用Mbius反演做地震道反射系数反演
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摘要
Mbius反演属于数论范畴。Mbius反演不仅仅是提供一种新的反演手段，更重要的是从数学上找到一种积分形式。Mbius反演是一种直接求解的方法，不需迭代，计算量小，稳定性好。文中介绍了该技术的反演基本原理，它主要是将地震记录进行对数坐标变换，从而引用Mbius的反演方法，其中主要一点是假设地震子波是非零完全积性函数。在反演基础上，再作反对数变换，就达到反演的目的。文中列出了Mbius反演详细的实现过程。
Mobius inversion belongs in number theory. It is a new seismic inversionmeans, and particularly an integration way from mathematics. Mobius inversion isa direct method, without iteration, and it needs less computation and brings goodstability. The technique includes some essential points: logarithmic coordinatetransform of seismic data, followed by Mdbius inversion which needs an assumptionthat seismic wavelet is a function of nonzero full integration. The final inversion isthen achieved by doing antilogarithmic transform after Mobius inversion. The detailed procedure of Mobius inversion is described in this article.
Mobius inversion belongs in number theory. It is a new seismic inversionmeans, and particularly an integration way from mathematics. Mobius inversion isa direct method, without iteration, and it needs less computation and brings goodstability. The technique includes some essential points: logarithmic coordinatetransform of seismic data, followed by Mdbius inversion which needs an assumptionthat seismic wavelet is a function of nonzero full integration. The final inversion isthen achieved by doing antilogarithmic transform after Mobius inversion. The detailed procedure of Mobius inversion is described in this article.
引文
1 Chen Nanxian.Modified Mobius inverse formula and its application in physics.Physical Review Letters, 1990,64(1):1193～1195
2 Maddox J.Mobius and Problems of inversion.Nature,1990, 344～377
3 柯台,孙琦.数论讲义,高等教育出版社,1986
2 Maddox J.Mobius and Problems of inversion.Nature,1990, 344～377
3 柯台,孙琦.数论讲义,高等教育出版社,1986
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