GEOPHYSICAL RESEARCH LETTERS, VOL. 23, NO. 8, PAGES 861-864, APRIL 15, 1996

Tsunami generation by horizontal displacementof oceanbottom

Yuichiro Tanioka

Dept. of GeologicalScience, University of Michigan,Ann Arbor

Kenji Satake SeismotectonicsSection, Geological Survey of Japan,Tsukuba

Abstract. Tsunami generationby an earthquakeis generally the input potentialenergy from the horizontalmovement is less modeledby water surfacedisplacement identical to the vertical than 1.5 % of that from the vertical movement. deformation of ocean bottom due to faulting. The effect of In this paper,we showthat there are someexceptions to the horizontaldeformation is usuallyneglected. However, when the thirdassumption and that horizontal displacement due to faulting tsunami source is on a steep slope and the horizontal can becomeimportant for tsunamigeneration. We showthis with displacementis large relative to the vertical displacement,the two recent :the 2 June 1994 Java (Ms effect becomes significant. We show this for two recent 7.2) which occurredalong the Sundatrench in Indonesia(this earthquakeswhich generatedmuch larger tsunamis than expected earthquakehad a very shallow-dippingfault planewith a thrust from seismic waves. In the case of the 1994 June 2 Java, typemechanism), and the 14 Nov. 1994 Mindoroearthquake (Ms Indonesia,earthquake, the focal mechanismwas a very shallow 7.1) (strike-slip mechanismrupturing perpendicularto the dippingthrust and the sourcewas near a very steeptrench slope. northern coast of Mindoro Island in the Philippines). Both In the case of the 1994 Nov. 14 Mindoro, Philippines, earthquakesgenerated much larger tsunamis than expected from earthquake,strike-slip faulting extendedfrom ocean to land the seismicwaves and causedextensive damage near the coast. perpendicularto the coastline. In both cases,we found that the Study of the tsunamigeneration mechanism of theseevents is horizontalmotion of slopehad an importantcontribution to the also very important for tsunami disaster prevention. The tsunamigeneration. numericalcomputation of the tsunamisfor thesetwo earthquake are carried out to find the significance of the horizontal displacementdue to faulting. Introduction

Numerical computations of tsunami caused by large Method earthquakeshave beencarried out on actualbathymetry by many Crustaldeformation due to faulting can be calculatedusing researchers[e.g. Aida, 1978; Shuto, 1991; Satake, 1995]. The elastic theory of dislocation. Steketee[1958] showed that the initial oceansurface condition is usuallyassumed to be identical surfacedisplacement u k on an elastic half-spacedue to a to the vertical deformationof the oceanbottom due to faulting, dislocationAu i acrossa faultsurface Z canbe calculatedas basedon three assumptions.First, tsunamisare assumedto be long waves, i.e., the wavelengthis much larger than the water depth. This is becausethe size of a large tsunamigenic ttk=71 I•I atti[/•Sijtt kn,n +p(tt•c' ij +it kj,i )]vjd• (1) earthquakeis several tens to hundredsof km while the ocean depth around the sourcearea is at most severalkm. For long where/•and p areLame constants, 8ijis Kronecker's delta, vj is the direction cosine of the normal to the fault surface element waves, the vertical accelerationof water particlesis neglected ß comparedto the gravitationalacceleration. This meansthat the d'2;, and u•cdenotes the kth componentof the surface water mass from the ocean bottom to the surface moves displacementdue to the ith componentof point force whose uniformlyin horizontaldirection. A more generaldescription of magnitude is F. An analytical solution of equation (1) (the surface deformation due to vertical deformation of ocean bottom horizontaldisplacements, ux and Uy, and the vertical is describedby Kajiura [1981]. Second,the verticaldeformation displacement,uz) for a finiterectangular fault [Okada, 1985] is of ocean bottom is assumed to be instantaneous. This is because used. the phasevelocity of a tsunami(0.2 km/s for a depthof 4000m) is If earthquakesoccur on a steep ocean slope, such as a muchslower than the propagationvelocity of earthquakerupture continental-slopeor a coastalslope, the horizontaldisplacement (2-3 km/s). Third, the horizontalmovement of oceanbottom due dueto faultingmoves the slope(see Figure lb). In thiscase, there to faulting is assumedto be negligiblein tsunamigeneration. are two componentsof water motion to consider: vertical and This assumptionis valid for faulting which occurson a flat or horizontal motions of water due to the horizontal movement of shallowly-dippingocean bottom. Berg et al. [1970] showthat for the slope.The experimentalstudy by lwasaki[1982] showsthat if a motion equivalentin magnitudeto that of the 1964 Alaskan the gradientof the slopeis lessthan 1/3, the tsunamigeneration earthquake(Mw 9.2) and actingnormal to the continentalslope, dueto the horizontalmovement of the slopeis dominatedby the verticalmotion of water,and the horizontalmotion is negligible. Hence we ignore the horizontal motion of water due to the Copyright1996 by the AmericanGeophysical Union. movementof slope,because most ocean bottom slopes, including steepslopes near the trenches,are lessthan 1/3. Papernumber 96GL00736 The vertical displacementof water due to the horizontal 0094-8534/96/96 G L-0073 6505.00 movementof the slope,u h , (shownin Figure1) is calculatedas

