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G.Beylkin 最近的研究促进了地震反演普遍理论的建立。本文将其有关反演理论的主要概念同经典的高频渐近线法和扰动法相结合,以使它们向实际可行的算法更靠近一步,其应用方案中包括对叠后及叠前地震资料的反演。基本假设为:地震资料具有比较可靠的振幅,并有较为准确的背景速度 c(x,y,z)可供使用,因此可找到在此背景上的扰动。因为自始至终使用了高频的近似式,所以最终所得到的算法实质上就是确定速度的不连续性。一个全3—D 速度反演表达式可以导出大致的数据曲面。在其普遍性的程度说来,该公式并不能提供一个切实可行的算法,主要是因为关键性的雅柯比行列式无法用实用项表示。然而,在一些重要的情况下,诸如零偏移距,共震源及共接收器的情况,这一缺点可得以克服而得到计算上切实可行的表达式。最终算法的实现包括:首先,应用 FFT 处理,进行振幅校正及滤波,及用反 FFT 处理。然后,对每一个输出点,将对它有影响的已经处理的数据部分求和。沿相互衔接各射线的最后的总和中包含一个振幅值和一个旅时值。最终所得的算法在计算上可与同类的偏移方法匹敌。
Recent research by G. Beylkin contributed to the establishment of a universal theory of seismic inversion. In this paper, the main concepts of inversion theory are combined with the classical high-frequency asymptotic method and perturbation method to make them closer to practical algorithms. The application of this method includes the analysis of post-stack and prestack seismic data Inversion. The basic assumption is that the seismic data have a more reliable amplitude and a more accurate background velocity, c (x, y, z), is available, so perturbations can be found on this background. Because the high-frequency approximation is used throughout, the resulting algorithm is essentially a determination of the speed discontinuity. A full 3-D velocity inversion expression exports the approximate data surface. To its degree of universality, the formula does not provide a viable algorithm, mainly because the key Jakobbi determinants can not be expressed in practical terms. However, in some important cases, such as zero offset, co-seismic source and common receiver, this shortcoming can be overcome to get the computationally feasible expression. The final realization of the algorithm includes: First, the application of FFT processing, amplitude correction and filtering, and the use of inverse FFT processing. Then, for each output point, the portion of the data that has been processed that has an effect on it is summed. The final sum of the rays along each other contains an amplitude value and a travel time value. The resulting algorithm is computationally comparable to the same offset method.