基于广义S变换的地震资料谱分解技术研究

[收稿日期]2007212207　[作者简介]郭爱华(19812),女,2003年大学毕业,工程师,现主要从事地震地质综合解释方面的研究工作。

基于广义S 变换的地震资料谱分解技术研究
郭爱华　(冀东油田分公司勘探开发研究院,河北唐山063004)
路鹏飞,刘　鹏　(中国科学院地质与地球物理研究所,北京100029)
张会来　(中国石油大学资源与信息学院,北京102249)
[摘要]谱分解技术一般采用短时Fourier 变换和连续小波变换。

短时Fourier 变换的分析时窗是恒定的,
不随频率的变化而自动调节,连续小波变换的尺度与频率的关系并不确定。

广义S 变换具有优良的时频
聚集性和时频分辨率,它综合了短时Fourier 变换和连续小波变换的一些优点,而克服了它们的不足,同
时通过调节时窗宽度因子可以获得更好的时频分辨率。

研究将其应用于地震资料的谱分解中,给出了基
于广义S 变换的谱分解业务流程,并对实际地震资料进行了分析。

结果表明该方法是可行的。

[关键词]谱分解;时频分析;连续小波变换;广义S 变换
[中图分类号]P631144[文献标识码]A [文章编号]100029752(2008)0320083204
谱分解技术是近年来发展起来的一项基于频率谱分解的储层特色解释技术,是地震属性分析中的重要组成部分[1～4]。

1999年,BP 1Amoco 石油公司的Greg Partyka 等人利用短时Fourier 变换(Short Time Fourier Transform ,STF T ),研究在短时窗内通过频谱分解来研究薄层变化,并提出了谱分解概念[5]。

2001年,Landmark 在此基础上推出了Spect raDecom 工具;随后,Schlumberger 公司与Land 2mark 公司合作在Geo Frame 软件中加入了Spect raDecom 工具;2004年,Paradigm 公司利用Gabor 2Morlet 小波变换推出了Spect ral Decompo sition 工具。

地震波在地层介质中传播,由于散射和吸收衰减等均与频率有关,严格意义上属非平稳信号。

由于Fourier 分析使用的是一种全局变换,无法表达信号的时频局部性质,而这种性质恰恰又是非平稳信号最根本和关键的性质。

由此,研究人员分别应用短时Fourier 变换、Gabor 变换[6]、连续小波变换(Continuous Wavelet Transform ,CW T )对谱分解中的频谱分析方法进行改进[7]。

1996年,R 1G 1Stockwell 综合短时Fourier 变换和小波变换的特点,提出了一种非平稳信号分析和处理的方法———广义S 变换,它是以Morlet 小波为基本小波的连续小波变换的延伸[8]。

同小波变换、短时Fourier 变换等方法相比,广义S 变换有其独特的优点,如信号的广义S 变换的时频谱分辨率与频率相关,不但有多尺度聚焦性,而且与其Fourier 谱直接相联系,保持频率的绝对相位;其基本变换函数不必满足容许性条件等。

同Wigner 分布、Cohen 等双线性变换相比,广义S 变换是线性的,不存在交叉项,更有利于分离信号,特别是存在噪声的情形[9,10]。

谱分解技术的核心模块为地震信号的时频分析,笔者将广义S 变换应用于地震资料的谱分解中,来提高刻画和识别特殊地质体的水平。

1　广义S 变换基本原理
设h (t )∈L 2(R ),(L 2(R )表示实数域上的平方可积函数空间),h (t )相对于分析小波w (t )的广义S 变换定义为:
S (τ,f )=∫∞-∞h (t )×g f (t -τ)×exp (-2πi f 0f t )d t (1)
式中,S (τ,f )是h (t )的广义S 变换;g f (t -τ
)=A |f |exp [-α(f (t -τ)-β)2]是高斯窗函数;t 是时间;・
38・石油天然气学报(江汉石油学院学报)　
2008年6月　第30卷　第3期Journal of Oil and G as T echnology (J 1J PI )　J un 12008　Vol 130　No 13
τ是控制时间轴上的位置;f 是频率;f 0为视频率。

分析小波为:
w (t )=A ×exp [-α(t -τ)2-2πif 0t ](2)式中,A 为分析小波的幅度;α为能量衰减率(α>0);β为能量延迟时间。

w f (t )=A |f |exp [-α((f t -τ)-β)2-2πi f 0f t ]=g f (t )exp (-2
πi f 0f t )(3)其中,高斯窗函数:
g f (t )=A |f |exp [-α(f t -β
)2](4)广义S 变换的反变换公式为:
h t
f 0=f 0×IFF T 1
A απ×y (f )(5)
IFF T 表示Fourier 反变换。

y (f )=
∫∞-∞S (τ,f )d τ(6)令f 0=1、α=2p 2f 2、β=0、A =|f |p ×2π,采用如下形式的广义S 变换公式:
S (τ,f )=∫∞-∞h (t )×|f |p ×2πexp -f 2(τ-t )22p 2exp (-2πi f t )d t (7)式中,p 为时窗宽度因子,大于0(当p <1时,时窗宽度随信号频率反变化的速度加快,反之,则减慢。

