基于S變換的軟閾值濾波在深地震反射數(shù)據(jù)處理中的應(yīng)用

曲中黨， 吳蔚， 賀日政， 高銳

中國(guó)地質(zhì)科學(xué)院地質(zhì)研究所, 國(guó)土資源部深部探測(cè)與地球動(dòng)力學(xué)重點(diǎn)實(shí)驗(yàn)室,大陸構(gòu)造與動(dòng)力學(xué)國(guó)家重點(diǎn)實(shí)驗(yàn)室, 北京 100037

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基于S變換的軟閾值濾波在深地震反射數(shù)據(jù)處理中的應(yīng)用

曲中黨， 吳蔚， 賀日政*， 高銳

中國(guó)地質(zhì)科學(xué)院地質(zhì)研究所, 國(guó)土資源部深部探測(cè)與地球動(dòng)力學(xué)重點(diǎn)實(shí)驗(yàn)室,大陸構(gòu)造與動(dòng)力學(xué)國(guó)家重點(diǎn)實(shí)驗(yàn)室, 北京 100037

深地震反射原始單炮數(shù)據(jù)是非平穩(wěn)的弱能量反射信號(hào), 信噪比較低. 如何提高信噪比一直是深地震反射數(shù)據(jù)前處理中的一大難題. S變換是一種適用于分析非平穩(wěn)信號(hào)的時(shí)頻變換方法. 同其他分析時(shí)變信號(hào)的方法相比, S變換的基本小波不必滿足小波在時(shí)間域均值為零的容許性條件, 它的時(shí)頻分辨率與分析信號(hào)的頻率有關(guān), 且其在時(shí)間域的積分可以得到傅里葉頻譜,其反變換也簡(jiǎn)單. 因此, S變換容易表示深地震反射信號(hào)復(fù)雜的時(shí)頻特性. 本文在S變換的基礎(chǔ)上, 利用軟閾值濾波方法對(duì)深地震反射數(shù)據(jù)進(jìn)行處理, 實(shí)驗(yàn)結(jié)果表明, 該方法有效地提高了信噪比, 壓制了有效頻帶范圍內(nèi)的混頻干擾, 突出了弱反射信號(hào), 使得波組信息更加豐富, 有利于連續(xù)追蹤有效反射波組和識(shí)別薄地層, 特別是提高了深部Moho界面反射層位的分辨率, 為深地震反射剖面后續(xù)處理和準(zhǔn)確解釋奠定了基礎(chǔ).

S變換； 深地震反射單炮； 軟閾值濾波； 前處理

1 引言

深地震反射剖面探測(cè)是地震學(xué)調(diào)查工具的首選, 能夠得到剖面下的精細(xì)結(jié)構(gòu), 便于準(zhǔn)確剖析復(fù)雜的構(gòu)造地質(zhì)問題(Clowes et al., 1987; 王海燕等, 2010). 因此, 深地震反射剖面一般穿越構(gòu)造復(fù)雜的結(jié)合帶, 而在這些構(gòu)造復(fù)雜地區(qū)(如地形起伏較大, 斷裂帶發(fā)育)中, 激發(fā)和接受條件都很差, 導(dǎo)致了深地震反射數(shù)據(jù)一般反射信號(hào)弱和信噪比低, 干擾類型多而復(fù)雜且差別大(Bois et al., 1988; 吳宣志等, 1995; 楊文采等, 1999; 崔興寶, 2003; Ross et al., 2004; 楊卓欣等, 2006; 劉金凱等, 2010; Karplus et al., 2011; Kumar et al., 2011). 此外, 為了兼顧獲得剖面下的淺、中、深層反射信息, 爆炸震源激發(fā)時(shí)采取不同藥量和井深組合以及變觀測(cè)系統(tǒng)接收, 從而導(dǎo)致激發(fā)、接收條件變化較大, 同一深地震反射剖面的地震信號(hào)在頻帶、振幅、能量、相位等方面都存在著較大的差異(朱小三等, 2013). 深地震反射數(shù)據(jù)的采集成本很高, 而且重復(fù)采集幾乎不可能, 如果這些炮集位于關(guān)鍵目標(biāo)構(gòu)造帶內(nèi), 就會(huì)對(duì)整個(gè)區(qū)域的構(gòu)造解釋產(chǎn)生很大的影響. 因此, 對(duì)于如何有效地從深地震反射數(shù)據(jù)中剔除干擾波, 提高信噪比, 前人曾做過大量嘗試(朱小三等, 2013), 雖然取得了一定的效果, 但仍有不足.

