Earthquake, Volcano and Tsunami
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1 A. Merapi Volcano Erpion Earhqake, Volcano and Tsnami Qesion Answer Marks A. Using Black s Principle he eqilibrim emperare can be obained Ths,.5 A. For ideal gas, pv e e RTe, hs.3 A.3 The relaive velociy rel can be expressed as where is a dimensionless consan. Using dimensional analysis, one can obain ha.5 3 Therefore / / / Toal score.3 Page of 8
2 B. The Yogyakara Earhqake Qesion Answer Marks B. From he given seismogram, fig..3.5 One can see ha he P wave arrived a :54:45 or ( ) seconds afer he earhqake occrred a he hypocener. Since he horizonal disance from he epicener o he seismic saion in Gamping is.5 km, and he deph of he hypocener is 5 km, he disance from he hypocener o he saion is.5 5 km 7.4 km Therefore, he P wave velociy is 7.4 Km 5.75 Km/s 4.7 s.. Page of 8
3 Qesion Answer Marks B. Direc wave:. direc SR v v s 86.9 s.6 As in he case of an opical wave, he Snell s law is also applicable o he seismic wave..4 Illsraion for he raveling seismic Wave Refleced wave: refleced SC CR v v 5 SC coscr cos 5 co 45 refleced s v sin Page 3 of 8
4 Qesion Answer Marks B.3 Velociy of P wave on he manle. The fases wave crossing he manle is ha propagaing along he pperpar of he manle. From he figre on refraced wave, we obain ha.4. v v sin ; sin ; cos v v v v cos ; x km; x km x cos cos 3 x 5 x x sin 5 45 an The oal ravel ime: x x x an v v v cos v v 3.5 cos 45 5 cos 45 sin where v and v. Arranging he eqaion, we ge whose solion is v 5v 45v 45 5 v v 45.3 From he seismogram, we know ha he fases wave arrived a Denpasar saion a :55:5, which is 75 s from he origin ime of he earhqake in Yogyakara. Ths v 7. km/s Page 4 of 8
5 Qesion Answer Marks B.4 By sing Snell s law and defining p sin v and v, we obain..4 p p ()sin ( z)sin ; sin z ( ) where z () vz () and is he iniial angle of he seismic wave direcion..5 dx sin p ; dz cos p ds ( z) ds ( z) dx dx ds p p p dz ds dz p x z z p p dz.7 Illsraion for he direcion of wave The disance X is eqal o wice he disance from epicener o he rning poin. The rning poin is he poin when 9. Ths z pv p ( z) ; z v az ap pv ( az) X dz p ( v az) p v ( p ( v az) ) ap Page 5 of 8
6 Qesion Answer Marks B.5 ds d For he ravel ime, d ; ( z). vz ( ) ds.. Ths d d ds dz ds dz ( p ) and herefore z z T dz dz ( ) ( p ) v az ( p ( v az) ) B.6 The oal ravel ime from he sorce o he Denpasar can be calclaed sing previos relaion T( p) z ( z) ( z) p dz Which is valid for a coninos z. () For a simplified sacked of homogeneos layers (Figre F), he inegral eqaion became a smmaion T( p) N i i z p i i second Noe ha he acal ravel ime from he epicener o Denpasar is 75 seconds. By varying he parameers of velociy and deph p o siable vale of observed ravel ime, physicis can know Earh srcre Toal score 5.7 Page 6 of 8
7 C. Java Tsnami Qesion Answer Marks C. The cener of mass of he raised ocean waer wih respec o he ocean srface is h/. Ths where ρ is he ocean waer densiy. C. Considering a shallow ocean wave in Fig. 5, he whole waer (from he srface nil he ocean floor) can be considered o be moving de o he wave moion. The poenial energy is eqal o he kineic energy. 4 4 Where x and U is he horizonal speed of he waer componen. The waer componen ha was in he pper par shold be eqal o he one ha moves horizonally for a half of period of ime, i.e.. Ths we have Accordingly, Ths C.3 Using he argmen ha he wave energy densiy is proporional o is amplide wih is amplide and is a proporional consan Becase he energy flx is conserve, hen for an area where he wave flow hogh. Then, (Therefore he snami wave will increase is amplide and become narrower as i approaches he beach) Toal score 3. Page 7 of 8
8 Toal Score for Problem : Secion A : Secion B : Secion C :.3 poins 5.7 poins 3. poins Toal : poins Page 8 of 8
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