广义S变换在瑞利波频散曲线提取中的应用

Study on extraction method of dispersion curve by generalized S-transform

虽然一些时频分析方法已经被用于频散曲线提取中,但是它们自身时频窗的缺陷使的所得频散曲线信息缺失或错误.本文首次尝试利用广义S变换分析瑞利波的频散特性.以半空间模型为例确定方法的可行性,频散曲线变化准确反映地层变化情况.不同炮检距设置对频散曲线有一定影响,采用大于勘测深度,小于4倍勘测深度可以得到较稳定的结果.最后,为了得到更加光滑稳定的频散曲线,提出了一种基于多道瑞利波的改进方法.用此方法对四种典型地层模型下的多道瑞利波数据进行分析,得到频散曲线光滑稳定,且比理论频散曲线和基于单道法获得频散曲线更能准确反映地层变化情况.这就为瑞利波勘探中的反演解释提供了更可靠依据.

Although several time-frequency analysis methods have been used to extract dispersion curve, the defects of time-frequency window make some information of dispersion curve missing or wrong. S-transform is an extension of the ideas of CWT, and is based on a moving and scalable localizing Gaussian window. It have some desirable characteristics that are absent in the STFT and CWT. In this paper we try to analyze the dispersive characteristics of Rayleigh wave by generalized S-transform. Firstly, through comparing time-frequency domain waveform of Rayleigh wave with its time-domain and the frequency-domain waveform, we find that the time-frequency domain waveform of Rayleigh wave respects the characteristic of Rayleigh wave accurately. And then, the method based on the single channel Rayleigh wave has been proposed. In order to testify the feasibility of the new method, the half-space model and four typical stratigraphic model are taken as an example to extract the dispersion curve of Rayleigh wave. Study results show that the GST method has great application value in the analysis of Rayleigh wave dispersion characteristics. We also talk about the stable of the new method by the measured data, and analyze the influence of different offset for the dispersion curve. The results show that too large or too small offset may produce inaccurate result. Under normal circumstances, taking offset between the exploration depth and 4 times of exploration depth, we can get good result. At last, in order to get more smooth and stable dispersion curve. We propose a new algorithm that is based on the multi-channel Rayleigh wave. Several examples are given to prove the new method, comparing the new curve to the dispersion curve getting by single-channel method and theoretical curve, we know the new dispersion curves reflect the situation of formation accurately, and it is more smooth. This provides reliable basis for inversion interpretation in Rayleigh wave exploration.