基于波动方程的上下缆地震数据鬼波压制方法研究

管西竹， 陈宝书, 符力耘, 陶杰, 李列

1 中国科学院油气资源研究重点实验室，中国科学院地质与地球物理研究所， 北京 100029 2 中海油研究总院, 北京 100027 3 中海石油(中国)有限公司湛江分公司, 广东湛江 524057



基于波动方程的上下缆地震数据鬼波压制方法研究

管西竹1， 陈宝书2, 符力耘1, 陶杰2, 李列3

1 中国科学院油气资源研究重点实验室，中国科学院地质与地球物理研究所， 北京 100029 2 中海油研究总院, 北京 100027 3 中海石油(中国)有限公司湛江分公司, 广东湛江 524057

本文发展基于波动方程的上下缆鬼波压制方法，推导了上下缆地震波场频率波数域波动方程延拓合并公式.基于Fourier变换的波场解析延拓确保上下缆资料振幅相位的一致性，消除了长拖缆远偏移距信号的计算误差，同时具有较高的计算效率；上下缆地震波场的波动方程法合并有效解偶鬼波干涉，实现综合利用上下缆地震数据压制鬼波.理论模型数据和实际采集地震数据的测试表明了方法的有效性.

海上地震采集； 上下缆； 鬼波压制； 波动方程延拓合并； 频率波数域

1 引言

随着海上地震勘探进入深水领域，特别是深部和超深部地质目标的勘探，遇到的瓶颈问题之一是深层反射能量弱，信噪比低.为了增强深层弱反射信号，可采用低频强能量组合枪阵激发，但受海水面的鬼波干涉影响，拖缆接收的地震信号存在严重的陷波作用，导致地震记录频带变窄，分辨率和信噪比降低，特别是持续的鬼波同相轴给地震地质解释造成困难.常规的海上水平单缆地震采集限制了鬼波压制技术的发展(陈金海等，2000).上世纪80年代发展起来的针对鬼波压制的上下缆海上地震采集技术(Sonnenland et al.，1986)，随着采集设备的改进，进入21世纪后得到了长足的发展和实用化应用，在北海、墨西哥湾、中东、中国南海等海域取得了较好的应用效果(Moldoveanu et al.，2007； Wire et al.，2006).

采用上下缆地震采集的目的主要是根据上下缆地震数据不同的陷波特征，设计合并技术来压制鬼波和拓宽频带.一般而言，深缆和浅缆除了陷波特征不同外，在分辨率与信噪比方面还有较大区别.浅缆地震数据低频能量较弱，视分辨率显高，但由于受拖缆漂移影响较大，信噪比较低；而深缆地震数据则相反.这种上下缆数据的不一致性与勘探的海洋环境和海底特征密切相关，极大地增加了合并技术的难度，也降低技术的普适性.早期的合并技术较为粗糙，仅通过简单的上下缆时移校正(相位校正)，然后进行简单相加合并来消去鬼波，拓宽地震频带.虽然算法简单，效率较高，但精度较低，会产生较大的振幅误差和严重的伪海面鬼波(赫建伟等，2013a).传统的上下缆数据相位求和压制鬼波的方法只对相位做校正，没有对振幅进行相应的校正.Posthumus(1993)提出在相位校正过程中，对数据振幅进行加权处理的上下缆合并方法.该方法在欧洲北海油田上下缆地震采集数据过程中进行了实际应用，取得了较好效果(Hill et al.，2006).Özdemir(2008)进一步改进了这种基于相位求和的上下缆合并方法，利用估计的不同缆数据噪声水平，通过最小二乘拟合优化合并结果的信噪比.Ferber(2008)提出了一种时移校正后相减的上下缆地震数据合并方法，有效消除了下行波，但会遗留一个伪海面鬼波.赵仁永等(2011)介绍了上下缆地震采集技术在在珠江口盆地的应用情况，取得了较好的应用效果.赫建伟等(2013)通过频率波数谱分析了上下缆采集资料的陷波特征和信噪比，提出一种噪声自适应信号处理的上下缆合并技术.高江涛等(2014)对模拟上下源、上下缆地震资料进行了处理，介绍了模拟上下源、上下缆的处理流程.总而言之，常规的上下缆合并压制鬼波技术主要基于地震波运动学方法，由于存在理论近似和固有的计算误差，不能有效解偶鬼波干涉和适应波场振幅变化，导致鬼波(特别是远偏移距的鬼波)压制不尽和有效信号畸变.

