Spectral Recomposition in Stratigraphic Interpretation*

Transcription

1 Spectral Recoposton n Stratgraphc Interpretaton* Yhua Ca 1, Sergey Foel 2, and Honglu Zeng 2 Search and Dscovery Artcle #41376 (2014)** Posted June 30, 2014 *Adapted fro oral presentaton gven at Geoscence Technology Workshop, Deepwater Reservors, Houston, Texas, January 28-29, 2014 **AAPG 2014 Seral rghts gven by author. For all other rghts contact author drectly 1 Shell, Houston, TX (yhua.ca@shell.co) 2 Unversty of Texas at Austn, Austn, TX Abstract Spectral recoposton splts the sesc spectru nto Rcker coponents. It provdes a tool for agng and appng teporal bed thcknesses and geologc dscontnutes. We propose separable nonlnear least-squares estaton n spectral recoposton. Eployng the Gauss-Newton ethod, separable nonlnear least-squares approach estates fundaental sgnal paraeters: peak frequences and apltudes. References Cted Chakraborty, A., and D. Akaya, 1995, Frequency-te decoposton of sesc data usng wavelet-based ethods: Geophyscs, v. 60/6, p Chen, G., G. Matteucc, B. Fahy, and C. Fnn, 2008, Spectral-decoposton response to reservor fluds fro a deepwater West Afrca reservor: Geophyscs, v. 73/6, p. C23-C30. Chopra, S., and K.J. Marfurt, 2007, Voluetrc curvature attrbutes addng value to 3D sesc data nterpretaton: The Leadng Edge, v. 26, p

2 Spectral Recoposton n Stratgraphc Interpretaton Yhua Ca*, Sergey Foel, and Honglu Zeng Unversty of Texas at Austn * Currently wth Shell

3 Outlne Motvaton and Background Spectral Analyss Spectral Recoposton Theory and Nuercal Method Theory Nuercal Method Separable Nonlnear Least Squares Estaton Synthetc and Real Data Exaples Applcaton of Spectral Recoposton Sesc Data Dsplay Stratal Slce Iagng and RGB Color Blendng Plot Te-frequency Analyss Estaton Suary

4 Spectral Analyss Spectral analyss: 1. Long wndow vs. short wndow; 2. Spectral decoposton for short wndow analyss. Spectral decoposton s helpful because: 1. Unpredctable geology and whtened spectru n a long wndow; 2. In short wndow analyss, local geology flters wavelet and overprnts t n frequency doan. Soe dffcultes n spectral decoposton: 1. Te-frequency resoluton lt; (Greg Partyka, Jaes Grdley, and John Lopez, 1999) 2. Resduals n frequency gathers. (Chakraborty and Okaya, 1995) Long Wndow Short Wndow (Chen, 2008)

5 Spectral Recoposton 1. Manually select coponent frequences; 2. Copute spectru of each coponent; 3. Scale apltude spectru of each coponent; 4. Su coponents up. (Mark Toasso, Renaud Bouroullec and Davd Pyles, 2010)

6 Model: d( f ) a and d( f ) n = 1 s the spectru of sesc data; Rcker spectru: a Ψ (, f ) Theory are the apltude and peak frequency of the -th Rcker coponent. To estate a sesc spectru, we need: 2 2 f f R( f ) = aψ(, f ) = a exp( ) 2 2 a = a, a,, a } and =,,, } { 1 2 n { 1 2 n Each coponent has ts own apltude and peak frequency ters.

7 Nuercal Method Separable Nonlnear Least Squares = Ψ = n j j j f a f d r 1 ), ( ) ( ) ( ), ( a 2 2, ), ( n a r a Let Optal least-squares estaton requres: The varable projecton algorth has been used. Assung, we have: d a ) = Ψ( where ) ( Ψ s the atrx coposed of ), ( j f Ψ Ψ + Ψ + Ψ + j j j j j j j f a f a f a r f r f d )], '( ), ( ' [ ), ( ), ( ) ( Gauss-Newton ethod has been used, hence (Golub & Pereyra, 1973) Lnear and nonlnear parts are solved separately by least squares ethod. (Scolnk, 1972) 2 2 ) ) ( ) ( ( n d I Ψ Ψ Havng a solved, we then need to solve

8 Spectral Recoposton Synthetc Data

9 Spectral Recoposton Real Data Exaple

10 Spectral Recoposton Data Fttng Exaple

11 Frequency Band Pckng t R t D t R = t D / 3 t D = 6 / f π

12 Applcaton of Spectral Recoposton Usng SNLS Sesc age dsplay Stratal slce agng and RGB color blendng Te-frequency analyss sulaton

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16 RGB Color Blendng Plot RGB color odel: an addtve color odel n whch red, green, and blue are added together to produce a broad array of colors. Usng color blendng plot, we can vsualze subtle geologc features Varous color blendng plots based on varous types of sesc attrbutes (Chopra and Marfurt, 2007)

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18 ) ~ h Ch.nnel o '<t - o - r<'> :IF:lt o - N o - ~L--2~~~~~~~~

19 Inferred sedent source IUe Incsed Hey fll delta 'fr Channel.urce Incsed vahey fll

20 Stratal Slce., I, (Honglu Zeng, and Tucker Hentz, 2004)

21 RGB Color Blendng Plot wth Sgnfcant Coponents pont bar IVF pont bar dstrbutary channel

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25 Suary Spectral recoposton as a new approach of spectral analyss extracts sgnfcant coponent frequences and ther apltudes reconstructs sesc spectru accurately and effcently proves sesc dsplay, color blendng plot and t-f analyss can be used n nverson, reservor characterzaton, etc. SNLS n spectral recoposton converges to local nu quckly allows nterpreter to choose nuber of coponents n estaton

26 Golub, G.H., and V. Pereyra, 1973, The dfferentaton of pseudonverses and nonlnear least squares probles whose varables separate: SIAM Journal on Nuercal Analyss, v. 10, p Partyka, G., J. Grdley, and J. Lopez, 1999, Interpretatonal applcatons of spectral decoposton n reservor characterzaton: The Leadng Edge, v. 18/3, p Scolnk, H.D., 1972, On the soluton of non-lnear least squares probles: IFIP Congress, IFIP Congress, p Toasso, M., R. Bouroullec, and D.R. Pyles, 2010, The use of spectral recoposton n talored forward sesc odelng of outcrop analogs: AAPG Bulletn, v. 94/4, p Zeng, H., and T.F. Hentz, 2004, Hgh-frequency sequence stratgraphy fro sesc sedentology: Appled to Mocene, Verlon Block 50, Tger Shoal area, offshore Lousana: AAPG Bulletn, v. 88/2, p