三参数W变换的可逆性
Reversibility of three-parameter W transform
刘保童 1刘启源 2黄翼坚 3康学福 1刘东林 1姜英爽1
作者信息
- 1. 天水师范学院电子信息与电气工程学院,甘肃天水 741001
- 2. 四川大学数学学院,四川成都 610064
- 3. 西北大学地质学系大陆动力学国家重点实验室,陕西西安 710069
- 折叠
摘要
三参数W变换(TPWT)是分析非平稳信号的有效工具,已成功应用于油气储层识别.然而,前人没有详细论述TPWT的可逆性.为此,首先回顾了 TPWT的基本原理,然后从理论上探讨了 TPWT的可逆性.理论分析与数值计算结果表明:①TPWT既解决了 S变换(ST)的低频时间分辨率低与时—频谱能量分布中心向高频偏移的问题,也克服了 W变换(WT)时—频谱在主频处的振幅分裂现象,能更准确地描述油气储层,更有利于地震解释.②在理论上TPWT不是严格可逆的,而是一种近似可逆的变换工具,这与傅里叶变换(FT)、ST不同.③合成地震数据与实际地震记录的数值计算结果显示,与原始地震数据相比,利用逆TPWT重建地震数据的相对误差为11.47％～21.35％,即理论上的不可逆导致较大的重建误差,严重影响TPWT的应用范围,在去噪、高分辨率处理等需要重建数据的处理领域不宜使用.
Abstract
The three-parameter W transform(TPWT)is an effective tool for analyzing non stationary sig-nals,and it has been successfully used in oil and gas reservoir identification.However,the reversibility of TPWT has not been discussed in detail in previous studies.Therefore,this paper first reviewed the basic principles of TPWT and theoretically analyzed the reversibility of TPWT.Both the theoretical analysis and numerical calculation results show that:①TPWT not only solves the problems of low time resolution at low-frequencies and shift of the distribution centroid of the time-frequency spectral energy toward higher frequen-cies in S transform(ST)but also overcomes the amplitude splitting phenomenon of the time frequency spec-trum at the dominant frequency in W transform(WT),which can characterize hydrocarbon reservoirs more accurately and is more beneficial for seismic interpretation.②In theory,TPWT is not strictly reversible but an approximately reversible transform tool,which is different from Fourier transform(FT)and ST.③The numerical calculation results of a synthetic seismogram and a real seismogram show that compared with origi-nal seismic data,the relative errors of seismic data reconstructed by inverse TPWT are 11.47％～21.35％,or in other words,the theoretical irreversibility leads to significant reconstruction errors,seriously affecting the application range of TPWT.TPWT is not applicable in fields that require data reconstruction such as de-noising and high-resolution processing.
关键词
时—频谱/三参数W变换/振幅分裂/重建地震数据Key words
time-frequency spectrum/three-parameter W transform/amplitude splitting/reconstruction of seis-mic data引用本文复制引用
出版年
2024
国家科技期刊平台
NSTL
万方数据