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物探与化探, 2018, 42(3): 528-536 doi: 10.11720/wtyht.2018.1216

方法研究·信息处理·仪器研制

海洋地震变深度电缆采集数据的频谱分析及消除鬼波研究

金明霞, 宋鑫, 易淑昌, 张冰

中海油田服务股份有限公司物探事业部物探研究院,天津 300451

The frequency analysis of VDS and its application to deghosting

JIN Ming-Xia, SONG Xin, YI Shu-Chang, ZHANG Bing

Geophysical Research Institute,COSL,TianJin 300451,China

责任编辑: 叶佩

收稿日期: 2017-05-15   修回日期: 2018-03-22   网络出版日期: 2018-06-05

基金资助: 中海油田服务股份有限公司物探专项.  WTB16YF013

Received: 2017-05-15   Revised: 2018-03-22   Online: 2018-06-05

Fund supported: .  WTB16YF013

作者简介 About authors

金明霞(1979-),女,工程师,2004年毕业于长江大学获硕士学位,目前在中海油服物探事业部物探研究院从事数据处理工作。 。

摘要

为拓宽有利于地震成像的频带范围,特别是拓宽对中深层地质构造成像有利的低频,物探工程师提出和改进了很多采集技术与方法,其中较为成功的技术是斜缆宽频采集技术,其原理是斜缆采集使得虚反射的陷波频率点不同。笔者重点分析了变深度电缆对地震资料频谱特征尤其是低频的影响,提出振幅曲线的陡度函数是测量信号在低频端丰富程度的有效方法,并通过模型正演比较了由等深的水平缆和变深度的斜缆采集的地震道频谱特征;然后针对虚反射引起的鬼波难题,采用修改的线性最小平方Radon变换方程来消除虚反射产生的鬼波,然后分别应用于正演模型和实际的南海斜缆地震资料,均取得较好的去鬼波效果。

关键词: 变深度拖缆 ; 陷波频率 ; 去鬼波 ; 最小平方Radon变换

Abstract

The quality of seismic data has been improved with the application of variable-depth streamers (VDS) acquisition,which leads to diversity of receiver ghost notch,and the key advantage is the utilization of notch diversity to combine different depth receivers,thus achieving the final better result which has no notches.This paper focuses on the effects of VDS acquisition on frequencies especially on low frequencies that benefit the images of deep geological structure.The slope function provided by this paper can effectively gauge the extent of low frequencies,and it is easy to find the frequency difference between shots modeled by conventional constant depth streamer (CDS) and ones modeled by VDS;In addition,considering the ghosts caused by the marine free surface,the method outlined in this paper derives a surface datum ghost free result of input shot gather data by using the modified least squares linear Radon equations.Its application to model data and real VDS seismic data shows that this deghost algorithm can effectively suppress the ghosts.

Keywords: variable-depth streamers ; notch frequency ; deghost ; the least squares linear Radon equation

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本文引用格式

金明霞, 宋鑫, 易淑昌, 张冰. 海洋地震变深度电缆采集数据的频谱分析及消除鬼波研究. 物探与化探[J], 2018, 42(3): 528-536 doi:10.11720/wtyht.2018.1216

JIN Ming-Xia, SONG Xin, YI Shu-Chang, ZHANG Bing. The frequency analysis of VDS and its application to deghosting. Geophysical and Geochemical Exploration[J], 2018, 42(3): 528-536 doi:10.11720/wtyht.2018.1216

0 引言

常规的拖缆采集中,拖缆的深度一般在5~10 m,这样的拖缆深度限制了有效信号的低频成分[1],并且由于近海水表层噪声太强使得接收到的信号信噪比较低。将拖缆沉放的深度增加有利于拓宽低频信号、减少噪声,但同时以牺牲高频为代价,这是由于检波器虚反射的第一个陷波频率造成的。

虚反射引起的频率陷波问题在震源和接收点都存在,对于震源虚反射引起的频率陷波通过采用多级不同深度的震源组合,然后通过延迟响炮的方式可有效消除虚反射的影响[2],而对于检波点虚反射引起的频率陷波,最早采用上下电缆的方法来克服[3,4,5],但这种方法采集成本过高;后来又在电缆的接收点压力检波器的基础上加上了速度检波器(对信号的传播方向敏感),即双检采集[6,7],不过这种技术对仪器性能要求很高;Robert等[8]提出的变深度电缆(即斜缆勘探)的采集方式,由于检波器的沉放深度影响着接收信号的有效频率,有效信号的低频和高频之间相互牵制,斜缆勘探中从最近的地震道开始,拖缆的深度随着炮检距的增大而变深,将拖缆保持在一个预定的目标深度,斜缆勘探中拖缆的深度可达60 m。