本文发展基于波动方程的上下缆鬼波压制方法,上下缆地震波场延拓采用高效率的Fourier变换波场解析延拓方法(符力耘等，2007)，从海平面的自由边界条件出发，根据波场叠加原理推导了延拓波场中鬼波与有效波干涉的的数学表达式，得到了基于上下缆延拓波场合并的有效波场计算公式，合并方法解决了鬼波与有效波的干涉问题，压制了鬼波的影响，拓展了地震波场的频带.本文利用5 m、17 m和23 m深度的三缆地震采集实际数据和理论模拟地震数据进行了方法测试，得到的合并单炮记录及其频谱特征与传统上下缆地震合并技术所得结果进行了比较，证实了本文方法的有效性和先进性.本文方法有效解偶鬼波干涉，解决鬼波压制不尽和有效信号畸变问题，拓宽了地震数据的有效频带，实际资料上下缆地震合并处理的叠偏剖面与常规单缆处理结果的比较显示了较大的改善.

2 方法原理

2.1 上下缆采集原理

图1为上下缆海上地震采集传播路径示意图，一般来说，海上地震采集资料受源鬼波和接收鬼波的影响，本文主要讨论对接收地震记录影响较大的接收鬼波压制问题.图2为零偏移距的不同沉放深度的上下缆的上行反射波与接收鬼波的干涉波形及其频谱响应特征示意图，图2a为上行反射波，图2b为接收深度为d1的上行反射波与接收鬼波的干涉波形，图2c为接收深度为d2的上行反射波与接收鬼波的干涉波形，图2d为上行反射波的频谱响应特征，图2e为接收深度为d的拖缆的海面鬼波的滤波作用的频谱响应特征，图2f为上行反射波与不同沉放深度的上下缆接收到的的干涉波形的频谱响应特征对比图.从图2可见，在电缆深度较深的情况下，上行反射波与其鬼波幅度相当，但相位相反，二者干涉导致的陷波作用主要与缆的沉放深度(d)、水速(v)有关，实际上下缆地震数据采集过程中鬼波的干涉还与水深、海底反射特征、海浪强度等因素密切相关.本文的目的就是要利用上下缆地震数据这种不同陷波特征来压制鬼波，恢复陷波带的频带信息，拓宽地震资料的频带.对于上下缆采集地震数据，最重要的要求是不同深度电缆要保持水平平行位于同一平面内，缆深的误差越小越好，这样才能更好的综合利用上下缆采集的优势获得更高品质的地震资料.

2.2 基于波场延拓上下缆合并压制方法

二维纵波传播方程为:

图1 上下缆海上地震采集地震波传播路径示意图Fig.1 The diagram of seismic wave propagation path in over/under towed strea mermarine seismic acquisition

图2 上行反射波与零偏移距的不同沉放深度的上下缆接收的干涉波形及其频谱响应特征示意图Fig.2 The diagram of upgoing reflection waveform and received interference waveform with zero offset of different towed depth streamers and response characteristics in spectrum

(1)

其中p=p(x,z,t)为二维时间空间域的纵波压力波场，v=v(x,z)为模型中的纵波速度.方程(1)描述了纵波在海水中传播的运动学和动力学特征.

对于勘探地震频率尺度，海水层可视为均匀介质.利用Fourier变换

(2)

将方程(1)变换到频率波数域形式

(3)

其中P=P(kx,y,ω)为二维频率波数域的纵波压力波场，ω为角频率，kx为水平波数.在均匀介质条件下，方程(3)可分解为

(4)

取

(5)

有

(6)

对于上下缆波场延拓问题，方程(6)可求解如下：

P(kx,z+Δz,ω)=P(kx,z,ω)exp(±jkzΔz)，

(7)

其中，Δz为延拓步长.在波场延拓过程中，通常给定波场传播的方向为正方向，kz取“+”时为正向延拓，取“-”时为逆向延拓.

