Deniko, Roman Viktorovich

Ivanchenkov, V. P.

Sidorenko, S. N.

Electronic archive of Tomsk Polytechnic University

XI ぜñ¢ÑÜÖíëÜÑÖí　 ÖíÜôÖÜ-äëí¡öóôñï¡í　 ¡ÜÖâñëñÖîó　 ïöÜÑñÖöÜç, íïäóëíÖöÜç ó ½Ü¿ÜÑ▲ê Üô、Ö▲ê «ぜÜ¿ÜÑ、¢á ó ïÜçëñ½ñÖÖ▲ñ óÖâÜë½íîóÜÖÖ▲ñ öñêÖÜ¿ÜÇóó» ___________________________________________________________________________  121 í¿ÇÜëóö½í – ぢごぱ ëíßÜöíñö ç κ…1β ëí£ ß▲ïöëññ ëíÖññ óïäÜ¿á£Üñ½ÜÇÜ í¿ÇÜëóö½í ぱだぢ.  げí¡¿0ôñÖóñ ぢÜ ëñ£Ü¿áöíöÜ½ óïï¿ñÑÜçíÖó　, ß▲¿Ü ç▲　ç¿ñÖÜ, ôöÜ í¿ÇÜëóö½ äë　½Üú óÖçñëïóó ぱÜëáñ Ñíñö Öíó¿Üôüññ ¡íôñïöçÜ ëñ¡ÜÖïöëÜ¡îóó ïëñÑó ëíï-ï½íöëóçíñ½▲ê íÖí¿óöóôñï¡óê ½ñöÜÑÜç. ぢÜ~öÜ½Ü, ÜÖ ß▲¿ ç▲ßëíÖ ó ëñí¿ó£ÜçíÖ Ñ¿　 óïäÜ¿ÖñÖó　 Öí Çëíâóôñï¡óê äëÜîñïïÜëíê. づñ£Ü¿áöíö▲ öñïöóëÜçí-Öó　 ï¡ÜëÜïöó ëñ¡ÜÖïöëÜ¡îóó äÜ¡í£í¿ó, ôöÜ, ÜÖ ç κ…1β ëí£ ß▲ïöëññ ïçÜñÇÜ ß¿ó¢íúüñÇÜ ïÜäñëÖó-¡í – í¿ÇÜëóö½í âó¿áöëÜçíÖÖÜÇÜ ÜßëíöÖÜÇÜ äëÜ-ñîóëÜçíÖó　, ¡ÜöÜë▲ú ÑÜ¿¢ñÖ ß▲öá £í½ñÖñÖ. ゑ êÜ-Ññ Ñí¿áÖñúüñú ëíßÜö▲ ½ñöÜÑ äë　½Üú óÖçñëïóó ぱÜëáñ ÑÜ¿¢ñÖ ß▲öá çÖñÑëñÖ ç ëíßÜôóú äëÜîñïï ïóïöñ½▲ UFO ó äëÜÇëí½½▲ PyHST.  ずóöñëíöÜëí 1. Weber M. et al. UFO2–Ultra fast X-ray imaging of scientific processes with on-line assessment and data-driven process control. 2. Mersereau R. M. Direct Fourier transform tech-niques in 3-D image reconstruction //Computers in biology and medicine. – 1976. – ど. 6. – ヽ. 4. – で. 247-IN4. 3. Matej S., Bajla I. A high-speed reconstruction from projections using direct Fourier method with optimized parameters-an experimental analysis //Medical Imaging, IEEE Transactions on. – 1990. – ど. 9. – ヽ 4. – で. 421-429. 4. Shepp L.A., Logan B.F. Reconstructing interior head tissue from x-ray transmissions // Nuclear Sci-ence, IEEE Transactions on. – 1974. – ど. 21. – ヽ 1. – で. 228-236. 5. Nadernejad E., Hassanpour H. A comparison and analysis of different PDE-based approaches for image enhancement //Proc. Int. Conf. on Signal Pro-cessing and Communication Systems ICSPCS. – 2007.  THE ALGORITHM FOR PREDICTING RESERVOIR PROPERTIES OF ROCKS BASING ON THE INFORMATION PROPERTIES OF THE MUTUAL PHASE SPECTRUM OF REFLECTED SEISMIC WAVES S.N. Sidorenko, V.P. Ivanchenkov, R.V. Deniko Tomsk Polytechnic University Lenina Avenue, 30, 634050, Tomsk, Russia E-mail: sofyasn@mail.ru  Nowadays, a number of methods for predicting the geological section have been created. There are soft-ware systems for processing and interpretation of seismic data, which widely use dynamic parameters of waves bound with the amplitude and the energy of reflections. The phase characteristics of reflections are used to a lesser extent [1]. Thus, there is an increased relevance for searching new ways to analyze seismic records in order to ex-tend the number of informative parameters. Among such parameters there is the mutual phase spectrum (MPS) of reflected waves. The law of signal phase spectrum change contains information allowing the most reliable detection of signals against intense noise and assessment of their kinematic parameters. The MPS of reflections carries information about acoustic properties, heterogeneity of absorption and dispersion of geological environ-ments [2]. The purpose of this work is the description of al-gorithm for predicting properties of geological section basing on the MPS of reflected waves. To achieve this goal the following objectives should be accomplished: 1. In order to isolate the information properties of MPS of reflected seismic waves a model of layered absorbing media should be considered. 