斜缆勘探观测方式的独特性,为斜缆宽频地震勘探带来了以下几点优势[9]:首先随着拖缆变深,远偏移距接收到的信号受到海水表层噪声的影响越来越小,地震资料的信噪比越来越高。其次,由于拖缆深度不同,虚反射陷波频率点存在差异,随着拖缆沉放的加深,检波器虚反射陷波频率点的数量会成倍的增加,而斜缆勘探就是利用虚反射陷波频率点的不同来消除虚反射陷波的影响。采集的资料中低频和高频更加丰富,频带范围可以达到2.5~200 Hz。由于采集到的地震资料有着丰富的低频、高频信息,这对于提高地震分辨率,深部地质体和复杂盖层之下的目的层的成像、地层内部构造的精细刻画都具有重要意义[10]

对于如何消除虚反射生成的鬼波,Wang等[11]采取F-XY域进行联合反演来压制鬼波;Soubaras[12,13,14]提出联合反褶积的方法来消除鬼波。国内许自强等[15]利用变深度电缆的原始炮集记录和生成的镜像炮集记录,然后使用最优化联合反褶积方法去鬼波;张振波等[16]以白云凹陷深水斜缆地震资料为例,详细说明了针对斜缆资料的处理流程;王冲等[17]采用计算出的下行波与实际下行波之间的平方误差最小理论来实现自适应反演迭代出最优鬼波,然后进行压制。

针对变深度电缆采集方式如何影响频谱,笔者做了较为详细的分析,尤其分析了斜缆采集能拓宽地震数据有效频带的机理及对中深层地质构造成像有利的低频信号强度,并通过模型正演分别对比了等深电缆和变深度电缆对地震道频谱的影响,再利用Poole[18]修改的线性最小平方Radon变换方程来消除虚反射产生的鬼波。正演模型和实际南海斜缆地震资料处理结果表明,去鬼波效果很好。

1 变深度电缆对频谱的影响分析

1.1 变深度电缆拓宽频率的机理分析

检波器虚反射的陷波频率与海水的速度c,检波器的深度d等因素有关,可用式(1)近似表示:

fn=nc2d n=0,1,2,

其中,fn表示沉放在d深度处检波器虚反射的第n个陷波频率。从公式分析可知,拖缆沉放越深,第一陷波频率越小,高频损失越严重。

在反射波垂直传播,即一维(1D)情形下 kz=w/c,根据w=2πf,虚反射算子的函数[13]是:

G(f,z)=1-e-i2zkz=1-e-i4πfz/c

利用式(2)将不同深度检波器虚反射的频谱进行叠加得到式(3)

G(f)=1Ni=1N(1-e-i2π),

发现不同深度检波点之间的陷波点得到了相互补偿,低频和高频成分得到了拓展。式中:τ= 2zic,其中zi是拖缆各个检波点的深度,c是水速。

根据式(2),虚反射的振幅谱的函数是:

|G(f,z)|=abs[2sin(2πfz/c)]

图1所示,检波点的沉放深度分别在7.5、15、35 m时,检波器虚反射陷波点不同,检波点在35 m时,虚反射的陷波点最多,出现的周期最短;当在7.5~50 m深度之间放置多个检波器,然后把不同深度检波器虚反射的频谱进行叠加,可以看到虚反射陷波点得到补偿,低频成分更加丰富,同时高频得到了拓展,如图1中红色曲线所示。

图1

图1   不同深度检波器虚反射频谱


比较图1中深度分别为7.5、15、30 m的频谱,发现接收点沉放的越深其振幅谱曲线越陡,并因此显著拓宽低频成分(如图1中蓝色曲线较之于紫色曲线低频成分明显提高),振幅曲线的陡度函数

slope(f,z0)=f|G(f,z)|=4πz0ccos2πz0cf 

即是振幅谱的导数。分析这个陡度函数发现在低频带尤其是1~12.5 Hz范围内,接受点越深,振幅谱越靠近振幅轴即接受到的信号低频成分越丰富,其原因是对于沉放深度是30 m的虚反射的振幅谱在12.5 Hz时信号达到峰值2(据公式4),图2截取了12.5 Hz以内的接受点深度分别是7.5、15、30 m的振幅谱曲线。

