基于波動方程的上下纜地震數(shù)據(jù)鬼波壓制方法研究

管西竹， 陳寶書, 符力耘, 陶杰, 李列

1 中國科學(xué)院油氣資源研究重點實驗室，中國科學(xué)院地質(zhì)與地球物理研究所， 北京 100029 2 中海油研究總院, 北京 100027 3 中海石油(中國)有限公司湛江分公司, 廣東湛江 524057

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基于波動方程的上下纜地震數(shù)據(jù)鬼波壓制方法研究

管西竹1， 陳寶書2, 符力耘1, 陶杰2, 李列3

1 中國科學(xué)院油氣資源研究重點實驗室，中國科學(xué)院地質(zhì)與地球物理研究所， 北京 100029 2 中海油研究總院, 北京 100027 3 中海石油(中國)有限公司湛江分公司, 廣東湛江 524057

本文發(fā)展基于波動方程的上下纜鬼波壓制方法，推導(dǎo)了上下纜地震波場頻率波數(shù)域波動方程延拓合并公式.基于Fourier變換的波場解析延拓確保上下纜資料振幅相位的一致性，消除了長拖纜遠(yuǎn)偏移距信號的計算誤差，同時具有較高的計算效率；上下纜地震波場的波動方程法合并有效解偶鬼波干涉，實現(xiàn)綜合利用上下纜地震數(shù)據(jù)壓制鬼波.理論模型數(shù)據(jù)和實際采集地震數(shù)據(jù)的測試表明了方法的有效性.

海上地震采集； 上下纜； 鬼波壓制； 波動方程延拓合并； 頻率波數(shù)域

1 引言

隨著海上地震勘探進(jìn)入深水領(lǐng)域，特別是深部和超深部地質(zhì)目標(biāo)的勘探，遇到的瓶頸問題之一是深層反射能量弱，信噪比低.為了增強(qiáng)深層弱反射信號，可采用低頻強(qiáng)能量組合槍陣激發(fā)，但受海水面的鬼波干涉影響，拖纜接收的地震信號存在嚴(yán)重的陷波作用，導(dǎo)致地震記錄頻帶變窄，分辨率和信噪比降低，特別是持續(xù)的鬼波同相軸給地震地質(zhì)解釋造成困難.常規(guī)的海上水平單纜地震采集限制了鬼波壓制技術(shù)的發(fā)展(陳金海等，2000).上世紀(jì)80年代發(fā)展起來的針對鬼波壓制的上下纜海上地震采集技術(shù)(Sonnenland et al.，1986)，隨著采集設(shè)備的改進(jìn)，進(jìn)入21世紀(jì)后得到了長足的發(fā)展和實用化應(yīng)用，在北海、墨西哥灣、中東、中國南海等海域取得了較好的應(yīng)用效果(Moldoveanu et al.，2007； Wire et al.，2006).

采用上下纜地震采集的目的主要是根據(jù)上下纜地震數(shù)據(jù)不同的陷波特征，設(shè)計合并技術(shù)來壓制鬼波和拓寬頻帶.一般而言，深纜和淺纜除了陷波特征不同外，在分辨率與信噪比方面還有較大區(qū)別.淺纜地震數(shù)據(jù)低頻能量較弱，視分辨率顯高，但由于受拖纜漂移影響較大，信噪比較低；而深纜地震數(shù)據(jù)則相反.這種上下纜數(shù)據(jù)的不一致性與勘探的海洋環(huán)境和海底特征密切相關(guān)，極大地增加了合并技術(shù)的難度，也降低技術(shù)的普適性.早期的合并技術(shù)較為粗糙，僅通過簡單的上下纜時移校正(相位校正)，然后進(jìn)行簡單相加合并來消去鬼波，拓寬地震頻帶.雖然算法簡單，效率較高，但精度較低，會產(chǎn)生較大的振幅誤差和嚴(yán)重的偽海面鬼波(赫建偉等，2013a).傳統(tǒng)的上下纜數(shù)據(jù)相位求和壓制鬼波的方法只對相位做校正，沒有對振幅進(jìn)行相應(yīng)的校正.Posthumus(1993)提出在相位校正過程中，對數(shù)據(jù)振幅進(jìn)行加權(quán)處理的上下纜合并方法.該方法在歐洲北海油田上下纜地震采集數(shù)據(jù)過程中進(jìn)行了實際應(yīng)用，取得了較好效果(Hill et al.，2006).?zdemir(2008)進(jìn)一步改進(jìn)了這種基于相位求和的上下纜合并方法，利用估計的不同纜數(shù)據(jù)噪聲水平，通過最小二乘擬合優(yōu)化合并結(jié)果的信噪比.Ferber(2008)提出了一種時移校正后相減的上下纜地震數(shù)據(jù)合并方法，有效消除了下行波，但會遺留一個偽海面鬼波.趙仁永等(2011)介紹了上下纜地震采集技術(shù)在在珠江口盆地的應(yīng)用情況，取得了較好的應(yīng)用效果.赫建偉等(2013)通過頻率波數(shù)譜分析了上下纜采集資料的陷波特征和信噪比，提出一種噪聲自適應(yīng)信號處理的上下纜合并技術(shù).高江濤等(2014)對模擬上下源、上下纜地震資料進(jìn)行了處理，介紹了模擬上下源、上下纜的處理流程.總而言之，常規(guī)的上下纜合并壓制鬼波技術(shù)主要基于地震波運動學(xué)方法，由于存在理論近似和固有的計算誤差，不能有效解偶鬼波干涉和適應(yīng)波場振幅變化，導(dǎo)致鬼波(特別是遠(yuǎn)偏移距的鬼波)壓制不盡和有效信號畸變.

