【正文】 en any two adjacent points having same phase. We usually use the terms wave number and frequency. The wave number is k=1/? and the frequency is f=1/T. Form the above, we know that the wave velocity can be obtained by V= ? /T. y=A sin[2? k(xVt)] 波數(shù)與頻率 固體地球物理學概論 第七章 平面波 Assume that the wave propagates only in xdirection and the particles move only in yz plane. This means that all particles move in phasethey form wave fronts. We say the waves are plane waves. The movement of the particles may be described by f(x,t)=A sin[2πk(xVt)] 平面波 固體地球物理學概論 第七章 球面波 For a point source, waves propagate in all directions. If particles move in phase and they constitute spherical wave fronts. We say they are spherical wave. Practically, for the far away point sources the spherical wave can be approximately considered as the plane waves. f(r,t)=A sin[2πk(rVt)] 球面波 固體地球物理學概論 第七章 Dispersion of body waves From a point source the P and Swaves spread radially from the source along a straight line. The spherical wave fronts still dilate, so that the energy of vibrating particles on the spheres decreases continually. Assume E is the energy of a seismic source, r is the radial distant from the source to a sphere. At one instant the energy per unit area of the sphere ΔE can be written in ΔE=E/(4πr2) At any point out of source, the energy is proportional to the inverse of the square of r and the amplitude is proportional to the inverse of r. They both decay with the increasing of the distance from the source. 球面波的擴散 固體地球物理學概論 第七章 Absorption and attenuation of body waves Up to now, we have assumed that rock or other materials are perfectly elastic. In fact, pure elastic material does not exist. The energy of the waves transform to heat due to the friction of vibrating particles. The energy and the amplitudes of the waves decay with the traveled distance and the frequency of the wave. A =A0 eαfr 地震波的吸收與衰減 固體地球物理學概論 第七章 地震波射線理論 地震體波的傳播 研究地震波傳播通常有兩種途徑，一個是依據(jù)波動方程的動力學理論，另一個是依據(jù)地震波走時的射線理論。因此縱波和橫波的速度滿足波動方程； 2)由于無旋位移場的散度是無旋應變，無散位移場的旋度是無散應變。 地震學研究及其意義 固體地球物理學概論 第七章 地震與介質(zhì)的彈性性質(zhì) 地震震源及地震波 ⑴ Earthquake sources Physically, earthquake sources are the abrupt release of the potential elastic energy stored in rocks over a period ranging from a few years to thousands of years. Only a small part of the energy converts heat to the surround rocks near the source, the most of energy is radiated away as elastic waves. In fact, rocks at an earthquake source generate plastic deformation but elastic deformation at the moment of earthquakes occurring. Up to now, no earthquake that locates deeper than 670 km has been observed. 地震震源 固體地球物理學概論 第七章 ⑵ Seismic waves Seismic waves are the elastic wave from the source. They are of various types. While traveling through the earth, these waves are influenced by the properties of the media they pass. We are able to understand and analyze the influence by applying mathematical and physical methods. In addition, we can determine the earth’s structures: the crust, the mantle, the outer core, the inner core, as well as the lateral changes near the surface. 地震波 固體地球物理學概論 第七章 ⑶ Receiving The main task of receiving is to record the seismic waves at desired positions to study earthquakes. It includes the sampling technology and the receiving system consisting of seismographs(地震儀 ), geophones(檢波器 ), and other instruments. The quality of recorded data is important to analysis and interpretation of the seismic waves and determination of earthquake sources. 地震波的接收 固體地球物理學概論 第七章 板塊構造與地震 At present the theory of plate tectonics is accepted by most of geoscientists, even though many of its details are still unclear or controversial. We can use a simplified dynamic model to describe the movement of continent. When the material in the mantle is heated, it expands and bees lighter. In spite of its high viscosity（粘性） , it rises more or less vertically in some places, especially under the oceanic ridges. With its losing pressure and heat during traveling upward, the material is forced to travel horizontally. They drag the lithosphere motion. The results of continent colliding form mountain chains (Himalayas) , and the results of their separating form ocean rifts (East Africa). So major earthquakes often cause near their collided boundaries. In the region of oceanic ridges, where new lithosphere is growing, small earthquakes occur frequently. 板塊構造與地震 固體地球物理學概論 第七章 板塊構造與地震分布圖 固體地球物理學概論 第七章 巖石彈性性質(zhì)基本概念 (1)形變 A material occurs deformation(形變） under a force act on itself. If it recovers as the force disappears, it is called elastic material. The shape change is called as elastic deformation. Otherwise, it is called as nonelastic deformation. Whether elastic deformation occurs depends on the magnitude of acting force, the acting period as well as the surrounding temperature. For most materials in the earth, this elastic property only exists in a short period. 彈性概念 —— 形變 固體地球物理學概論 第七章 (2)應力 Stress tensor（ 張量 ） Definition: Here stress means a force acts on unit area of a body against the elastic deformation caused by the action of an external force. Describe any stress needs consider two factors, direction and outer normal(法向 ） of a face. We generally express it by pst. Here s means t