由Fourier 变换的尺度变化性质可知,时窗函数在时域的窗长压缩对应其在频域的频带拉伸,反之亦然。

根据Heisenberg 不确定性规则,为了获得较好的时间分辨率,要选择窗长较窄的窗函数,频率域分辨率必然受到损失;为了提高频率分辨率,选择频率窗较窄的窗函数,其时间窗就较宽,故达不到很好的时间分辨率);
τ是控制时间轴上高斯函数g f (τ-t )=|f |p ×2
πexp -f 2(τ-t )22p 2的位置。

其反变换为: h (t )=∫+∞-∞∫+∞-∞S (τ,f )d τexp (2πi f t )d f (8)
2　基于广义S 变换的地震资料谱分解技术
211　谱分解技术基本原理
谱分解技术的理论基础是薄层反射系统可产生复杂的谐振反射原理,通过分频处理技术得到各频率下的地震能量属性和相位属性。

实际的地震波常常是地下多个薄层的综合响应。

但是由这些薄层组成的层组所产生的复杂的调谐反射在频率域却是唯一的,由于每个薄层产生的地震反射在频率域都有一个与之相对应的特定频率成分,该频率成分可以指示薄层的时间厚度。

对于厚度小于1/4波长的薄层而言,在时间域,随着薄层厚度的增加,地震反射振幅逐渐增加。

当薄层厚度增加至1/4波长的调谐厚度时,反射振幅达到最大值。

然后,随着薄层厚度的增加(越来越大于1/4波长),反射振幅逐渐减小。

时间域的最大反射振幅值,对应着频率域的最大振幅能量值。

频率的横向变化是指示油气可能存在的另一重要信息,当地震波通过含油气地层时,主频向低频方向移动,在浅层频移范围较大,深层由于反射频率随层深的增加高频衰减,移动范围小。

频率的横向变化代表了岩性的横向变化,如果频率横向变化小,说明地层稳定,往往出现在低能环境中;如果频率横向变化大,说明岩性迅速变化,产生在高能沉积环境中。

谱分解主要包含单频体(单一频率能量体和单一频率相位体)和调谐体(调谐能量体和调谐相位体)。

212　谱分解技术业务流程
谱分解技术主要包含确定广义S 变换中时窗宽度因子(多道统计)、单一频率能量体和单一频率相位体、调谐能量体和调谐相位体几个部分。

21211　确定广义S 变换中时窗宽度因子
在地震数据分析中,为了获得较好的时间分辨率,要选择窗长较窄的窗函数,频率域分辨率必然受到损失;为了提高频率分辨率,选择频率窗较窄的窗函数,通过调整时窗宽度因子可以实现这一目的。

・48・　石油天然气学报(江汉石油学院学报)2008年6月
图1　单频体分析业务流程图　图2　调谐体分析业务流程图时窗宽度因子的确定制约着广义S 变换的分辨
率。

在实际工作时,可以根据所研究目的层,选取几道地震数据进行时频分析实验,来确定
时窗宽度因子。

在单频体与调谐体的计算中,
选择上述确定的时窗宽度因子参与运算。

21212　单频体计算
单频体的计算是整道地震数据参与运算,
根据目标地质体的尺度,选择适合的频率值。

输出的数据体,包含两种形式单一频率能量体
和单一频率相位体。

可以以切片的形式进行分
析和研究。

其实现流程如图1所示。

21213　调谐体计算
调谐体的计算是沿层位开时窗,利用广义
S 变换计算目的层位的单一频率或相位值,根
据目标地质体的尺度,选择适合的频率值。

计
算的结果赋给曾为数据的网格点上。

通过谱平
衡处理消除子波重叠效应。

其实现流程如图2所示。

3　实际地震数据广义S 变换谱分解
图3　某工区二维地震剖面
图3为某工区一段二维
地震数据,共73道,每道
401个样点,采样率2ms ,
起止时间为500～1300ms 。