(8)

(9)

(10)

在波场延拓计算过程中，一般采用最高有效频率或主频对应的地震波波长作为估计延拓步长的标准.用主频对应的波长, 将影响高频分量的成像, 降低了成像的分辨率，本文采用最高有效频率.为了控制空间假频，波场延拓步长应该满足以下的条件(张剑锋等，2008)：

(11)

其中，v为海水层速度，f为最高有效频率.海水层速度一般取为1500 m·s-1，对于海上地震勘探的地震数据，最高有效频率为125 Hz左右,计算得到的最大延拓步长为3 m.

令w=exp(ikzΔz)，利用公式(10)将上下缆的波场分别化简为

(12)

(13)

对于频率波数域内的波场延拓，由于网格点相互耦合，傅里叶变换的周期性需要在计算边界上设置波场衰减过渡带(李信富等，2007)，本文采用如下的过渡带衰减因子：

G=exp(-[a(N-k)]2),

(14)

(14)式中，a是边界振幅衰减系数或衰减率，N是过渡带的网格数，k是过渡带的网格(1≤k≤N)，G是衰减因子且是上述几个量的函数．

3 理论模型数据试验

图3为基于水平海底理论模型的5、17m和23m深度拖缆的单炮记录，图4为图3所示的5、17m和23m深度拖缆的单炮记录的f-k频谱响应特征.模型大小为1000×600 m，水深为300 m，海水速度为1500 m·s-1，海底地层速度为2500 m·s-1.可见，由于鬼波的干涉影响，在不同深度缆的f-k谱上，可见具有不同周期特征的陷波作用.各模拟单炮地震记录的频谱图显示了陷波特征随电缆沉放深度和偏移距的巨大变化，主要表现为：(1)不同深度拖缆接收的海底反射信号与其鬼波干涉的复合波特征差异较大，5 m缆的海底反射与其鬼波几乎重合相消，而在23 m缆上二者较为分开，鬼波干涉特征稍弱；(2)在同一深度缆上近偏移距与远偏移距的海底反射与其鬼波干涉的复合波特征差异也较大，随着偏移距增大，二者走时差减小，干涉特征增强.

本节根据方程(13)对图3水平海底理论模型的上下缆地震模拟数据进行波场延拓合并压制鬼波，以验证本文方法的正确性.图5所示为17 m和23 m缆地震数据波场延拓合并压制鬼波后的单炮地震记录及其f-k谱.可见鬼波被彻底压制，陷波带完全恢复.图6为图3单炮地震记录中震源子波、三条缆的零炮检距道频谱及任意二缆合并后频谱.可见，由于是理论模型数据，任意二缆合并结果完全相同.

4 实际数据试验

理论模型试验结果表明，本文提出的上下缆地震数据合并压制鬼波的方法是有效的，本节利用2009年在中国南海实施的上下缆地震采集资料进一步验证这种方法的实际应用效果.不同深度三缆(深度分别为5 m、17 m和23 m)采集的数据缆长7 km，道间距6.25 m，采样率2 ms.图7和图8分别为不同深度三条缆接收的单炮地震记录及其对应的f-k谱.可见，从单炮记录上很难看出陷波的影响，但在f-k谱上，不同深度采集数据的陷波作用非常突出，其陷波特征与理论模型资料的基本一致.图9为不同深度三条缆的近偏移距单道地震记录及其对应的频谱，可见波形的陷波特征明显，陷波频谱特征符合上下缆地震采集理论.

图3 基于水平海底理论模型的5 m (a)、17 m (b)和23 m (c)深度电缆模拟的单炮地震记录Fig.3 The synthetic seismic datasets of towed streamer with depth 5 m, 17 m and 23 m based on flat seabed model

图4 图3所示的单炮记录对应的f-k谱(a) 5 m电缆; (b) 17 m电缆; (c) 23 m电缆.Fig.4 The f-k amplitude spectraof the shots in Fig.3

图5 17 m和23 m缆地震数据波场延拓合并压制鬼波后的单炮地震记录(a)及其f-k谱(b)Fig.5 The result shot record obtained by the proposed method with towed streamer with depth 17m and 23 m (a) and the f-k spectrum of the result (b)

图6 震源子波、5 m、17 m 和23 m缆零炮检距道的归一化频谱(a)及任意二缆合并后的频谱(b)Fig.6 The normalized spectrum of the zero offset trace with towed depth of 5 m, 17 m, 23 m and source wavelet (a) and any two streamer combined spectrum (b)