2. The algorithm for predicting geological section properties basing on the MPS of reflected waves should be described. δОЭ’Ь МШЧЬТНОЫ ЭСО ЦШНОХ ШП ХКвОЫОН КЛЬШЫЛТЧР formations. The construction of such a model with horizontal interfacial boundaries represents the whole thing in the form of a linear system, which introduces some changes in the oscillation [3]. The example of a simple model of a plane-parallel layered absorbing formation (Fig. 1a) shows the essence of the approach (fig. 1b).  a b Fig. 1. The model of plane-parallel layered absorbing formation: )(0 tS  – the initial seismic signal, )(1 tS , )(2 tS  – signals reflected from top and bottom of the observed formation II, )(12 fk  and )(23 fk  – the reflection coefficients from top and bottom of layer II, )(12 fr  and )(21 fr  – the refraction coefficients on the top of layer II, )( fH  – frequency characteristic of the absorbing layer  The spectra of the waves reflected from the top and bottom of the layer II: XI ぜñ¢ÑÜÖíëÜÑÖí　 ÖíÜôÖÜ-äëí¡öóôñï¡í　 ¡ÜÖâñëñÖîó　 ïöÜÑñÖöÜç, íïäóëíÖöÜç ó ½Ü¿ÜÑ▲ê Üô、Ö▲ê «ぜÜ¿ÜÑ、¢á ó ïÜçëñ½ñÖÖ▲ñ óÖâÜë½íîóÜÖÖ▲ñ öñêÖÜ¿ÜÇóó» ___________________________________________________________________________  122 1 ( )11 12 0( ) ( ) ( ) ( )j fS f k f S f S f e    , (1) where 121 0( ) ( ) ( )kf f f     defines the phase spectrum of the reflected wave )(1 fS , which depends on the argument of the reflection coefficient )( fk , and the initial phase of the incident wave )(0 f . 22 0 12 23 21( )2( ) ( ) ( ) ( ) ( ) ( )( ) j fS f S f r f H f k f r fS f e   , (2) where12 23 212 0( ) ( ) ( ) ( ) ( ) ( )Sr H k rf f f f f f           defines the phase spectrum of the reflected wave )(2 fS , )(1 fS , which depends on the arguments of the coefficients refraction )( fr  and reflection )( fk , as well as the phase-frequency characteristics of the system )( fH , and the initial phase of the incident wave )(0 f . An important factor used for the prediction of res-ervoir rock properties is the absorption. In absorbent environments there is velocity dispersion. Absorbing and dispersive properties of layered media can be measured by the MPS of a wave. Assuming that the processes )(1 tS  and )(2 tS  are de-terministic, then the mutual spectral density is: )(122*11212)()]()([)( fjefQfSfSfQ  , where )(1 fS  and )(2 fS  complex spectra of the reflected waves )(1 tS  and )(2 tS , )(12 fQ  – mutual energy spec-trum, )()()( 1212 fff    – MPS. (3) Substituting the values of (1) and (2), it is possible to obtain: 2 *12 0 12 23 12 21( ) ( ) ( ) ( ) ( ) ( ) ( )Q f S f k f k f