在1050～1085ms 、38～43
道间存在一个小透镜状砂体。

在剖面中取几道地震数据进
行分析,以确定广义S 变换
的时窗宽度因子,本研究选
用019。

利用单频体分析业
务流程,提取29Hz 频率能
量和相位数据,并在图4、5中显示对应的剖面数据。

在
原始地震剖面中无法识别出上述的透镜状砂体,在29Hz 频率能量剖面中可以很好地刻画。

4　结 论
1)广义S 变换综合了短时Fourier 变换和小波变换的优点,是目前非平稳信号分析和处理的较优方法;与短时Fourier 变换、小波变换等时频域分析方法相比,不但有多尺度聚焦性,而且与其Fourier 谱直接联系,保持频率的绝对相位;分析时窗随频率的变化而自动调节。

通过调节时窗宽度因子可以获得更好的时频分辨率。

2)谱分解技术提供了利用三维地震资料的多尺度信息对储层进行高分辨率成像、并刻画储层时间厚度变化的工具。

该技术可应用于描述沉积相和沉积环境,如检测河道砂体的空间分布,对侵蚀充填的・58・第30卷第3期郭爱华等:基于广义S 变换的地震资料谱分解技术研究　
砂体空间分布进行成像等。

谱分解技术的核心模块为地震信号的时频分析。

研究将广义S 变换应用到谱分解中,并给出了相应的处理和解释流程。

3)研究中的谱分解方法,也适用于三维地震资料的构造、岩性分析和解释。

图4　29H z 能量剖面
图5　29H z 相位剖面
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[编辑]　弘　文
・68・　石油天然气学报(江汉石油学院学报)2008年6月
tion;College of Geophysics and Oil Resources,Yangtze Universit y,J ingz hou434023,H ubei,China)
Abstract:To truly reproduce t he underground geologic model of t he sout hern Fault Block Hu7in Huzhuangji Oilfield,on t he basis of structural characteristic analysis wit h3D seismic data,a fault section contour map of main fault s was plotted by using more dense well pattern data,by which t he fault sectional style and it s structural high point s of t he main fault were proven for t he purpose of making more precise structures1On t he basis stated above,a3D model was established wit h rational simulating met hods,a contour map was drawn by5m vertical interval1The determined modeling met hod is used to establish a3D structural model of t he sout hern Fault Block Hu71it can be seen t hat on t he basis of restudy of structures,local structural high point s are newly found,t he established fault model and structural model provide a solid basis for establishing a precise geologic model1
K ey w ords:structural pore;fault model;structural model;sout hern Fault Block Hu7
75Method of U nrestricted Datum W avef ield Imaging with Irregular Surfaces
XI ONG X iao2jun,HE Zhen2hua,H UANG De2ji　(S tate Key L aboratory of Oil and Gas Reservoi r Geolog y and Ex ploration, Cheng du Uni versit y of Technolog y,Cheng du610059,S ichuan,China)
Abstract:A new met hod of post2stack seismic forward modeling under complex surface conditions was proposed from t he point of seismic modeling1It used t he t heory of submerse topography and zero2velocity layer,t he new met hod firstly transformed t he original surface(in2 put datal)to a level(output datal),and got a new model1Then,t he original surface was just one part of t he new model1Secondly,it set a zero2wavefield transmission layer between t he input data and t he output data in t he course of wavefield continuation wit h traditional wavefield continuation operators,and realized t he post2stack seismic forward modeling under complex surface conditions1Based on t he new met hod,an integrated wavefield continuation flow wit h unrestricted data is developed and t he wavefield continuation is expanded to
a optional data,which is very important for studying t he transmitting principle of seismic wave,following migration and seismic interpre2
tation1Result s of t heoretical model prove t he correctness and validity of t he new met hod1
K ey w ords:wavefield imaging;unrestricted datal level;irregular surface;post2stack seismic forward modeling;wavefield continuation 78Magnetic Interfacial Inversion Using Du al Interface P attern B ased on P arker Algorithm XI ANG Peng,LI U Zhan　(College of Georesources and I nf ormation,Chi na Universit y of Pet roleum,Dong ying257061,S han2 dong,Chi na)
Abstract:A unstable factor,t hat was a downward continuation operator was included in Parker interface inversion,by which unsteady was caused1The common practice was to put a low pass filter in inversion to control t he high frequency oscillation1This met hod was to avoid high frequency false wave and compress t he effective signals and cause t he decrease on inversion precision1The inversion formula was rederived1Formulae for inversion of dual magnetic interfacial pattern and a met hod for solving t he problem of inversion divergence were proposed1The forward inversion equation is rational and adaptable in application,an approach is provided for solving t he inversion divergence ensuring t he convergence1Key techniques and measures for implementing t he algorit hm are discussed1Modeling is used to prove it s accurate and adaptability,it can be found t hat t he met hod is high accuracy wit h error of018%to4%1The met hod is used for magnetic data processing,better effect is obtained1
K ey w ords:dual2interface pattern;interfacial inversion;magnetic inversion;Parker met hod
83Spectral Decomposition T echnique for Seismic Data B ased on G eneralized S T ransform(G ST)
