By the convolutional model of the seismic trace, the convolution of a seismic wavelet, which has a starting point, with the reflection series, a series of spikes, brings about the singularity features of the seismic traces. The detected singularity of seismic traces can improve resolution of seismic data visibly. As a result, it should expose more geological phenomena on seismic section and benefit sequence stratigraphic studies, accurate correlation of reservoir tops and bottoms and detailed delineation of reservoir structures. The results also lie a good foundation for lithological prediction. In this paper, a wavelet package constructed with a scaling function differing from the literatures is used to detect it. The synthetic example shows the procedure of singularity analysis, and the practical example shows the validity and reliability of the algorithm.


Today whether the exploration or the reservoir description and manage, it starves for high resolution of seismic data, but can't now. There are problems in two aspects.

The first, because seismic wavelet isn't well and truly pick up and there is some change of the wavelet with the space and time both, after the deconvolution, that now is good for improving resolution of seismic data, always a residual wavelet is leave behind. The band-limited residual wavelet badly restricts the resolution of seismic data.

The second, on one hand maybe people is restricted by the viewpoint of band-limited seismic data, which insists on that the bandwidth of seismic data is a deadline of the resolution, so processing must be all-pass in frequency domain (Li, Q., 1993). On the other hand because low resolution is so easy to process and interpret, and higher resolution is more difficult, maybe people prefer easy to difficult (Kerekes, A. K., 1998).

It is believed by a lot of successful experiment of the coherency slices, that there is plenty geologic information in the singularity feature of the seismic data. The coherency slices character the singularity of seismic data in spatial domain (Marfurt, M. J., et al 1999), whereas in temporal domain it is not yet sufficiently understood and used so far. My work (Cao, Y., 1996) exposed the fact that seismic data in temporal domain have abundant singularity too. And thed-spline function was used to construct a wavelet package for singularity analysis of seismic traces. Then the singularity analysis alternates with deconvolution, the residual wavelet was compressed availably and the resolution of seismic section could be improved visibly. In this paper, a formula of detecting singularity is used as scaling function to construct a wavelet package to get over the problem of residual wavelet. It is equivalent to the revised d-spline fitting of the regular component of a seismic trace in substance.

The singularity of a seismic trace

There are many interfaces of layers, faults, change of epositional facies and so on inside the earth.

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