本文發(fā)展基于波動方程的上下纜鬼波壓制方法,上下纜地震波場延拓采用高效率的Fourier變換波場解析延拓方法(符力耘等，2007)，從海平面的自由邊界條件出發(fā)，根據(jù)波場疊加原理推導(dǎo)了延拓波場中鬼波與有效波干涉的的數(shù)學(xué)表達(dá)式，得到了基于上下纜延拓波場合并的有效波場計算公式，合并方法解決了鬼波與有效波的干涉問題，壓制了鬼波的影響，拓展了地震波場的頻帶.本文利用5 m、17 m和23 m深度的三纜地震采集實際數(shù)據(jù)和理論模擬地震數(shù)據(jù)進(jìn)行了方法測試，得到的合并單炮記錄及其頻譜特征與傳統(tǒng)上下纜地震合并技術(shù)所得結(jié)果進(jìn)行了比較，證實了本文方法的有效性和先進(jìn)性.本文方法有效解偶鬼波干涉，解決鬼波壓制不盡和有效信號畸變問題，拓寬了地震數(shù)據(jù)的有效頻帶，實際資料上下纜地震合并處理的疊偏剖面與常規(guī)單纜處理結(jié)果的比較顯示了較大的改善.

2 方法原理

2.1 上下纜采集原理

圖1為上下纜海上地震采集傳播路徑示意圖，一般來說，海上地震采集資料受源鬼波和接收鬼波的影響，本文主要討論對接收地震記錄影響較大的接收鬼波壓制問題.圖2為零偏移距的不同沉放深度的上下纜的上行反射波與接收鬼波的干涉波形及其頻譜響應(yīng)特征示意圖，圖2a為上行反射波，圖2b為接收深度為d1的上行反射波與接收鬼波的干涉波形，圖2c為接收深度為d2的上行反射波與接收鬼波的干涉波形，圖2d為上行反射波的頻譜響應(yīng)特征，圖2e為接收深度為d的拖纜的海面鬼波的濾波作用的頻譜響應(yīng)特征，圖2f為上行反射波與不同沉放深度的上下纜接收到的的干涉波形的頻譜響應(yīng)特征對比圖.從圖2可見，在電纜深度較深的情況下，上行反射波與其鬼波幅度相當(dāng)，但相位相反，二者干涉導(dǎo)致的陷波作用主要與纜的沉放深度(d)、水速(v)有關(guān)，實際上下纜地震數(shù)據(jù)采集過程中鬼波的干涉還與水深、海底反射特征、海浪強(qiáng)度等因素密切相關(guān).本文的目的就是要利用上下纜地震數(shù)據(jù)這種不同陷波特征來壓制鬼波，恢復(fù)陷波帶的頻帶信息，拓寬地震資料的頻帶.對于上下纜采集地震數(shù)據(jù)，最重要的要求是不同深度電纜要保持水平平行位于同一平面內(nèi)，纜深的誤差越小越好，這樣才能更好的綜合利用上下纜采集的優(yōu)勢獲得更高品質(zhì)的地震資料.

