摘要
讨论在诸多波动现象中 ,由波动方程 2 Q/ t2 =v2 ( x) ΔQ反演波速 v( x)或弹性系数等其它重要参数的方法是否近似可用 ,指出了在非均匀介质条件下用此波动方程不能正确描述波的传播特性 ,因它不能保证弹性力在间断面上连续 .以三维双层介质为例 ,分别从此方程和原始波动方程出发推导波的反射与透射公式 ,得到不同的反射系数与透射系数表达式 ,两者相差很大 ,不可能是近似的关系 .
The difference between two mathematical models in describing wave phenomena is discussed by this paper.We show that the wave-equation 2 Q/ t2 v(· ) ΔQ, which can't stand up the continuity of the elastic force on the disconnected surface and does not depict the wave propagation correctly in uneven medium.Also we pointoutthat the right way to get certain physical coefficients is to compute directly from the initial wave-equation d(· ) 2 Q/ t2 =div[K(· ) grad Q] .The greatdifference between the reflec- tion and transmission coefficients calculated from the two equations above shows thatthey can't be considered 'approximate'.
关键词
波动方程
数学模型
反射系数
双曲型方程
波现象
Wave-equations
Penetration rate
Mathematical model
/Reflection coefficients