861 862 TANIOKA AND SATAKE: TSUNAMI GENERATION BY HORIZONTAL MOVEMENT

Initial condition of tsunami 8's a) vertical movement due to faulting

//'•"'• Lowerplate b) horizontalmovement ofslope 10ø ....

Figure 1. A schematicillustration of tsunamiinitial conditionsfor underthrusttype earthquakes.The left side showsthe ocean 12' bottombefore faulting and the right sideshows the oceanbottom 111 ø 112' 113' 114' 115" 116øE after faulting.Vertical displacementdue to faultingis shownin Figure 2. The bathymetrymap near the epicenter(a star) of the (a). Horizontalmovement of slopeis shownin (b). Thick lines 1994 Java earthquakewith the focal mechanismand aftershock representthe regionswhere faulting occurs. Solid arrowsshow distribution(solid circles). The rectangleshows the fault model. the fault motion. Open arrows show the vertical (z) and Triangles show the locations where tsunami waveforms are horizontal (x) motion of water due to the horizontalmovement of computed. slope. that the horizontalmovement of the slopemay have significant contributionsto the verticaldisplacement of water. 3H 3H The fault model,shown in Figure2, (length90 km, width 60 tth = tt x • +try ay (2) km) is usedto computethe tsunamiinitial condition.We use a purethrust type fault (strike=280ø, dip=15ø, rake=90ø).From the whereH is thewater depth and u x andUy are the horizontal seismicmoment of 3.5 X102øNm of the Harvard CMT and a displacementsdue to faulting. Note that uh is taken positive upward but H is positive downward in equation (2). As rigidityof 4 x 101øN/m 2, the average slip is calculated tobe 3.24 mentionedbefore, the aboveexpression is invalid for a very steep m. A comparisonof the verticaldisplacement due to faulting (>1/3) slope. In an extreme case (such as a vertical cliff), the (Uz),the vertical displacement due to thehorizontal movement of horizontal motion of water dominates the tsunami generation theslope (Uh), and the total displacement (uh + uz ) is shownin [Iwasaki, 1982], but such a case is unrealistic for earthquake Figure3. The maximumamplitude of uz, uh andu h + uz , are tsunamis.The spatialderivative of waterdepth is computedusing 1.02 m, 0.44 m, and 1.29 m, respectively;the maximum the central-difference scheme. Finally, the total vertical amplitudeof uh is 43%of themaximum amplitude of uz. Figure displacement,uh + uz , is calculatedas the initial conditionof 4 comparesthe computedwaveforms at threelocations from two tsunamis. initialconditions, from the verticaldisplacement uz only and The methodof tsunaminumerical computation is describedin fromthe total vertical displacement uh + uz , Thewaveforms are Satake [1995]. The finite differencecomputation of the linear long wave equationand the equationof continuityon a staggered a) b) c) grid systemis carriedout on actualbathymetry data with a grid 8"S size of 20 sec.For comparison,the numericalcomputation from the initial conditionof only verticaldisplacement, uz, is also carried out.

The 1994 Java earthquake The 2 June 1994 Java earthquakeoccurred off the southern I] coast of Java, Indonesia, along the Sunda trench. The NEIS Preliminary Determination of Epicenters(PDE) provides the source parameters: origin time, 18:17:34.0GMT; epicenter, 10.477øS, 112.835E; depth, 18 km; magnitude, Ms 7.2. It generateddevastating tsunamis that killed morethan 250 people on Java Island [Tsuji et al., 1995]. The focal mechanismof the 1994 Javaevent indicates thrust type faultingwith a very shallow 112 ø 114*E dip angle (15ø ) (Figure 2). The horizontaldeformation due to Figure3. The compaqsonof (a) the ve•ical displacementdue to faulting is larger than the vertical deformation. Aftershock faulting, (b) the vertical displacementdue to the horizontal distributionfrom the PDE catalog showsthat the sourcearea is movementof the slope, and (c) the total displacementfor the very closeto the Sundatrench axis andjust beneaththe steepest 1994 Javaearthquake. Solid •d dashedheavy contours are for slope (Figure 2). The direction of horizontal motion near the uplift and ,respectively, with a 20 cm interval.The steepslope is almostnormal to the slope.Therefore, we expect bathymet• (light contours)is shownin (b). TANIOKA AND SATAKE: TSUNAMI GENERATION BY HORIZONTAL MOVEMENT 863