S變換結(jié)合了短時(shí)傅里葉變換與小波變換的優(yōu)點(diǎn), 克服了短時(shí)傅里葉變換時(shí)頻窗口在時(shí)頻平面中不可變的問題, 其時(shí)窗寬度隨頻率呈反向變化, 又無須滿足小波變換中小波在時(shí)間域均值為零的容許性條件(Stockwell et al., 1996; 趙淑紅和朱光明, 2007; 陳學(xué)華等, 2008). 因此, S變換是非平穩(wěn)信號(hào)時(shí)頻分析的良好工具, 其高質(zhì)量的時(shí)頻表示為具體應(yīng)用中設(shè)計(jì)有效的時(shí)頻濾波器提供了保證. S變換與傅里葉變換的直接聯(lián)系使得其算法實(shí)現(xiàn)簡(jiǎn)潔高效(Stockwell et al., 1996). 本文利用S變換的這些優(yōu)點(diǎn)重新處理了西南天山深地震反射剖面中的廢炮數(shù)據(jù)(高銳等, 2008; He et al., 2008; Gao et al., 2013), 通過綜合對(duì)比分析, 效果明顯, 這些廢炮數(shù)據(jù)得以重新使用.

2 基于S變換的軟閾值濾波

2.1 S變換

S變換是由美國(guó)地球物理學(xué)家Stockwell于1996年提出的一種類似于短時(shí)傅里葉變換(Gabor, 1946)的時(shí)頻譜表示方法, 函數(shù)h(t)的S變換定義為(Stockwelletal., 1996)：

(1)

圖1 不同頻率f所對(duì)應(yīng)的時(shí)窗函數(shù)w(t,f,τ)(其中τ=0)Fig.1 Gaussian time window function w(t,f,τ) for various values of f (τ=0)

S變換也可以由h(t)的傅里葉頻譜H(f)表示(Stockwell, 1999)：

(2)

從式(2)可以得到離散的S變換:

(3)

(4)

S變換表示的是局部的頻譜特征, 將其在時(shí)間方向積分可以容易地得到傅里葉頻譜(Stockwell et al., 1996)：

(5)

因此,h(t)也可以由S(τ,f)準(zhǔn)確的反變換得到：

}ei2πftdf,

(6)

其離散表達(dá)形式為：

(7)

2.2 軟閾值濾波

閾值濾波主要分為硬閾值法和軟閾值法, 最早是由斯坦福大學(xué)的Donoho D L和Johnstone I M在估計(jì)小波系數(shù)時(shí)提出的(Donoho and Johnstone, 1994a, 1994b; Donoho et al., 1995; Donoho, 1995).硬閾值法是指: 信號(hào)的系數(shù)大于一個(gè)確定的閾值λ時(shí), 保持不變, 系數(shù)小于閾值λ時(shí)置零. 硬閾值法運(yùn)算量小, 操作簡(jiǎn)單, 但函數(shù)在閾值λ處不連續(xù), 估計(jì)的方差較大, 對(duì)數(shù)據(jù)的微小變化敏感(DonohoandJohnstone, 1994a, 1994b; 侯建華, 2003).軟閾值法是指: 信號(hào)的系數(shù)大于一個(gè)確定的閾值λ時(shí), 系數(shù)逐漸變小使λ趨近于0, 系數(shù)小于閾值λ時(shí)置零. 軟閾值法估計(jì)的偏差較大, 對(duì)代表有用信息的數(shù)據(jù)進(jìn)行了壓縮, 易出現(xiàn)過平滑現(xiàn)象(Donohoetal., 1994a, 1994b; 侯建華, 2003). 但對(duì)大多數(shù)的信號(hào)而言, 軟閾值濾波的效果要好于硬閾值濾波(YoonandVaidyanathan, 2004). 因此本文采用軟閾值濾波方法對(duì)數(shù)據(jù)進(jìn)行處理, 軟閾值法的函數(shù)表達(dá)式為(Donoho, 1995)：

