地球物理学基础作业01

地球物理学基础（2013）作业011/2地球物理学基础（2013）作业01布置时间：2013-9-17(周二)交作业时间：2013-9-24（周二）1.将下面的英文翻译成中文Althoughthemanyadvancesingeophysicalresearchdependstronglyontheaidofcomputerscience,thefundamentalprinciplesofgeophysicalmethodsremainthesame;theyconstitutethefoundationonwhichprogressisbased.Inrevisingthistextbook,IhaveheededtheadviceofteacherswhohaveuseditandwhorecommendedthatIchangeaslittleaspossibleandonlyasmuchasnecessary(toparaphrasemedicaladviceontheuseofmedication).Thereviewsofthefirstedition,thefeedbackfromnumerousstudentsandteachers,andtheadviceoffriendsandcolleagueshelpedmegreatlyindecidingwhattodo.Thestructureofthebookhasbeenchangedslightlycomparedtothefirstedition.Thefinalchapterongeodynamicshasbeenremovedanditscontentsintegratedintotheearlierchapters,wheretheyfitbetter.Text-boxeshavebeenintroducedtohandlematerialthatmeritedfurtherexplanation,ormoreextensivetreatmentthanseemedappropriateforthebodyofthetext.Twoappendiceshavebeenaddedtohandlemoreadequatelythethree-dimensionalwaveequationandthecoolingofahalf-space,respectively.Attheendofeachchapterisalistofreviewquestionsthatshouldhelpstudentstoevaluatetheirknowledgeofwhattheyhaveread.Eachchapterisalsoaccompaniedbyasetofexercises.Theyareintendedtoprovidepracticeinhandlingsomeofthenumericalaspectsofthetopicsdiscussedinthechapter.Theyshouldhelpthestudenttobecomemorefamiliarwithgeophysicaltechniquesandtodevelopabetterunderstandingofthefundamentalprinciples.2.WritedownKepler’sthreelawsofplanetarymotion.Whichlawisaresultoftheconservationofmomentum?Whichlawisaresultoftheconservationofenergy?3.WhataretheLameconstantsinseismictheory?4.Calculatethebulkmodulus(K),theshearmodulus(μ)andPoisson’sratio(υ)forthelowercrust,uppermantleandlowermantle,respectively,usingK=−V𝑑𝑝𝑑𝑉=𝜌𝑑𝑝𝑑𝜌andg(r)=−G𝑚(𝑟)𝑟2=−𝐺𝑟2∫4𝜋𝑥2𝜌(𝑥)𝑑𝑥𝑟0andthevaluesfortheP-waves(α)andS-waves(β)velocities,anddensity(ρ)giveninthefollowingtable.Page192RegionDepth[km]α[kms-1]β[kms-1]ρ[kmm-3]Lowercrust337.44.83100Uppermantle4008.512.23900Lowermantle220012.27.05300(SeealsoExercise1inthetextbook“FundamentalsofGeophysics“P203)地球物理学基础（2013）作业012/25.Forasphere,momentofinertiaisgivenasI=KM𝑅2，pleaseprovebelowthreesituations：Page150曾融生(a)Ifthesphereishomogenous(uniformdensity),K=0.40;(b)Ifallthemassofthesphereisontheoutside,K=0.67;(c)Foratwolayerearthwithadensercorewhoseradiusis0.50thatoftheentireplanet,withthedensityofcoreisthreetimesgreaterthanrim,K=0.33.以下三个题目，任选两个：6.TheradiusoftheMoonis1738kmanditsmeandensityis3347kgm-3.IftheMoonhasacorewithradius400kmandtheuniformdensityoftheoverlyingmantleis3300kgm-3,whatisthedensityofthecore?7.Anaircraftleavesacityatlatitude𝜆1andlongitudeϕ1andfliestoasecondcityatlatitude𝜆2andlongitudeϕ2.Deriveanexpressionforthegreatcircledistancebetweenthetwocities。Applytheaboveformulatocomputethegreatcircledistancesbetweenthefollowingpairsofcities:(a)NewYork(λ=40∘43’N,ϕ1=74∘1’W)—Madrid(λ=40∘25’N,ϕ1=3∘43’W);(b)Seattle(λ=47∘21’N,ϕ1=122∘12’W)—Sydney(λ=33∘52’S,ϕ1=151∘13’E);(c)Moscow(λ=55∘45’N,ϕ1=37∘35’E)—Paris(λ=48∘52’N,ϕ1=2∘20’E);(d)London(λ=51∘30’N,ϕ1=0∘10’W)—Tokyo(λ=35∘42’N,ϕ1=139∘46’E).8.Previewthethree-dimensionalwaveequations.（RefertoAppendixAinthetextbook“FundamentalsofGeophysics“P363.）注意：1、以上所有题目（英译汉除外），用中文或者英文回答都可以；2、请使用A4打印纸或者同等大小的纸张作答，无需再抄题目，标清楚题号即可，手写或者电子打印都可以；3、请在第一页页首位置写上你的信息，格式是“姓名+单位+学号”。