Prigi Bandiolit tsunamirunup heightsat three locations,Prigi, Bandialit, and i i i ! i i i i i i •. i i , Triangwulasari,(Figure 2) are 3-4 m, 5-10m,and 4-5m [Tsujiet al., 1995]. The computedmaximum heightsat theselocations (Figure4) are 1.1m,4.0m, and 2.7 m, whichare almosthalf of the observedtsunami heights. These discrepanciesmay become small if we use a finer grid systemand includenon-linear and I I I I I I I 40 50 60 70 •!0 90 1O0 run-upeffects [Shuto, 1991; Satake and Tanioka,1995]. time, mm

Triongwulosori i i i i .i The 1994 Mindoro earthquake The 14 Nov. 1994 Mindoro earthquake occurred near the northern coast of Mindoro Island, Philippines.The NEIS PDE providesthe sourceparameters' origin time, 19:15:30.7 GMT; epicenter,13.532øS, 121.087E; depth33 km; magnitude,Ms 7.1. It generateddevastating tsunamis that killed more than 70 people on Mindoro Island. Some surface rupture was observedon the 3b 4b 5b 6b 7b 8b 9b 10 20 30 40 ,50 60 70I 0TM northern pa.rt of MindoroIsland although the epicenter is located time, mm time, mm .... vert•col only • vert•col ond hor•zontol in the ocean(Figure 5) [lmamura et al., 1995]. The right lateral Figure4. The comparisonof the computedwaveforms at Prigi, surface displacementmeasured by the Philippine Institute of Bandialitand Triangwulasarifor two differentinitial conditions, Volcanology and (PHIVOLCS) was about 2 m the verticaldisplacement due to the faulting(dashed curves) and [PHIVOLCS Quick Response Teams, 1994]. The focal the totalvertical displacement (solid curves) caused by the 1994 mechanism is shown in Figure 5. It shows strike-slip type faulting. The surfacerupture and the focal mechanismsindicate Javaearthquake. thatthe strike-slipfaulting occurred almost normal to the slopeof the coast.Like the 1994Java earthquake case, we expectthat the very similar but the amplitudesare different.The amplitude horizontal movement of the slope may have significant difference is as much as 30%. Therefore, the horizontal contributionsto the vertical displacementof water. movementdue to faulting is significantlyimportant for the The fault model, shownin Figure 5, with lengthand width of tsunamigeneration for the 1994Java earthquake. The observed 35 km and 15 km respectively,are used to computethe initial condition of the tsunami. We assume a vertical right-lateral strike-slipfault (strike=160ø, dip=90ø, rake=180ø). We use the

-- 13ø45'N a) 13'35'Nl

13'30'

13'25'

' ,Q •,,,••__•--- 13ø30' 121'00' 121'05' 121'10'E '

13'35'N

13'30'

13'25' 13'15'

120ø00 ' 120ø15'E Figure5. The bathymetrymap nearthe epicenter(star) of the Figure 6. The comparisonof (a) the verticaldisplacement due to 1994Mindoro earthquake with the focalmechanism. Inset shows faulting, (b) the vertical displacementdue to the horizontal the tectonicsetting near the Philippines.A solidline showsthe movementof the slope, (c) the total displacementfor the 1994 fault model. A dashedline showswhere the surfaceruptures are Mindoro earthquake.Solid and dashedheavy contoursare for observed[PHILVOLCS Qu!ck Response Teams, 1994]. Solid uplift and subsidence,respectively, with a 2 cm interval. The circlesshow where tsunamiwaveforms are computed. bathymetry(light contours)is shownin (b). 864 TANIOKA AND SATAKE: TSUNAMI GENERATION BY HORIZONTAL MOVEMENT

Boco Wawa Calapan Acknowledgments. We thank Jean Johnsonand Nathan Winslow for i i i i ! ! i I i i helpfulcomments and Larry Ruff for constructivediscussions and comments.This work was supportedby NSF (EAR-9405767).