(8)

(9)

3 數(shù)據(jù)分析與處理

本文所用到的數(shù)據(jù)來自盆山結(jié)合帶深部結(jié)構(gòu)與油氣遠(yuǎn)景研究項(xiàng)目 (Heetal., 2008; 侯賀晟等, 2012;Gaoetal., 2013). 地表?xiàng)l件復(fù)雜, 經(jīng)過平原帶、山前帶、高山區(qū)等各種類型的地形和構(gòu)造結(jié)合帶, 原始單炮資料屬典型的山地低信噪比資料 (高銳等, 2008;Heetal., 2008;Gaoetal., 2013), 這類資料在深地震反射剖面 (Alsdorfetal., 1998;Langinetal., 2003;Karplusetal., 2011;Kumaretal., 2011)中普遍存在. 在數(shù)據(jù)采集過程中, 如圖2所示的炮集遇到不明震源干擾. 當(dāng)時(shí)無法很好地排除其影響, 只能棄之不用. 考慮到數(shù)據(jù)缺失對(duì)整個(gè)區(qū)域構(gòu)造解釋的影響, 本文選取其中一個(gè)廢炮記錄進(jìn)行處理, 以期最大可能的獲得有用信號(hào). 該單炮的激發(fā)藥量為40kg, 炮點(diǎn)埋深為24m, 炮點(diǎn)樁號(hào)為1541.5, 檢波器排列的起止樁號(hào)為1042-2041, 道間距為50m, 共1000道, 采樣率為4ms. 文中選取樁號(hào)1042-1441共400道30s的數(shù)據(jù)進(jìn)行嘗試性處理(高銳等, 2008;Heetal., 2008;Gaoetal., 2013).

圖2為原始單炮記錄, 顯示該炮集中的干擾波能量較強(qiáng), 信噪比較低, 5s以上反射波組較弱, 連續(xù)性差, 很難識(shí)別有效信號(hào). 圖3為所有道集的頻譜疊加圖, 該單炮記錄的能量主要集中在5～50Hz范圍內(nèi), 其中5～25Hz的頻帶范圍(圖中方框a區(qū)域)包含了該單炮深部和淺部有效信號(hào)的主要能量; 25～50Hz的頻帶范圍(圖中方框b區(qū)域)包含少量的淺部有效信號(hào), 但以強(qiáng)干擾噪聲為主. 這與處理報(bào)告分析結(jié)果相似(高銳等, 2008). 由于深地震反射主要目的是為了探測(cè)深部結(jié)構(gòu)信息, 目標(biāo)信號(hào)以低頻為主, 且25～50Hz頻帶范圍內(nèi)的強(qiáng)干擾噪聲對(duì)突出顯示有用信號(hào)不利, 因此本文只針對(duì)5～25Hz范圍內(nèi)的信號(hào)進(jìn)行精細(xì)化處理.

