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提出了克希霍夫(Kirchhoff)波动方程的一种形式,这对地球物理学家进行地震反射资料的振幅解释是有用的。将克希霍夫的延迟位方程进行简单整理,反射过程可以看作震源子波的导数对所谓的“波前扫描速度”(“Wavefront Sweep Velocity”)的褶积。这个波前扫描速度是入射波前覆盖反射界面的速率的度量。通过对具有不同曲率的地质模型的波前扫描速度的比较,人们对绕射波振幅和反射波振幅与界面曲率的关系会得到一个直观的概念。同样,根据波动方程的这个褶积式,很容易得到反射波振幅的几何光学解。但是更重要的是,根据波前扫描速度方法,可以发展一种图解法使地球物理学家能够应用圆规和直尺来估算曲率与绕射对地震波振幅的影响。
A form of the Kirchhoff wave equation is proposed, which is useful for geophysicists to interpret the amplitude of seismic reflection data. The Kirchhoff’s delay-bit equation is simply organized and the reflection process can be seen as the convolution of the derivative of the source wavelet with the so-called “Wavefront Sweep Velocity”. This wavefront scan speed is a measure of the rate at which the incident wavefront covers the reflective interface. By comparing the wavefront sweep speeds of geological models with different curvatures, one can obtain an intuitive concept of the relationship between the amplitude of the diffracted wave and the amplitude of the reflected wave and the curvature of the interface. Also, based on this convolution of the wave equation, it is easy to get a geometrical optical solution of the amplitude of the reflected wave. More importantly, however, based on the wavefront scanning speed method, a graphical method can be developed that enables geophysicists to apply compasses and rulers to estimate the effect of curvature and diffraction on seismic amplitude.