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常用公式中研究的是由垂向非均质层组成的介质内的弹性波、声波和电磁波。垂向非均质介质的频谱函数就是由于第一层顶部中脉冲源所造成的向下传播的能通量。传播一不变量形式可用来推导出几种反射和传播矩阵的恒等式。当顶层是由一个自由面为界时,表达式之一就可简化成由 Kunetz 为一维波动方程推导的公式。向上和向下辐射的声源能以一种传播一不变量形式提供等于声源能量的间断波。当声源正好位于各层的顶部界面之下时,便可推导出一个新公式。
Among the commonly used formulas are the elastic waves, acoustic waves and electromagnetic waves in a medium composed of vertical inhomogeneous layers. The spectral function of a vertically inhomogeneous medium is the downward flux energy flux caused by the pulse source in the top of the first layer. Propagating an invariant form can be used to derive identities of several reflection and propagation matrices. When the top layer is bounded by a free surface, one of the expressions can be reduced to a formula derived by Kunetz for the one-dimensional wave equation. An upward and a downward radiated sound source can provide a discontinuous wave equal to the energy of the sound source in a propagation-invariant form. A new formula can be deduced when the sound source is just below the top interface of the layers.