利用巴特沃斯時(shí)不變帶通濾波器, 保留有效頻帶5～25Hz范圍之內(nèi)的信號(hào). 地震波在地下介質(zhì)傳播, 由于大地吸收衰減使得地震波的能量隨著傳播距離的增加而逐漸的衰減, 尤其對(duì)于大偏移距(超過數(shù)公里, 甚至十多公里)的深地震反射而言, 這種現(xiàn)象尤為明顯. 為了突出顯示深部的有效能量信號(hào), 對(duì)經(jīng)過帶通濾波之后的單炮記錄進(jìn)行瞬時(shí)自動(dòng)增益. 在實(shí)際處理中選取的瞬時(shí)自動(dòng)增益時(shí)間門值通常在256～1024ms范圍內(nèi)(渥·伊爾馬滋, 1994), 本文選取512ms的瞬時(shí)自動(dòng)增益時(shí)間門對(duì)帶通濾波之后的單炮記錄進(jìn)行處理, 處理結(jié)果如圖5所示. 帶通濾波的效果明顯, 有效濾除了大部分的干擾噪聲, 信噪比得到顯著的提高, 深部和淺部的有效能量信號(hào)均得以突顯, 淺部10s以上的殼內(nèi)反射信息豐富, 深部20～25s范圍內(nèi)Moho界面反射清晰可見. 但是在5～25Hz的通帶范圍內(nèi)依然存在混頻干擾噪聲, 這部分噪聲嚴(yán)重影響了相鄰的有效波組之間的區(qū)分, 同時(shí)掩蓋了部分深部弱反射的有效信號(hào). 因此, 為了更加清晰地區(qū)分有效波組和突出顯示弱反射有效信號(hào), 本文利用基于S變換的軟閾值濾波方法對(duì)瞬時(shí)自動(dòng)增益后的帶通數(shù)據(jù)(圖4)進(jìn)行處理, 逐頻點(diǎn)壓制有效頻帶范圍(5～25Hz)內(nèi)的混頻噪聲.

圖2 原始單炮記錄(方框A1、B1、C1為圖8中對(duì)比分析區(qū)域)Fig.2 The raw shot set ( boxes A1, B1, C1 are used to compare in Fig.8)

圖3 原始單炮記錄頻譜疊加分析圖(方框a反映深淺部主要有效信息，方框b反映強(qiáng)干擾噪聲和部分淺部有效信息)Fig.3 The stacked Fourier amplitude spectra of raw shot set (The box of a reveals seismic reflection signals, the box of b reveals strong disturbing waves and a little shallow layers reflection signals)

圖4 時(shí)不變帶通濾波(5～25 Hz)后瞬時(shí)自動(dòng)增益的單炮記錄(方框A2、B2、C2為在圖8中效果對(duì)比區(qū)域, 與圖2中A1、B1、C1分別代表相同時(shí)窗)Fig.4 The shot set after time-invariant bandpass filtering (5～25 Hz) and AGC (boxes A2, B2, C2 are used to compare in Fig.8, which are the same time windows with A1，B1，C1 shown in Fig.2，separately)

圖5 閾值λ隨道號(hào)和頻率的變換Fig.5 The variation of threshold λ with trace and frequency

圖6 基于S變換的軟閾值濾波后的單炮記錄 (方框A3、B3、C3為圖8中的對(duì)比區(qū)域, 與圖2中A1、B1、C1和圖4中A2、B2、C2分別代表相同時(shí)窗)Fig.6 The shot set after S-transform-based soft threshold filtering (boxes A3, B3, C3 are used to compare in Fig.8, which are the same time windows with A1，B1，C1 shown in Fig.2 and A2，B2，C2 shown in Fig.4，separately)

圖7 第1292道數(shù)據(jù)在不同數(shù)據(jù)處理階段的波形及其對(duì)應(yīng)的S變換時(shí)頻分析圖(a) 原始單道記錄; (c) 時(shí)不變帶通濾波(5～25 Hz)后瞬時(shí)自動(dòng)增益的單道記錄; (e)基于S變換的軟閾值濾波后的單道記錄; (b), (d), (f)分別對(duì)應(yīng)圖(a), (c), (e)的S變換時(shí)頻分析圖.Fig.7 The seismic record of trace 1292 and its S transform amplitude spectra on different data processing stages(a) The raw record; (c) The record after time-invariant bandpass filtering and AGC; (e) The record after soft threshold filtering; (b), (d) and (f) are the S transform amplitude spectra of the Fig.(a), (c) and (e).