G UO Ai2hua　(I nstit ute of Oil Ex ploration and Development,J i dong Oil f iel d Com pany,CN PC,T angshan063004,Hebei,Chi2
na)
LU Peng2fei,LI U Peng　(Research I nstit ute of Geology and Geop hysics,Chi nese A cadem y of S ciences,Bei j i ng100029,China) ZH ANG Hui2lai　(Facult y of Resources and I nf ormation,China Universit y of Pet roleum,B ei j ing102249,China)
Abstract:Short2time Fourier Transform(STF T)and continous wavelet transform(CWT)were generally used in spectral decomposi2 tion1Time2window analysis of STF T was constant,it was not automatically adjusted wit h frequency changes;while t he relation between size and frequency of CW T was not certain1Generalized S transform(GST)had high time2frequency resolution and good time2frequency localization1It had t he advantages of STF T and CW T and overcame t heir shortcomings,t hus better time2frequency resolution could be obtained by adjusting t he factors of time2window widt h1GST is used for spectral decomposition of seismic data and it s flow chart is pro2 vided,it is used for actual analysis of seismic data1Application shows t hat it is feasible1
K ey w ords:spectral decomposition;time2frequency analysis;CW T;GST
87W avelet Frequency2division Process for Seismic Signals
H UANG Han2dong,ZH ANG Ru2wei　(Facult y of Resources and I nf ormation,China Universit y of pet roleum,Bei j i ng102249,
China)
G UO Y ing2chun　(Research I nstit ute of Geosciences,S hengli Oil f iel d Co1L t d1,S I N O P EC,Dong ying257062,S handong,Chi2
na)
Abstract:Wavelet transform had t he characteristics of multi2resolutions and“mat hematical microscope”,it was widely used in pre2stack and post2stack data process1It was different from commonly used high resolution process,wavelet transform could improve t he resolu2 tion of seismic recording and effectively avoid t he interference of noise1The basic principle of wavelet frequency division is first denoted, by forward and inverse transform of seismic signals synt hesized wit h t heoretical model,deep implication of frequency2division of seismic data is fully revealed1The seismic signals are processed based on t he studied met hod,better application effect is obtained1Important ba2 ses are provided for t he introduction and application1
K ey w ords:wavelet transform;high resolution;noise removal;t heoretical model;seismic signal
92R esearch and Application of Seismic Forw ared Modeling of T riassic R eservoir in T ahe Oilf ield CAI Cheng2guo,ZH AO Y ing2yue　(College of Geop hysics and Geomatics,Chi na Universit y of Geosciences,W uhan430074,H u2 bei,China)
G U Han2ming　(College of Geophysics and Geomatics,China Universit y of Geosciences,W uhan430074,H ubei,China;Key L abo2
ratory of Tectonics and Pet roleum Resources(China Universit y of Geosciences),Mi nist ry of Education,W uhan430074,H ubei,Chi2 na)
Abstract:In Tahe Oilfield,t here existed lateral heterogeneity,seismic response characters were complex,reservoir prediction was seri2 ous multiplicity and low drilling success ratio in Triassic reservoirs,to find out t he sensitive attribute of clastic rock reservoirs was badly needed for improving t he interpreting accurate1A model for Triassic sandstone reservoirs was established based on well logging,drilling and testing data,t he staggered finite difference of2D acoustic wave equation derived under heterogeneous condition was used for forward calculating t he sandstone reservoir by using field data acquisition system1The CMP record was processed by conventional flow,and stacked and deviated sections were obtained,t he response characters of pinchout sand bodies are analyzed,t he seismic attributes such as root2mean2square amplitude and it s variation are determined as sensitivety parameters of oil and gas reservoirs,a concept seismic2geologic model of sublacustrine fan reservoir is established,by which t he multiplicity and limitation are reduced for prediction,a basis is provided for seismic interpretation1
K ey w ords:forward simulation;seismic attribute;reservoir prediction;Tahe Oilfield
96Seismic Attribute Optimization and Its Application in R eservoir Prediction by Using K2L T ransform WANG X iao2yang,G UI Zhi2xian,G AO Gang,ZH ANG Wei　(Key L aboratory of Ex ploration Technologies f or Oil and Gas Resources(Yangtze Universit y),Minist ry of Education;College of Geop hysics and Oil Resources,Yangtze Universit y,J ingz hou 434023,H ubei,China)
Abstract:on t he basis of fine interpretation of seismic data and in combination wit h seismic attribute optimization,t he original seismic at2
Ⅶ。