图2

图2   截取图1中不同深度的小于12.5 Hz的频谱曲线


在低频带取频率分别为2、3.5、5 Hz,并求解其振幅强度如表1所示。

表1   图2中沉放不同深度检波点在不同低频的振幅值

深度/m频率/Hz
23.55
7.50.12560.21950.3129
150.25070.43630.6180
300.49740.85161.1756

新窗口打开| 下载CSV


表1分析得出:较之于7.5 m的沉放深度,15 m和30 m的信号振幅强度在2、3.5、5 Hz大幅提高,如表2所示。

表2   沉放深度15、30与7.5 m振幅强度比较(分贝显示)

深度/m频率/Hz
23.55
156 dB5.97 dB5.91 dB
3011.95 dB11.78 dB11.50 dB

新窗口打开| 下载CSV


综上可知,斜缆地震勘探有两个显著优势:①利用检波器虚反射陷波频点的不同,其叠加效果可拓宽频带和补偿陷频点能量;②检波点越深低频信号(小于5 Hz)的振幅越强。所以,采集到的地震资料信噪比较高、频带较宽,这是获取高信噪比、高分辨率、宽频带地震资料的基础和前提。

1.2 等深电缆和变深度电缆对地震道频谱的影响分析

通常虚反射产生的鬼波对一次波的影响主要跟它们之间的时差有关,当时差较小时,鬼波和一次波重叠在一起并因此改变了一次波的波形;当时差增大到半个周期时,鬼波对一次波的影响最大;当时差大于一个周期后,鬼波独立地跟在一次波之后形成尾巴。对于斜缆观测系统,由于检波器的深度随着偏移距的增加而变深,因此,鬼波和一次波的时差越来越大,表现在炮记录上为检波器鬼波与一次波逐渐分开。

图3是设计的速度模型,模型大小3 000 m(水平长度)×2 100 m(垂直深度),网格大小1 m×1 m。观测系统参数为:震源深度5 m,水平电缆缆深度15 m,斜缆深度15~67.37 m,接收点间距10 m。分别在水平缆和斜缆观测系统下进行波动方程正演模拟,进而研究其波场特征。

图3

图3   速度模型与水平缆观测系统(左)、斜缆观测系统(右)


正演模拟结果如图4a、4b所示。对水平缆资料分别取第10、30、50道数据 ,进行频谱分析(图5)。

图4

图4   正演模拟的炮集

a—水平缆;b—斜缆


图5

图5   对水平缆中第10(左)、30(中)、50(右)道数据频谱分析结果


对于检波器的深度为15 m,水层速度为1 500 m/s,由公式f= nv2d可知,陷波点出现在50、100、150 Hz、…的位置。由于水平缆上所有检波器都位于同一深度,所以水平缆上每一道地震数据对应的陷波点都相同(如图5中各道数据的频谱分析结果所示),那么将不同偏移距的数据合并之后,依然会在相同的位置上出现陷波点(图6)。

图6

图6   对水平缆正演结果进行频谱分析的结果


对于斜缆数据,也取第10、30、50道数据,进行频谱分析,结果如图7所示。

图7

图7   对斜缆数据中第10(左)、30(中)、50(右)道数据频谱分析结果


由于斜缆中检波器深度随偏移距的增加而增加,使每一道数据的陷波点都不相同,各道数据第一陷波频率点逐渐向左移动,因此,将不同偏移距的频率进行叠加之后,各道数据的陷波点相互补偿,最终达到了增加有效频带宽度的效果(图8)。

图8

图8   对斜缆数据进行频谱分析的结果


2 变深度电缆虚反射的消除方法

2.1 修改的线性最小平方Radon变换

已知的频率域τ-p变换是:

d(xn)=Lm(pj),

其中,L= e-iwτi,j, i=1,2,…,N,j=1,2,…,M。式中,w=2πf,τi,j=pjxi,f是瞬时频率,xi表示炮集中第i道的炮检距,pj表示τ-p模型中第j道的慢度值,m(pj)是映射得到的τ-p域数据,根据式(6)采用最小平方法使目标函数J=‖d-Lm2最小,得到m

在斜缆勘探中需要对水平缆线性Radon变换的方程进行修改[18],由于斜缆数据中既存在一次波,也存在虚反射,因此,斜缆线性Radon变换的算子需要改写为两个部分:

Lud=Lu+RLd,

其中:Lu=exp(-ipr),Ld=exp(-igh)。

Lu表示一次波反变换算子,应用此算子可以得到电缆数据;Ld表示虚反射的反变换算子,应用此算子可以得到镜像电缆数据,τpr表示一次波的旅行时间,τgh表示虚反射的旅行时间。因此,可以利用这两个算子求解斜缆线性Radon变换的方程,从而得到海平面没有虚反射的数据。