圖8 處理效果局部對(duì)比圖(A1、B1、C1為原始記錄, 見圖2; A2、B2、C2為時(shí)不變帶通濾波(5～25 Hz)后瞬時(shí)自動(dòng)增益的記錄, 見圖4; A3、B3、C3為基于S變換軟閾值濾波之后的記錄, 見圖6)Fig.8 Comparison of local shot set (A1, B1, C1 is the raw record in Fig.2; A2, B2, C2 is the record after time-invariant bandpass filtering (5～25 Hz) and AGC in Fig.4; A3, B3, C3 is the record after soft threshold filtering based on S transform in Fig.6)

為了更好地說明濾波效果, 圖7給出了第1292道數(shù)據(jù)在不同處理階段的地震波形態(tài)及其相對(duì)應(yīng)的S變換時(shí)頻分析圖. 初至波大致在2.2s左右到達(dá)(如圖7中紅線所示). 原始數(shù)據(jù)(圖7a)的S變換時(shí)頻分析圖(圖7b)可以看出地震波的有效信號(hào)主要集中在5～25Hz的頻帶范圍內(nèi)(圖7b黃色方框所示), 再次印證了圖3頻譜分析圖所確定的時(shí)不變帶通濾波的通帶范圍(5～25Hz)的合理性. 同時(shí)也明顯地看出深部地震信號(hào)能量較弱, 不利于地震信號(hào)的分析處理. 因此在帶通濾波之后, 對(duì)地震信號(hào)進(jìn)行瞬時(shí)自動(dòng)增益處理, 以便突出顯示深部的有效能量, 處理結(jié)果如圖7c所示. 為了壓制5～25Hz范圍內(nèi)的混頻噪聲干擾, 本文運(yùn)用基于S變換的軟閾值濾波方法對(duì)圖7c數(shù)據(jù)進(jìn)行處理, 之后的處理結(jié)果(圖7e)清晰地顯示該方法能夠明顯壓制有效頻帶范圍(5～25Hz)內(nèi)的干擾波, 初至之前的噪聲被顯著地壓制, 而在初至之后, 干擾波被壓制的同時(shí), 有效信號(hào)的能量基本被保留, 顯著地提高了信噪比.

為了進(jìn)一步突出顯示整體濾波效果, 選取了三個(gè)子區(qū)域(A、B和C)在不同處理階段的結(jié)果進(jìn)行對(duì)比, 如圖8所示.A1、B1和C1區(qū)域?yàn)樵夹盘?hào)(圖2);A2、B2和C2區(qū)域?yàn)榻?jīng)過時(shí)不變帶通濾波(有效頻帶范圍5～25Hz)并進(jìn)行瞬時(shí)自動(dòng)增益后的信號(hào)(圖4);A3、B3和C3區(qū)域是在A2、B2和C2處理基礎(chǔ)之上執(zhí)行S變換軟閾值濾波的結(jié)果(圖6).