2.2 基于波場延拓上下纜合并壓制方法

二維縱波傳播方程為:

圖1 上下纜海上地震采集地震波傳播路徑示意圖Fig.1 The diagram of seismic wave propagation path in over/under towed strea mermarine seismic acquisition

圖2 上行反射波與零偏移距的不同沉放深度的上下纜接收的干涉波形及其頻譜響應(yīng)特征示意圖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)為二維時間空間域的縱波壓力波場，v=v(x,z)為模型中的縱波速度.方程(1)描述了縱波在海水中傳播的運動學(xué)和動力學(xué)特征.

對于勘探地震頻率尺度，海水層可視為均勻介質(zhì).利用Fourier變換

(2)

將方程(1)變換到頻率波數(shù)域形式

(3)

其中P=P(kx,y,ω)為二維頻率波數(shù)域的縱波壓力波場，ω為角頻率，kx為水平波數(shù).在均勻介質(zhì)條件下，方程(3)可分解為

(4)

取

(5)

有

(6)

對于上下纜波場延拓問題，方程(6)可求解如下：

P(kx,z+Δz,ω)=P(kx,z,ω)exp(±jkzΔz)，

(7)

其中，Δz為延拓步長.在波場延拓過程中，通常給定波場傳播的方向為正方向，kz取“+”時為正向延拓，取“-”時為逆向延拓.

(8)

(9)

(10)

在波場延拓計算過程中，一般采用最高有效頻率或主頻對應(yīng)的地震波波長作為估計延拓步長的標(biāo)準(zhǔn).用主頻對應(yīng)的波長, 將影響高頻分量的成像, 降低了成像的分辨率，本文采用最高有效頻率.為了控制空間假頻，波場延拓步長應(yīng)該滿足以下的條件(張劍鋒等，2008)：

(11)

其中，v為海水層速度，f為最高有效頻率.海水層速度一般取為1500 m·s-1，對于海上地震勘探的地震數(shù)據(jù)，最高有效頻率為125 Hz左右,計算得到的最大延拓步長為3 m.

令w=exp(ikzΔz)，利用公式(10)將上下纜的波場分別化簡為

(12)

(13)

對于頻率波數(shù)域內(nèi)的波場延拓，由于網(wǎng)格點相互耦合，傅里葉變換的周期性需要在計算邊界上設(shè)置波場衰減過渡帶(李信富等，2007)，本文采用如下的過渡帶衰減因子：

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

(14)

(14)式中，a是邊界振幅衰減系數(shù)或衰減率，N是過渡帶的網(wǎng)格數(shù)，k是過渡帶的網(wǎng)格(1≤k≤N)，G是衰減因子且是上述幾個量的函數(shù)．

3 理論模型數(shù)據(jù)試驗

圖3為基于水平海底理論模型的5、17m和23m深度拖纜的單炮記錄，圖4為圖3所示的5、17m和23m深度拖纜的單炮記錄的f-k頻譜響應(yīng)特征.模型大小為1000×600 m，水深為300 m，海水速度為1500 m·s-1，海底地層速度為2500 m·s-1.可見，由于鬼波的干涉影響，在不同深度纜的f-k譜上，可見具有不同周期特征的陷波作用.各模擬單炮地震記錄的頻譜圖顯示了陷波特征隨電纜沉放深度和偏移距的巨大變化，主要表現(xiàn)為：(1)不同深度拖纜接收的海底反射信號與其鬼波干涉的復(fù)合波特征差異較大，5 m纜的海底反射與其鬼波幾乎重合相消，而在23 m纜上二者較為分開，鬼波干涉特征稍弱；(2)在同一深度纜上近偏移距與遠(yuǎn)偏移距的海底反射與其鬼波干涉的復(fù)合波特征差異也較大，隨著偏移距增大，二者走時差減小，干涉特征增強(qiáng).

本節(jié)根據(jù)方程(13)對圖3水平海底理論模型的上下纜地震模擬數(shù)據(jù)進(jìn)行波場延拓合并壓制鬼波，以驗證本文方法的正確性.圖5所示為17 m和23 m纜地震數(shù)據(jù)波場延拓合并壓制鬼波后的單炮地震記錄及其f-k譜.可見鬼波被徹底壓制，陷波帶完全恢復(fù).圖6為圖3單炮地震記錄中震源子波、三條纜的零炮檢距道頻譜及任意二纜合并后頻譜.可見，由于是理論模型數(shù)據(jù)，任意二纜合并結(jié)果完全相同.

