthe slip amounts of TA1-TA3 are almost identical to Taniokaand Satake’s (2001b) result.

The 1946 Nankai earthquake

Baba et al. (2002) estimated the slip distribution of the 1946Nankai earthquake using a method similar to ours. The signifi-cant difference in analysis between this study and Baba et al.(2002) is that ours included the horizontal displacement effectwhereas Baba et al. (2002) did not. By including the effect ofhorizontal displacement on tsunami generation, the slip distri-bution obtained using our model should be more accurate thanthat obtained in Baba et al. (2002). Subfaults N5A, N6A andN7A on the 1946 Nankai earthquake of Baba et al. (2002)have 3.6, 3.2 and 3.0m slips, respectively. These slip amountsare larger than those obtained in the present study (N5A:2.21m, N6A: 2.36m, N7A: 2.71m). This difference can beattributed to the effect of horizontal displacement on tsunamigeneration. This effect can be significant in an area of steeplydipping seafloor topography, such as an ocean trench, and itsneglect likely led Baba et al. (2002) to overestimate the slipamount. The asperity of the Kii Peninsula (N7B: 3.37m) isnow much more clearly defined due to the small slip along thetrench. The asperity coincides with the location of a large

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subevent detected by seismic wave analysis (Hashimoto andKikuchi, 1999; Cummins et al., 2002). We conclude that therupture of the 1946 Nankai earthquake started off Kii Peninsu-la and propagated deep along the plate boundary, with themain rupture occurring near Cape Shiono.

Conclusions

The coseismic slip distributions on the plate boundaries dur-ing the 1944 Tonankai and 1946 Nankai earthquakes were esti-mated from inversions of tsunami waveforms. Although theinversion method was almost identical to that of Tanioka andSatake (2001a, b), two improvements were made. (1) We useda more reliable plate model, which was constructed by combin-ing 15 seismic survey results. (2) We included the effect ofhorizontal displacement of ocean bottom topography. In the1946 Nankai earthquake, slip amounts near the trench off KiiPeninsula decreased to about 2m due to horizontal displace-ment effect. As a consequence, an asperity off the Kii Peninsu-la was resolved. This asperity coincides with the location of thelargest subevent detected by previous seismic wave studies. Onthe other hand, for the 1944 Tonankai earthquake, gentler dipof plate configuration and horizontal movement effect tend tocancel out, so that the slip amounts near the trench are almostidentical to Tanioka and Satake’s (2001b) result.

Acknowledgments. We thank Y. Tanioka (MRI) for providing uswith his tsunami analysis tools and waveforms for the 1944 Tonankaiand 1946 Nankai earthquakes.

References

Ando, M., Source mechanisms and tectonic significance of historicalearthquake along the Nankai tough, Japan, Tectonophysics, 27,119-140, 1975,

Baba, T., Y. Tanioka, P. R. Cummins, and K. Uhira, The slip distribu-tion of the 1946 Nankai earthquake estimated from tsunami inver-sion using a new plate model, Phys. Earth Planet. Inter., 132, 59-73, 2002.

Cummins, P. R., T. Baba, S. Kodaira, and Y. Kaneda, The 1946Nankaido 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 Nankaiearthquake from seismogram (in Japanese), Monthly Chikyu, 24,16-20, 1999.

Kanamori, H., Tectonic implications of the 1944 Tonankai and the1946 Nakaido earthquake, Phys. Earth Planet Inter., 5, 129-139,1972.

Kato, T., and M. Ando, Source mechanisms of the 1944 Tonankai and1946 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 ofLarge Earthquakes in Japan inferred from Low-gain HistoricalSeismograms, 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 ahalf-space, Bull. Seismol. Soc. Am., 75, 1135-1154, 1985.

Sagiya, T., and W. Thatcher, Coseismic slip resolution along a plateboundary magathrust: The Nankai Trough, southwest Japan, J.Geophys. Res., 104, 1111-1129, 1999.

Satake, K., Depth distribution of coseismic slip along the NankaiTrough, Japan, from joint inversion of geodetic and tsunami data,J. Geophys. Res., 98, 4553-4565, 1993.

Tanioka, Y., and K. Satake, Tsunami generation by horizontal dis-placement of ocean bottom, Geophys. Res. Lett., 23, 861-864,1996.

Tanioka, Y., and K. Satake, Coseismic slip distribution of the 1946Nankai 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 the1944 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? Jack-knifing, bootstrapping, and earthquake depth, EOS, 70, 593, 605-606, 1989.

Yabuki, T., and M. Matsu’ura, Geodetic data inversion using aBayesian information criterion for spatial distribution of fault slip,Geophys. J. Int., 109, 363-375, 1992.

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Table 1. Subfaults & slip distribution of the 1944 Tonankai earth-quake

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 dashedlines show vertical and horizontal motions of slopes due to faulting. Modified from Tanioka andSatake (1996).

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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.

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Figure 4. Comparison of the observed (solid) and calculated (dashed) tsunami waveforms at tide gauges. Time 0 indicates the earthquake origin time.

slip distributions of the 1944 tonankai and 1946 nankai ... satake’s (2001b) result. the 1946...

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