地球物理学基础作业01

����������� ������������
= ������
������������ ������������
and g r = −G
������ ������ ������ 2
=−
������ ������ ������ 2 0
4������������ 2 ������(������)������������
-1
β [km s ] 4.8 12.2 7.0
-1
ρ [km m ]
-3
3100 3900 5300
(See also Exercise 1 in the textbook “Fundamentals of Geophysics “ P203)
地球物理学基础（2013）作业 01
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5. For a sphere, moment of inertia is given as I = KM������ 2 ，please prove below three situations： (a) If the sphere is homogenous (uniform density), K = 0.40; (b) If all the mass of the sphere is on the outside, K = 0.67; (c) For a two layer earth with a denser core whose radius is 0.50 that of the entire planet, with the density of core is three times greater than rim, K=0.33. 以下三个题目，任选两个： 6. The radius of the Moon is 1738km and its mean density is 3347kgm-3. If the Moon has a core with radius 400km and the uniform density of the overlying mantle is 3300 kgm-3, what is the density of the core? 7. An aircraft leaves a city at latitude ������1 and longitude ϕ1 and flies to a second city at latitude ������2 and longitudeϕ2 . Derive an expression for the great circle distance between the two cities 。 Apply the above formula to compute the great circle distances between the following pairs of cities: (a) New York (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. Preview the three-dimensional wave equations. （Refer to Appendix A in the textbook “Fundamentals of Geophysics “ P363. ）
地球物理学基础（2013）作业 01
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地球物理学基础（2013）
布置时间： 2013-9-17(周二)
1. 将下面的英文翻译成中文
作业 01
交作业时间： 2013-9-24 （周二）
Although the many advances in geophysical research depend strongly on the aid of computer science, the fundamental principles of geophysical methods remain the same; they constitute the foundation on which progress is based. In revising this textbook, I have heeded the advice of teachers who have used it and who recommended that I change as little as possible and only as much as necessary (to paraphrase medical advice on the use of medication). The reviews of the first edition, the feedback from numerous students and teachers, and the advice of friends and colleagues helped me greatly in deciding what to do. The structure of the book has been changed slightly compared to the first edition. The final chapter on geodynamics has been removed and its contents integrated into the earlier chapters, where they fit better. Text-boxes have been introduced to handle material that merited further explanation, or more extensive treatment than seemed appropriate for the body of the text. Two appendices have been added to handle more adequately the three-dimensional wave equation and the cooling of a half-space, respectively. At the end of each chapter is a list of review questions that should help students to evaluate their knowledge of what they have read. Each chapter is also accompanied by a set of exercises. They are intended to provide practice in handling some of the numerical aspects of the topics discussed in the chapter. They should help the student to become more familiar with geophysical techniques and to develop a better understanding of the fundamental principles. 2. Write down Kepler’s three laws of planetary motion. Which law is a result of the conservation of momentum? Which law is a result of the conservation of energy? 3. What are the Lame constants in seismic theory? 4. Calculate the bulk modulus 体积模量(K),the shear modulus 剪切模量(μ) and Poisson’s ratio 泊松比 (υ) for the lower crust 地壳 ,upper mantle and lower mantle, respectively, using K = −V
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and the values for the P-waves(α) and S-waves(β) velocities, and density(ρ) given in the following table.
Region Lower crust Upper mantle Lower mantle Depth [km] 33 400 2200 α [km s ] 7.4 8.5 12.2