4 實際數(shù)據(jù)試驗

理論模型試驗結(jié)果表明，本文提出的上下纜地震數(shù)據(jù)合并壓制鬼波的方法是有效的，本節(jié)利用2009年在中國南海實施的上下纜地震采集資料進(jìn)一步驗證這種方法的實際應(yīng)用效果.不同深度三纜(深度分別為5 m、17 m和23 m)采集的數(shù)據(jù)纜長7 km，道間距6.25 m，采樣率2 ms.圖7和圖8分別為不同深度三條纜接收的單炮地震記錄及其對應(yīng)的f-k譜.可見，從單炮記錄上很難看出陷波的影響，但在f-k譜上，不同深度采集數(shù)據(jù)的陷波作用非常突出，其陷波特征與理論模型資料的基本一致.圖9為不同深度三條纜的近偏移距單道地震記錄及其對應(yīng)的頻譜，可見波形的陷波特征明顯，陷波頻譜特征符合上下纜地震采集理論.

圖3 基于水平海底理論模型的5 m (a)、17 m (b)和23 m (c)深度電纜模擬的單炮地震記錄Fig.3 The synthetic seismic datasets of towed streamer with depth 5 m, 17 m and 23 m based on flat seabed model

圖4 圖3所示的單炮記錄對應(yīng)的f-k譜(a) 5 m電纜; (b) 17 m電纜; (c) 23 m電纜.Fig.4 The f-k amplitude spectraof the shots in Fig.3

圖5 17 m和23 m纜地震數(shù)據(jù)波場延拓合并壓制鬼波后的單炮地震記錄(a)及其f-k譜(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)

圖6 震源子波、5 m、17 m 和23 m纜零炮檢距道的歸一化頻譜(a)及任意二纜合并后的頻譜(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)

圖8 圖7所示單炮地震記錄對應(yīng)的f-k譜Fig.8 The f-k amplitude spectra of the shots in Fig.7

圖9 不同深度三條纜近偏移距單道地震記錄(A)及其對應(yīng)的頻譜(B)Fig.9 The single seismic trace with near offset of three streamers at different towed depth (A) and the spectrum (B)

圖10 23 m纜地震單炮記錄(a)，時移(相位)校正合并(b)與波動方程延拓合并(c)兩種方法處理的地震單炮記錄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)

圖11 圖10對應(yīng)的單炮記錄f-k譜(a) 23 m電纜； (b) 時移(相位)校正合并； (c) 波場延拓合并.Fig.11 The f-k amplitude spectra of the shots in Fig.10

圖12 23 m纜單炮近偏移距5道波形顯示(a)，時移(相位)校正合并(b)與波動方程延拓合并(c)兩種方法的處理結(jié)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)

圖13 23 m纜單炮遠(yuǎn)偏移距7道波形顯示(a)、時移(相位)校正合并(b)與波動方程延拓合并(c)兩種方法的處理結(jié)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)

從圖7至圖9可知，17 m和23 m拖纜接收的地震記錄由于沉放深度接近，二者的噪聲分布和頻帶特征較為一致.為了便于對比分析合并效果，免受其他不同因素的影響，我們以這兩條纜的地震數(shù)據(jù)為例進(jìn)行上下纜合并鬼波壓制方法測試.資料處理步驟如下：(1)按照常規(guī)地震資料處理流程和技術(shù)，對兩條纜采集的原始地震數(shù)據(jù)進(jìn)行干擾波和多次波壓制、能量補(bǔ)償、以及數(shù)據(jù)規(guī)則化等常規(guī)的地震疊前資料預(yù)處理；(2)利用本文的方法進(jìn)行上下纜合并鬼波壓制處理，形成新的疊前道集數(shù)據(jù)；(3)按照常規(guī)地震處理流程和技術(shù)進(jìn)行速度分析和偏移成像處理.圖10和圖11分別比較了23 m纜地震單炮記錄，上下纜時移(相位)校正合并與波動方程延拓合并兩種方法處理的地震單炮記錄，以及這三個單炮記錄對應(yīng)的f-k譜.從f-k譜上可見，與合并前比較，合并后數(shù)據(jù)的陷波帶得到了很好的恢復(fù)，而且波動方程延拓合并方法在大波數(shù)上的譜分量明顯比時移(相位)校正合并方法的結(jié)果豐富.