图8 图7所示单炮地震记录对应的f-k谱Fig.8 The f-k amplitude spectra of the shots in Fig.7

图9 不同深度三条缆近偏移距单道地震记录(A)及其对应的频谱(B)Fig.9 The single seismic trace with near offset of three streamers at different towed depth (A) and the spectrum (B)

图10 23 m缆地震单炮记录(a)，时移(相位)校正合并(b)与波动方程延拓合并(c)两种方法处理的地震单炮记录Fig.10 The shots after denoising at depth 23 m (a), the combined results obtained by the traditional dephase method (b) and the combined results obtained by the proposed method (c)

图11 图10对应的单炮记录f-k谱(a) 23 m电缆； (b) 时移(相位)校正合并； (c) 波场延拓合并.Fig.11 The f-k amplitude spectra of the shots in Fig.10

图12 23 m缆单炮近偏移距5道波形显示(a)，时移(相位)校正合并(b)与波动方程延拓合并(c)两种方法的处理结果Fig.12 The five near offset primary reflection wave traces in the shots at depth 23 m (a), the combined results obtained by the traditional method (b) and the combined results obtained by the proposed method (c)

图13 23 m缆单炮远偏移距7道波形显示(a)、时移(相位)校正合并(b)与波动方程延拓合并(c)两种方法的处理结果Fig.13 The seven far offset primary reflection wave traces in the shots at depth 23 m (a), the combined results obtained by the traditional method (b) and the combined results obtained by the proposed method (c)

从图7至图9可知，17 m和23 m拖缆接收的地震记录由于沉放深度接近，二者的噪声分布和频带特征较为一致.为了便于对比分析合并效果，免受其他不同因素的影响，我们以这两条缆的地震数据为例进行上下缆合并鬼波压制方法测试.资料处理步骤如下：(1)按照常规地震资料处理流程和技术，对两条缆采集的原始地震数据进行干扰波和多次波压制、能量补偿、以及数据规则化等常规的地震叠前资料预处理；(2)利用本文的方法进行上下缆合并鬼波压制处理，形成新的叠前道集数据；(3)按照常规地震处理流程和技术进行速度分析和偏移成像处理.图10和图11分别比较了23 m缆地震单炮记录，上下缆时移(相位)校正合并与波动方程延拓合并两种方法处理的地震单炮记录，以及这三个单炮记录对应的f-k谱.从f-k谱上可见，与合并前比较，合并后数据的陷波带得到了很好的恢复，而且波动方程延拓合并方法在大波数上的谱分量明显比时移(相位)校正合并方法的结果丰富.

图12和图13以波形放大显示的形式进一步比较了这两种合并方法在近偏移距和远偏移距上的鬼波压制效果.可见对近偏移距道而言两种方法结果几乎一样；但远偏移距道处理效果差别很大，即本文提出的波动方程延拓合并方法能有效压制远偏移距道上的鬼波，而常规基于时移(相位)校正合并的方法效果较差，导致远偏移距道上的有效波波形畸变.

图14分别为5 m、17 m和23 m深度单条缆常规地震叠偏处理剖面.如前述，5 m浅缆剖面分辨率相对较高，信噪比较低；而17 m和23 m深缆叠偏处理剖面低频较丰富，信噪比较高.在这些剖面上存在明显的鬼波干涉现象，特别是海底附近和3 s附近的两个波组表现为典型的鬼波干涉波形特征.图15为17 m和23 m两条缆地震资料波动方程延拓合并压制鬼波后的叠偏处理剖面.与图14比较可见，鬼波得到有效压制，剖面信噪比明显提高，盆地内幕反射波组特征明显、层次突出，合并处理效果明显,优于单缆处理的效果.图16比较了17 m和23 m两条缆波动方程延拓合并处理与其单条缆常规地震处理的叠偏剖面频谱.可见合并处理结果的陷频特征基本消除，低频和高频段得到补偿，与单条缆处理结果的频谱互补特征基本符合理论预测.

