弹性波理论研究──关于球面波首项(Ⅰ)

The theoretical study of the elastic wave:on the first term of spherical wave

石油大学(北京),北京 102200

University of Petroleum Beijing, Beijing 102200

本文推导了球面波在弹性介质中传播的首项公式,包括直达波、反射波和透射波的首项。通过对球面波分解,用柱面波合成球面波;在界面上由压力和速度连续条件,给出入射波、反射波和透射波的表达式;对汉格尔函数用大自变量展开,用最陡下降法分别求出这三种波的首项解析表达式。利用VSP观测系统来数值模拟点震源球面波在界面上产生反射和透射的振幅和相位的关系,结果证明文中推导的解析式是正确的。这些公式可以应用于AVO分析;并为几何绕射理论在地震学中应用提供了基础。

The formula of the first term for spheric wave propogating in ealstic medium has been derived,including the first terms of direet wave,reflection wave,and transmitted wave. By decomposing the spherical wave,we synthesize the spherical wave using the cylindrical wave. According to the continous condition of pressure and velocity on interface, the expressions of the incidence wave,reflection wave,and transmitted wave are given By expanding Hankel function with large independent variable, we derive the analytie expressions of the first terms of these three kinds of waves by means of the stcepest descent mothod. A VSP layout is utilized to numerically model the relations of amplitude and phase between the refleetion and transmission waves of point soure produced on the interface. Thc results show the analytie expressions derived in the paper are correct.The formulas can be used in AVO analysis,and provide the basis for the application of the geometric diffraction theory to seismology.