2017地球物理学基础作业01及参考答案

1.

Although the many advances in geophysical research depend strongly on aid of computer science,the fundamental principles 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 use of medication).The reviews of the first edition,the feedback from numerous students and teachers,and the advice of friends and colleagues help 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.

虽然地球物理研究方面的许多进展在很大程度上依赖于计算机科学的帮助，但是地球物理方法的基本原理仍旧保持不变，他们构成了进步的基础。在修订这本教科书时，我听从了使用过它的老师们的建议，他们建议我尽可能少地改变，并尽必要多地修改（就像医学建议改述药物使用一样）。对第一版的评论，许多学生和老师的反馈，以及朋友和同事的建议在我决定该做什么方面极大地帮助了我。

与第一版相比，本书地结构有了些轻微的变化。原来关于地球动力学的最后一章已经被删除，它的内容被整合到了前面更合适的章节。文本框的引入用来处理那些值得进一步解释的材料，或与正文相比似乎适合更广泛处理的材料。增加了两个附录来更充分地处理三维波动方程和半空间的冷却方程。每一章的结尾都有一单复习题，可以帮助学生评估他们所读的知识。每一章还附有一套练习。它们的目的是提供处理本章讨论的主题的一些数值方面的实践。他们应该帮助学生更加熟悉地球物理技术，更好地理解基本原理。

2.

地震学-Seismology；地磁学-Geomagnetism；地热学-Geothermics；测地学-Geodesy；正演模拟-Forward Modeling；反演-Inversion；

里氏震级-Richter Magnitude Scale；弹性特征-Elastic Behavior；

波动方程-Wave Equations；脆性变形-Brittle Deformation；Geophysics-地球物理学；moment of inertia-转动惯量；heterogeneity-不均匀性；anisotropy-各向异性；

boundary conditions-边界条件；focal mechanism-震源机制；

free oscillation-自由震荡；asthenosphere-软流圈；lithosphere-岩石圈、mantle-地幔；

3.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?The laws may be formulated as follows:(1)the orbit of each planet is an ellipse with the Sun at one focus;

每一个行星绕太阳的轨道都是椭圆，太阳在椭圆的一个焦点上（椭圆定律）；

(2)the orbital radius of a planet sweeps out equal areas in equal intervals of time;

在相等的时间间隔内，行星的轨道半径扫过的面积相等（面积定律）；

(3)the ratio of the square of a planet’s period (T 2)to the cube of the semi-major axis of its orbit (a 3)is a constant for all the planets,including the Earth.

所有行星，包括地球，绕太阳一周的周期的平方（T2）与它们轨道长半轴(a3)的立方之比是一个常量（调和定律)。

Kepler’s 2nd law is a result of the conservation of momentum.

开普勒第二定律是动量守恒的一个结果。

Kepler’s 3rd law is a result of the conservation of energy.

开普勒第三定律是能量守恒的一个结果。

4.For a sphere,moment of inertia is given as I=KMR2，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 0.50that of the entire planet,with the density of core is three times greater than rim,K=0.33.Solves ：(a)均匀球体的转动惯量2MR 52I =，又I=KMR 2,则K=0.40(b)球壳的转动惯量2MR 32I =，又I=KMR 2,则K=0.67(c)根据球壳的转动惯量，由微分法可知两层模型的转动惯量

22R 212023

232dm r dm r I R R ⎰⎰+=，其中dr r dV dm 21433πρρ==，

dr r dV dm 224πρρ==,所以K=0.335.已知一矢量场zx a xy a F

y x -=,试求：

（1）该矢量场的旋度;

（2）该矢量沿半径为3的四分之一

圆盘的线积分，如图所示，验证斯托克斯定理。

解：（1）已知矢量y x a zx a xy -=F ，则该矢量场的旋度为：