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文中通过常用的方程研究了由垂向非均匀层组成的介质中的弹性波、声波和电磁波。垂向非均匀介质的谱函数就是由于第一层顶部脉冲源造成的向下的能通量。文章利用传播不变形式,推导了在反时和透射基质的几种恒等式。当顶层被一自由面作为边界时,那么其表达式之一可简化成 Kunetz 在一维波动方程情况下推导获得的公式。脉冲源向上和向下辐射时,在传播不变的形式下可产生与震源能量相同的不连续性。文中还在震源恰好位于地层顶界面下时,导出了一个新的公式。
In this paper, we study the elastic wave, acoustic wave and electromagnetic wave in the media composed of vertical non-uniform layers by the commonly used equations. The spectral function of a vertically inhomogeneous medium is the downward flux due to the pulse source at the top of the first layer. In this paper, by using the propagation invariant form, several identities at the transversal and transmissive substrates are deduced. When the top layer is bounded by a free surface, one of its expressions can be reduced to Kunetz’s formula derived in the one-dimensional wave equation. When the pulsed sources radiate upwards and downwards, discontinuities of the same energy as the source energy can be produced in the same propagation mode. The article also derives a new formula when the source is located just below the top boundary of the formation.