图14 5 m (a)、17 m (b)和23 m (c)深度单条缆常规地震叠偏处理剖面Fig.14 The conventional processing seismic section results of single streamer at 5 m (a), 17 m (b) and 23 m depth (c)

图15 17 m和23 m两条缆地震数据波动方程延拓合并鬼波压制叠偏处理剖面Fig.15 The result shot record obtained by the proposed method with towed streamer with depth 17 m and 23 m

图16 17 m和23 m两条缆波动方程延拓合并处理与单条缆常规地震处理的叠加偏移剖面频谱对比Fig.16 The spectrum contrast of the result shot record obtained by the proposed method (blue) and the conventional processing seismic section results of single streamer at 17 m (red) and 23 m depth (light blue)

5 结论与认识

通过对海上地震勘探中鬼波与来自地下的有效波相互干涉的分析，本文研究基于频率波数域波动方程进行上下缆地震数据合并压制鬼波的方法.由于海水面是一个自由表面，来自地下的有效反射波到达海水面产生了一个与有效反射波相位相反的鬼波，根据频率波数域波动方程理论，不同深度电缆接收到的波场可以看成是来自海水面的有效波逆向延拓和鬼波正向延拓的叠加，从而导致不同电缆接收到地震数据产生了与电缆深度相关的陷波带.应用上下缆方式采集的地震数据陷波带特征的差异，对上下缆地震数据进行合并处理能在一定程度上弥补常规海上地震数据采集方式中因陷波导致的降频现象，从而有效拓宽低频、消除陷波、改善资料品质.本文发展了利用波动方程延拓实现上下缆地震数据的叠前合并的方法，理论模拟数据和实际地震资料的处理结果表明本方法有效的拓宽了上下缆地震资料合并处理结果的有效频带，极大地压制了鬼波的影响，有效地重建了水下地层的真实波场.

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(本文编辑 汪海英)

The study of a deghosting method of over/under streamer seismic data based on wave equation

GUAN Xi-Zhu1, CHEN Bao-Shu2， FU Li-Yun1, TAO Jie2, LI Lie3

1InstituteofGeologyandGeophysics,ChineseAcademyofSciences,Beijing100029,China2CNOOCResearchCenter,Beijing100027,China3CNOOCChinaLtd.,GuangdongZhanjiang524057,China