圖12和圖13以波形放大顯示的形式進(jìn)一步比較了這兩種合并方法在近偏移距和遠(yuǎn)偏移距上的鬼波壓制效果.可見對近偏移距道而言兩種方法結(jié)果幾乎一樣；但遠(yuǎn)偏移距道處理效果差別很大，即本文提出的波動方程延拓合并方法能有效壓制遠(yuǎn)偏移距道上的鬼波，而常規(guī)基于時移(相位)校正合并的方法效果較差，導(dǎo)致遠(yuǎn)偏移距道上的有效波波形畸變.

圖14分別為5 m、17 m和23 m深度單條纜常規(guī)地震疊偏處理剖面.如前述，5 m淺纜剖面分辨率相對較高，信噪比較低；而17 m和23 m深纜疊偏處理剖面低頻較豐富，信噪比較高.在這些剖面上存在明顯的鬼波干涉現(xiàn)象，特別是海底附近和3 s附近的兩個波組表現(xiàn)為典型的鬼波干涉波形特征.圖15為17 m和23 m兩條纜地震資料波動方程延拓合并壓制鬼波后的疊偏處理剖面.與圖14比較可見，鬼波得到有效壓制，剖面信噪比明顯提高，盆地內(nèi)幕反射波組特征明顯、層次突出，合并處理效果明顯,優(yōu)于單纜處理的效果.圖16比較了17 m和23 m兩條纜波動方程延拓合并處理與其單條纜常規(guī)地震處理的疊偏剖面頻譜.可見合并處理結(jié)果的陷頻特征基本消除，低頻和高頻段得到補(bǔ)償，與單條纜處理結(jié)果的頻譜互補(bǔ)特征基本符合理論預(yù)測.

圖14 5 m (a)、17 m (b)和23 m (c)深度單條纜常規(guī)地震疊偏處理剖面Fig.14 The conventional processing seismic section results of single streamer at 5 m (a), 17 m (b) and 23 m depth (c)

圖15 17 m和23 m兩條纜地震數(shù)據(jù)波動方程延拓合并鬼波壓制疊偏處理剖面Fig.15 The result shot record obtained by the proposed method with towed streamer with depth 17 m and 23 m

圖16 17 m和23 m兩條纜波動方程延拓合并處理與單條纜常規(guī)地震處理的疊加偏移剖面頻譜對比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 結(jié)論與認(rèn)識

通過對海上地震勘探中鬼波與來自地下的有效波相互干涉的分析，本文研究基于頻率波數(shù)域波動方程進(jìn)行上下纜地震數(shù)據(jù)合并壓制鬼波的方法.由于海水面是一個自由表面，來自地下的有效反射波到達(dá)海水面產(chǎn)生了一個與有效反射波相位相反的鬼波，根據(jù)頻率波數(shù)域波動方程理論，不同深度電纜接收到的波場可以看成是來自海水面的有效波逆向延拓和鬼波正向延拓的疊加，從而導(dǎo)致不同電纜接收到地震數(shù)據(jù)產(chǎn)生了與電纜深度相關(guān)的陷波帶.應(yīng)用上下纜方式采集的地震數(shù)據(jù)陷波帶特征的差異，對上下纜地震數(shù)據(jù)進(jìn)行合并處理能在一定程度上彌補(bǔ)常規(guī)海上地震數(shù)據(jù)采集方式中因陷波導(dǎo)致的降頻現(xiàn)象，從而有效拓寬低頻、消除陷波、改善資料品質(zhì).本文發(fā)展了利用波動方程延拓實現(xiàn)上下纜地震數(shù)據(jù)的疊前合并的方法，理論模擬數(shù)據(jù)和實際地震資料的處理結(jié)果表明本方法有效的拓寬了上下纜地震資料合并處理結(jié)果的有效頻帶，極大地壓制了鬼波的影響，有效地重建了水下地層的真實波場.

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(本文編輯 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.

國家自然科學(xué)基金項目(41130418, 40925013)和國家科技重大專項(2011ZX05025-001-02)聯(lián)合資助.

管西竹，男，1983年生，主要研究方向為地震波模擬與地震數(shù)據(jù)處理與反演．E-mai：guanxz@mail.iggcas.ac.cn

10.6038/cjg20151025

P631

2014-09-19，2015-09-15收修定稿

管西竹， 陳寶書, 符力耘等. 2015. 基于波動方程的上下纜地震數(shù)據(jù)鬼波壓制方法研究.地球物理學(xué)報，58(10):3746-3757,