广义S变换在背景噪声数据处理中的应用①

李红光1， 孙刚1， 邢艺兰2

(1.中国地震应急搜救中心，北京 100049； 2.北华航天工业学院，河北 廊坊 065000)

摘要：广义S变换解决了标准S变换中基本小波形态固定的缺陷，在分析非平稳信号时能更好地刻画其时频特性。编写广义S变换的计算程序，并用它对地震背景噪声数据进行去噪处理。结果显示：广义S变换处理过的数据信噪比大大提高，可以为数据反演提供更精确的数据。

关键词：广义S变换; 背景噪声; 信噪比； 提高

收稿日期：①2014-12-25

基金项目：国家重大科学仪器设备开发专项(2012YQ16018506)

作者简介：李红光,男,高级工程师，主要从事地震工程、地震信号处理等工作。E-mail：fengzhe122@126.com。

中图分类号:P631文献标志码：A

DOI:10.3969/j.issn.1000-0844.2015.03.0867

Application of Generalized S-transform in Ambient

Seismic Noise Data Processing

LI Hong-guang1, SUN Gang1, XING Yi-lan2

(1.NationalEarthquakeResponseSupportService,Beijing100049,China;

2.NorthChinaInstituteofAerospaceEngineering,Langfang065000,Hebei，China)

Abstract：In this study, we used the generalized S-transform method to improve the signal-to-noise ratio of ambient seismic noise data, and improved the efficiency of geophysical inversion. The S-transform method is a time-frequency representation of local spectral phase properties. A key feature of the S-transform method is that it can uniquely combine a frequency dependent resolution of the time-frequency space and absolutely reference local phase information. As such, the phase in a local spectrum setting can be defined, and this makes possible the production of many desirable wave characteristics. The scaling property of the Gaussian window is reminiscent of the scaling property of continuous wavelets, because one Fourier frequency wavelength is always equal to one standard deviation of the window. In this study, we introduce a variant of the original S-transform, which replaces f with λfp. In this variant, one standard deviation of the Gaussian window contains λfp wavelengths of the Fourier sinusoid at all frequencies. The generalized S-transform solves the defect in the analysis of non-stationary signals caused by the fixed form of the basic wavelet in the S-transform, and the time-frequency characteristics can better describe the non-stationary signals. We wrote a computer program for the generalized S-transform, and for ambient seismic noise we used data denoising. The results showed that the signal-to-noise ratio is greatly improved through the generalized S-transform denoising, and yields more accurate data for the inversion process. There have been few studies on the denoised processing of background noise data using the generalized S-transform, and the resolution of our processing results is better than that achieved by the ordinary S-transform.

Key words： generalized S-transform; ambient noise; signal-to-noise ratio; improvement

0引言

在分析非平稳信号时，传统的傅里叶变换只能将信号从时域对应到一维频域，不能有效地反映非平稳信号的频率随时间的变化，因此很难分析信号的时频变化特性。时频分析方法是将一维的时域信号变换到二维时频平面上，然后在时频域平面上区分并提取信号分量。常用的时频分析方法有短时傅里叶变换、Wigner-Vile分布和小波变换等[1]。

1996年美国地球物理学家Stockwell等[2]提出一种加时窗傅里叶变换方法(S变换)，它吸收并发展了短时傅里叶变换和小波变换[3]。信号S变换的分辨率与频率有关，且其结果具有无损可逆性[4]。但是S变换中的基本小波函数是固定的，这使其在实际应用中受到了限制。高静怀等[5]提出根据“实际需要”恰当地选择或构造基本小波函数的广义S变换方法，并将其应用在地震数据的时频分析工作中。……