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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。
This paper deduces the first formula for the propagation of spherical waves in elastic media, including the first of direct wave, reflected wave and transmitted wave. By decomposing the spherical wave, the spherical wave is synthesized by the cylindrical wave. The expressions of the incident wave, the reflected wave and the transmitted wave are given by the continuous conditions of pressure and velocity at the interface. The steepest descent method were the first of these three kinds of wave analysis of the expression. The VSP observation system is used to numerically simulate the relationship between the amplitude and the phase of the reflection and transmission at the interface generated by the point source spherical wave. The results show that the analytic formula in the paper is correct. These formulas can be applied to AVO analysis and provide the basis for the application of the theory of geometrical diffraction in seismology.