, References

Aida, I., Reliability of a tsunami source model derived from fault parmeters, J. Phys. Earth, 26, 57-73, 1978. 2½rn I I I ! I I I Berg, E., et al., Field surveyof the tsunamisof 28 March 1964 in Alaska, lo 20 and conclusionsas to the origin of the major tsunami, in edited by time, rnin time, rnin time, rnin Hawaii Instituteof Geophysics,Honolulu, Hawaii, t 970. .... verticol only •verticol ond horizontol Imamura,F., C.E. Synolakis,E. Gica, E. Titov, E. Listanco,and H.J. Lee, Figure7. The comparisonof the computedwaveforms at Baco, Field surveyof the 1994 Mindoro Island, Philippinestsunami, Pure Wawa and Calapan for two different initial conditions,the Appl. Geophys.,144, 875-890, 1995. Iwasaki, S., Experimentalstudy of a tsunamigenerated by a horizontal verticaldisplacement due to faulting(dashed curves) and the total motionof a slopingbottom, Bull. Earthq.Res. Inst. Univ. Tokyo,239- verticaldisplacement (solid curves) caused by the 1994Mindoro 262, 1982. earthquake. Kajiura, K., Tsunamienergy in relationto parametersof the earthquake faultmodel, Bull. Earthq. Res. Inst., Univ: Tokyo, 56, 415-440,1981. slip of 2 m from the observed surface displacement.A Kanamori, H., Mechanismof tsunamiearthquakes, Phys. Earth Planet. inter., 6, 246-259, 1972. comparisonof the verticaldisplacement due to faulting(Uz), the

Okada, Y., Surfacedeformation due to shearand tensile faults ., i.n a half- vertical displacementdue to the horizontalmovement of the space,Bull. Seisin.Soc. Am., 75, 1!35-1154, 1985. slope(Uh), and the total displacement(u h +uz) is shownin PHILVOLCSQuick Response Teams, The 15 November 1994 Mindoro Figure6. Themaximum amplitudes of uz, uh , and uh + uz , are earthquake,Report of I.nve•stigation, PHIVOLCS Special Report, No. 2, 0.14 m, 0.08 m, and0.13 m, resPeCtively.The maximum 36 pp., 1994. amplitudeof uh is 57% of themaximum amplitude 'of uz. Figure Satake, K., Linear and nonlinearcomputations of the 1992 Nicaragua 7 comparesthe computedwaveforms at threelocations from two earthquaketsunami, Pure Appl. Geophys.,144, 455-470, 1995. initial conditions,the vertical displacement due to faultingu z and Satake, K., and Y. Tanioka, Tsunami generationof the 1993 Hokkaido thetotal displacement uh + uz Thetwo initial conditions produce Nansei-okiearthquake, Pure Appl. Geophys., 144, 803-822, 1995. maximumamplitudes which are similar'butwaveforms that are Shuto,N., Numerical simulationof tsunamis-Itspresent and near future, in Tsunami Hazard, edited by E. N. Bernard, 171-191, Kluwer markedly different. Again, the horizontal movementdue to Academic, 1991. faultingis asimportant as the verticalmovement due to faulting. Steketee, J.A., On Volterra's dislocationsin a semi-infinite elastic The computedmaximum heights at threelocations, Baco, Wawa, medium, Can. J. Phys.,36, 192-205, 1958. and Calapan(Figure 5) are 0.07 m, 0.09 m, and0.09 m (Figure Tsuji, Y., F. Imamura, H. Matsutomi, C.E. Synolakis,P.T. Nanang, 7). The observedtsunami runup heights are, however, much Jumadi,S. Harada,S.S. Han, K. Arai, andB. Cook, Field surveyof the larger,1-4 m, 1-4 m, and2-3m at theselocations [Imamura et al., east Java earthquake and tsunami of June 3, 1994, Pure Appl. 1995].Another generation mechanism, such as landslide, may be Geophys.,144, 839-854, 1995. necessaryto explainthe observedtsunami.

Conclusion K. Satake, SeismotectonicsSection, Geological Survey of Horizontaldisplacement due to faultingbecomes important for Japan,Tsukuba, Ibaraki 305, Japan(e-mail: [email protected]) tsunamigeneration under two conditions;(1) large horizontal Y. Tanioka, Dept. of GeologicalSciences, Univ. of Michigan, motionof a steepslope and (2) horizontalmotion much larger AnnArbor, MI 48i09-1063. (e-mail: [email protected]) thanthe verticalmotion, such as a strike-slipfaulting or a dip-slip faultingon a very shallowlydipping fault. This mechanismmay be importantfor explainingtsunami earthquakes [Kanamori, (ReceivedNovember 20, 1995; revisedJanuary 15, 1996; 1972] which usuallyoccurred near a trenchaxis. acceptedFebruary 14, 1996.)