原始單炮局部記錄(圖8的A1)中可以看到有效波組, 但是波組毛刺較多, 經(jīng)過帶通濾波后瞬時(shí)自動(dòng)增益的單炮局部記錄(圖8的A2)中反射波組更加圓滑, 反射波同相軸更加的清晰, 再經(jīng)過基于S變換軟閾值濾波后的單炮局部記錄(圖8的A3)部分反射波同相軸更加連續(xù), 同時(shí)使得部分弱反射波組更加突出. 原始單炮局部記錄(圖8的B1)中1215-1240道有較強(qiáng)的高頻噪聲, 有效波混雜其中, 經(jīng)過帶通濾波后瞬時(shí)自動(dòng)增益的單炮局部記錄(圖8的B2)高頻噪聲被有效去除, 再通過基于S變換軟閾值濾波后(圖8的B3)不僅反射波同相軸更加連續(xù), 而且反射波組相當(dāng)豐富, 相鄰反射波組也被有效地分開, 有效弱反射信號(hào)能量進(jìn)一步增強(qiáng), 有利于薄地層的識(shí)別和同相軸的追蹤. 原始單炮局部記錄(圖8的C1)中有較強(qiáng)的高頻噪聲, 基本看不出有效反射波信息, 經(jīng)過帶通濾波后瞬時(shí)自動(dòng)增益的單炮局部記錄(圖8的C2)高頻噪聲被有效去除, 可以識(shí)別出幾個(gè)連續(xù)的有效反射波組, 再經(jīng)過基于S變換軟閾值濾波后(圖8的C3)背景噪聲被進(jìn)一步壓制, 較弱有效反射波得到進(jìn)一步的突顯, 信噪比顯著提高. 從圖8的對(duì)比可以看出, 基于S變換的軟閾值濾波在深地震反射單炮數(shù)據(jù)濾波處理中取得了顯著的效果.

雖然經(jīng)過本文精細(xì)化處理之后, 原來的廢炮數(shù)據(jù)現(xiàn)得以重新使用, 但如圖6所示的單炮記錄中不明震源所形成的規(guī)則強(qiáng)干擾仍未完全消除, 為減少?gòu)?qiáng)干擾數(shù)據(jù)對(duì)后續(xù)共深度點(diǎn)疊加數(shù)據(jù)的影響, 需要剔除強(qiáng)干擾信號(hào). 如果壞道或強(qiáng)干擾波出現(xiàn)在關(guān)鍵構(gòu)造目標(biāo)區(qū)內(nèi), 剔除后所造成的數(shù)據(jù)缺失將不利于揭示該區(qū)域復(fù)雜的地質(zhì)構(gòu)造, 重建剔除區(qū)域的地震波場(chǎng)(吳蔚等, 2014)十分重要. 因此, 關(guān)于深地震反射數(shù)據(jù)的處理仍需進(jìn)一步研究.

4 結(jié)論

本文運(yùn)用了基于S變換的軟閾值濾波方法對(duì)西南天山的廢炮數(shù)據(jù)進(jìn)行實(shí)驗(yàn)性的去噪處理, 取得了較好的效果. 與傳統(tǒng)的濾波方法(朱小三等, 2013)相比, 基于S變換的軟閾值濾波方法去噪效果明顯, 壓制了有效頻帶范圍內(nèi)的混頻干擾噪聲, 突出了弱反射信號(hào), 提高了信噪比, 更便于有效反射波組的連續(xù)追蹤和薄地層的識(shí)別. 另外,S變換可以在頻率域?qū)崿F(xiàn), 有較高的計(jì)算效率. 因此, 基于S變換的軟閾值濾波方法不僅可以用于地震反射數(shù)據(jù)去噪處理, 也適用于其他地震學(xué)數(shù)據(jù)去噪處理.

致謝 感謝中國(guó)石化集團(tuán)華東石油局第六物探大隊(duì)采集了大量的野外資料,感謝侯賀晟副研究員從數(shù)據(jù)庫(kù)中提取了本文處理所需的原始數(shù)據(jù), 感謝北京派特森科技發(fā)展有限公司在數(shù)據(jù)處理中提供的寶貴經(jīng)驗(yàn), 感謝中國(guó)地質(zhì)科學(xué)院地質(zhì)研究所巖石圈中心的所有成員對(duì)作者寫作過程中的指導(dǎo)與幫助. 文中的數(shù)據(jù)處理和成圖是通過Matlab、Mathematica和CorelDRAW軟件來完成的.

