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Tsunami Generation by Horizontal Displacement of Ocean Bottom

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Tsunami Generation by Horizontal Displacement of Ocean Bottom 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 earthquakes:the 2 June 1994 Java earthquake(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 fault 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 (15 ø) (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 subsidence,respectively, with a 20 cm interval.The steepslope is almostnormal to the slope.Therefore, we expect bathymet• (light
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