In marine seismic acquisition, ghost effect due to the strong reflection of the sea surface causes serious notch trap in the spectrum. Ghost effect can be reduced by over/under towed streamer acquisition. However, most of deghosting technology for over/under streamer acquisition is based on seismic kinematics method, which cannot effectively solve the ghost wave interference and brings incomplete ghost suppression and distortion of the effective signal.It is necessary to develop the deghosting technology for over/under streamer. Cases studies of synthetic and real seismic data sets demonstrate that our seismic wavefield extrapolation based on Fourier transform ensures the consistency of the seismic amplitude and phase of over/under streamer seismic data and significantly eliminates the amplitude and phase error of far offset especially for the long streamer condition,which helps to decouple the real wave and the ghost wave and fill notch effect in the spectrum.In order to take advantage of both shallow and deep streamers, it has been proposed to record the pressure field at two different depths and to combine optimally all the measurements. We propose adeghosting method of over/under streamer based on seismic wave equation continuation formula in the frequency wavenumber domain, which eliminate far offset signal calculation error of the long streamer contract to the traditional dephase and sum algorithm.The analytical seismic wave continuation based on Fourier transform ensure the consistency of the amplitude and phase of seismic signal from over/under streamer seismic acquisition with high computing efficiency, suppress the ghost signal that interference the up-going signal from the earth under water effectively and fill the notchesin the amplitude spectrum.A synthetic single shot gather is used to verify the performance of the proposed method. Finally,we apply the proposed method on a real over/undermarine data set from China. The results show that the proposed method can simultaneously achieve good imaging of shallow and deep targets, seismic data wide frequency band width by effectively suppressing the ghost.In conventional streamer marine seismic acquisition, the pressure sensor in a towed streamer records two wavefields that interfere with each other. The two wavefields are the upgoing pressure wavefield propagating directly to the pressure sensor from the streamer below, and the downgoing pressure wavefield reflected downwards from thefree (sea) surface immediately above the streamer. The downgoing pressure wavefield like a “ghost”of the upgoing pressure wavefield. The receiver ghost from free surface cancels or degrades the signal at some frequencies, resulting steep notches in amplitude-frequency spectrum at low as well as high frequency.A streamer towed at shallow depth, the lower frequencies arestrongly attenuated and cannot be recovered by a simple deconvolution as usually the swell noise is too strong, but it is good at receiving high-frequency components, because the frequency notches shifts to higher frequency. In contrast,a streamer at a deeper depth, it is good at receiving low-frequency components and the swell noise is normally strongly attenuated for it is exponentially decaying with depth, but the notching frequencies within the bandwidth hence limiting the useful frequencies.For simplicity, we take a simple two-layered model with flat sea bottomas an example to test the method.The synthetic seismic data sets of over/under towed streamer with depth 17m and 23m without direct wave and multiple wave and thef-kspectrum of the synthetic seismic datasets. It can be seen that the arrival time of reflect wave and ghost wave in the synthetic seismic recording of 17m streamer and 23m streamer is obviously different.It can be also shown that the difference value between the up-going wave and the ghost wave at near offset and far offset increases, therefore the interference of up-going wave and ghost wave enhanced. Because of the effect of the ghost, there are periodic notches in the frequency wavenumber amplitude spectra, which are caused by the ghost.The resultshot record obtainedby the proposed method and thef-kspectrum of the resultare shown, respectively. It is clear that the proposed method can remove the ghost wave effectively and fill the notches well. To demonstrate the performance of the proposed method, we applied it on a real over/under dataset.The acquisition configuration of this dataset is set as following：An over/under source were deployed at 6 m depth and 12 m depth,and two streamers were deployed at depths of 17 m and 23 m,respectively.the shots after denoising at depths of 17 m, 23 m, and thef-kamplitude spectraof the shotsat depths of 17 m, 23 m and the shots at depth 23 m, the combined results obtained by the traditional dephase and sum method and the combined results obtained by the proposed method and thef-kamplitude spectra, it is clear that the result obtained bythe proposed method has much richer frequencies components at big wavenumber. Furthermore, the notches at small wave number are well filled and the energy is also enhanced.From the near offset primary reflection wave of the seabed in the shots at depth 23 m,the combined results obtained by the traditional dephase and sum method and the combined results obtained by the proposed method and the far offset primary reflection wave of the seabed in the shots at depth 23 m, the combined results obtained by the traditional dephase and sum method and the combined results obtained by the proposed method.It is visible that both traditional dephase and sum method and proposed method can remove the ghost well. It is shown that the wave is so distort that it is not possible to find the reflection wave.Incontrast, the reflection wave can be easy to distinguish, the wave are comprised of the reflection wave and the source ghost. Clearly the proposed method suppresses the receiver ghost better than the traditional method.We propose a new deghosting method forover/under streamer acquisiton based on analyticalf-kdomain seismic wavefield extrapolation characterized by high computing efficiency. In the proposed method, the computing of the upgoing wavefield from pressure measurements acquired at different towdepths corresponding to wave equation continuation results from the data. Compared with the traditional methods, the proposed method has much richer frequencies components at big wavenumber. Furthermore, the proposed method suppresses the receiver ghost at far offset better. Synthetic and realdata examples demonstrate that the proposed method can obtains a deghosting result with rich lowand high frequencies and fill the notches inf-kamplitude spectra well.

Marine seismic acquisition; Over/under streamer; Deghosting; Combination based on seismic wave field continuation; Frequency wavenumber domain

10.6038/cjg20151025.

Guan X Z, Chen B S, Fu L Y, et al. 2015. The study of a deghosting method of over/under streamer seismic data based on wave equation.ChineseJ.Geophys. (in Chinese),58(10):3746-3757,doi:10.6038/cjg20151025.

国家自然科学基金项目(41130418, 40925013)和国家科技重大专项(2011ZX05025-001-02)联合资助.

管西竹，男，1983年生，主要研究方向为地震波模拟与地震数据处理与反演．E-mai：guanxz@mail.iggcas.ac.cn

10.6038/cjg20151025

P631

2014-09-19，2015-09-15收修定稿

管西竹， 陈宝书, 符力耘等. 2015. 基于波动方程的上下缆地震数据鬼波压制方法研究.地球物理学报，58(10):3746-3757,