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(本文編輯 何燕)

Soft threshold filter based on S transform and its application to data processing of deep seismic reflection

QU Zhong-Dang, WU Wei, HE Ri-Zheng*, GAO Rui

StateKeyLaboratoryofContinentalTectonicsandDynamics,KeyLaboratoryofEarthProbeandGeodynamics,InstituteofGeology,ChineseAcademyofGeologicalSciences,Beijing100037,China

Shot-gather data in deep seismic reflection profiling have complicated characteristics of non-stationary, weak energy, a wide variety of strong noise, and so on. How to increase signal to noise ratio of the shot gather has been one big hard nut to crack. We use the soft threshold filter based on S transform to process the obsolete data and show its chart flow is valid.Stockwell (1996) proposed S transform, which is a time-frequency transformation method to analyze non-stationary signal. Compared with other methods for analyzing time-varying signal, the basic wavelet of S transform does not meet an admissibility condition of zero mean in the time domain. The broadness of time window in S transform has an inverse ratio to frequency, which is wide at low frequency and narrow at high frequency. So, the time-frequency resolution in S transform is related to the signal frequency, which has high frequency resolution at low frequency and high time resolution at high frequency. A simple operation of sum along the time axis in the S transform domain can get the Fourier spectrum. Therefore, it is simple to invert S transform. The hard threshold and the soft threshold are the most common methods in de-noising. The soft threshold is better than the hard threshold generally, though it may cause over-smoothing effects. The threshold is calculated from the noise before the first break in the S transform domain.The data are collected in the junction of the southwest Tian Shan and Tarim Basin, northwestern China. This shot set is exploded with 40 kg charge placed in a 24 m-deep borehole and gathered on a 2 ms sampling rate with a 50 m group interval. The raw shot set has a variety of strong noise, and the signal after 5 s is difficult to recognize. After time-invariant bandpass filtering (5～25 Hz) and AGC, the signal to noise ratio is obviously improved. However, mixing interference in 5～25 Hz hampers the identification of thin layers at depth. So, we filter the data further using the soft threshold filter based on S transform to highlight the weak reflection and the Moho reflector.We use the soft threshold filter based on S transform to process the deep seismic reflection data. Our results show that the processing flow does improve signal to noise ratio in deep seismic reflection effectively, which suppresses the frequency mixing interference and enhances weak reflection signal, favorable to track wave groups and further to recognize thin layers. The method increases stratigraphic resolution of the Moho discontinuity especially, which provides the base for subsequent data processing and interpretation of deep seismic reflection profiling. In addition, S transform can be calculated in the frequency domain with the benefits of high calculation efficiency. So, the soft threshold filter based on S transform can also be used in de-noising of other seismic data.

S transform; Shot data of deep seismic reflection profiling; Soft threshold filter; Pre-processing

曲中黨，吳蔚，賀日政等. 2015. 基于S變換的軟閾值濾波在深地震反射數(shù)據(jù)處理中的應(yīng)用.地球物理學(xué)報(bào)，58(9):3157-3168,

10.6038/cjg20150912.

Qu Z D, Wu W, He R Z, et al. 2015. Soft threshold filter based on S transform and its application to data processing of deep seismic reflection.ChineseJ.Geophys. (in Chinese),58(9):3157-3168,doi:10.6038/cjg20150912.

10.6038/cjg20150912

P315

2014-10-24，2015-07-31收修定稿

中國(guó)地質(zhì)調(diào)查局項(xiàng)目(12120115027101); 國(guó)家自然科學(xué)基金項(xiàng)目(40974060, 41274095, 41430213); 國(guó)土資源部公益行業(yè)基金項(xiàng)目(SinoProbe02, 201011044)資助.

曲中黨, 男, 1991年生, 碩士研究生, 固體地球物理學(xué)專業(yè), 主要從事地震學(xué)研究. E-mail:quzhongdang@163.com

*通訊作者 賀日政, 男, 1973年生, 博士, 研究員, 主要從事青藏高原深部結(jié)構(gòu)與構(gòu)造研究. E-mail:herizheng@cags.ac.cn