在二维观测系统平面波传播情况下(图9),斜缆勘探中上行的一次波(蓝色线)到达检波点的时间相对于海平面的检波点接收的一次波时间提前了Δτ,而斜缆中下行的鬼波(粉色线)相比于海平面上检波点接收的一次波时间推迟了Δτ,因此,水平缆的Radon变换方程(6)在此不再适用,根据图9中给出的射线关系和已知量可以得到斜缆中的上行一次波和下行的虚反射到达斜缆检波点的时间。

τpr=(xn+Δhn,m)pm-Δτn,mτgh=(xn-Δhn,m)pm+Δτn,m

其中:

sinθ=pmvw;Δhn,m=zrtanθ;Δτn,m=zr2+Δh2/vw

θ表示射线角,vw是地震波在海水中的传播速度,检波点所在位置的炮检距是xn其对应的深度为zr,pm射线参数,Δhn,m表示斜缆中检波点与对应海平面上检波点的水平距离,Δτn,m表示斜缆一次波与虚反射相对于海平面接收的一次波的时差;τpr表示一次波的旅行时间,τgh表示虚反射的旅行时间。

图9

图9   斜缆勘探二维观测系统平面波传播示意


根据上述对斜缆Radon变换消除虚反射的原理,形成了两种处理流程(图10a、10b)。实际资料处理的经验表明:对于浅水海域,如渤海地区,由于直达波与有效波混在一起,不能切除直达波,采用图10a的流程;对于深海深水海域,如南海地区,采用图10b流程进行处理比较合理。

图10

图10   斜缆线性Radon变换消除虚反射的两种处理流程


2.2 消除斜缆虚反射的应用

2.2.1 正演模型测试

设计如图11的一个凹陷地质模型,模型大小4 201 m(水平长度)×6 100 m(垂直深度),网格大小1 m×1 m;采集参数参数是:震源深度5 m,检波点深度由4 m变化到48.6 m,最小炮检距125 m,道间距12.5 m,每炮240道,共300炮。

图11

图11   凹陷模型


图12

图12   正演模拟对应的斜缆观测系统


图13a是原始单炮记录,清楚地看出存在虚反射(鬼波),图13b是利用改进的线性Radon变换方法消除虚反射(鬼波)后的单炮记录。图14a是消除虚反射之前的叠偏剖面,图14b是消除虚反射后的叠偏剖面,消除鬼波后的凹陷边界成像更加清晰。

图13

图13   消除虚反射前(a)后(b)对应的炮记录


图14

图14   消除虚反射前(a)后(b)的偏移叠加剖面


2.2.2 实际资料应用

以南海实际斜缆地震资料为例,该资料是深水资料,水深在1 500 m以上,资料信噪比较好,斜缆数据中一次波和虚反射在同相轴表现为随着炮检距的增加,二者时差也越来越大,该炮记录已进行了相应的去噪处理,但未做去多次波。

图15是消除虚反射前、后的斜缆炮记录,其中蓝色箭头所指的位置是虚反射同相轴消除前后的比较,其中多次波的虚反射能量也得到一定压制。从图16中可以看到消除虚反射后,原始炮记录频谱中虚反射的陷波点得到补偿,且消除虚反射之后的频带有所拓宽。

图15

图15   原始炮记录(a)及消除虚反射的炮记录(b)


图16

图16   消除虚反射前后的频谱曲线


比较原始数据叠加(图17)和消除虚反射数据后的叠加剖面(图18),在叠加剖面上虚反射得到了消除(尤其是图中的矩形框和箭头所指位置)。通过频谱分析(图19)比较,消除虚反射之后的叠加剖面频谱(红色线)的低频和高频成分比原始叠加剖面的频谱能量(蓝色线)更丰富,频带也得到了一定拓宽。

图17

图17   原始数据的叠加剖面


图18

图18   消除虚反射之后的叠加剖面


图19

图19   图16、17中方框的频谱分析对比


3 结论

在反射波垂直传播即一维(1D)情形下,通过对变深度电缆的虚反射的频谱分析得出:①检波器沉放深度不同使得接收点的虚反射陷波频率点存在不同,其叠加结果会使频谱拓宽;②分析频谱曲线的陡度函数,沉放较深的检波点使得在低频端尤其小于5 Hz的低频信号的振幅强度显著增强。

与等深的水平缆产生的鬼波相比,斜缆采集方式使得虚反射引起的鬼波在中远道与一次波逐渐分离;正演模型和南海实际斜缆地震资料应用效果表明,采用修改的线性最小平方Radon变换方程(不同于水平缆的去鬼波方法)能够有效压制鬼波。

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