H f r f r f       (4) 23 12 122112 ( ) ( ) ( ) ( ) ( )( )k k H rrf f f f ff        , (5) where )(12fk , )(23 fk – phase shifts introduced by the reflection of waves from the top and bottom of layers; )(12fr , )(21 fr – phase shifts associated with the refraction of the waves, which are directly linked to the petrophysical parameters of the environment. From the expressions (4) and (5) it is possible to deduce that the absorbing and dispersive properties of the environment II appear in the MPS of a wave. It ЬСШЮХН КХЬШ ЛО ЧШЭОН ЭСКЭ НТЬЭШЫЭТШЧ НШОЬЧ’Э КППОМЭ ЭСО evaluation of absorption and dispersion of the ob-served formation, calculated through the MPS of waves. Therefore, the spectral characteristics of the mutual reflection of the observed formation provide more reliable and stable estimates. To assess the information content of MPS the fol-lowing parameters can be introduced [1]: 1. Mean value of MPS 12 1211( ) ( )niif fn   . 2. The central point of the 2nd order for the MPS 212 122 1( ( ) ( ))1niif fn   . 3. The average value of the phase delay 1( )niif   , where 12 ( )( ) 2iiifff  – mutual phase delay at the i-th frequency. 4. The central point of the 2nd order for mutual phase delay 22 1( ( ) ))1niifn    . Thus, the parameters (1-4) may be used as in-formative while studying reservoir rock properties using the MPS of reflected waves. In accordance with the considered properties the MPS of waves, an algorithm for predicting the reser-voir rock properties has been developed [1]. The flowchart of the algorithm is shown in Fig.2. It shows the following: 1. Seismic section is read from the file. 2. The waves which reflect from the top and bot-tom of observed formation are identified, and their temporary position is determined using the algorithm of phase-frequency tracking (PFT). 3. The assessment of MPS is carried out with the help of PFT algorithm quality function. 4. The results of PFT are used in building axes, called object-oriented sections. 5. In accordance with certain predetermined axes and reflecting boundaries, the analysis windows are installed. 6. The complex spectra of waves are deter-mined1 2( ),  ( )S t S t : 1 ( )1 1 1 1( ) ( ) ( ) ( )  j fFS t S t e A f jB f     2 ( )2 2 2 2( ) ( ) ( ) ( )  j fFS t S t e A f jB f   , where F – the operator of the direct Fourier transform. The phase spectrum of a signal1( )S t : 111( )( ) 2( )B ff arctg mA f     (6) 212( ) ( )cos(2 )TT iA f S t ft dt  212( ) ( )sin(2 )TT iB f S t ft dt , where T – the size of the analysis window. In the discrete form of the Fourier transform: 212( ) cos(2 )nnk k i iA f A S kf t    212( ) sin(2 )nnk k i iB f B S kf t   , where , ,Tnt – number of reports in the analysis win-dow, , ,k it – number of samples of the discrete frequen-cy step and time, ,f t   – discretization intervals in frequency and time. 2 ( )kA f  and 2 ( )kB f  for the second signal are de-fined in the similar way. XI ぜñ¢ÑÜÖíëÜÑÖí　 ÖíÜôÖÜ-äëí¡öóôñï¡í　 ¡ÜÖâñëñÖîó　 ïöÜÑñÖöÜç, íïäóëíÖöÜç ó ½Ü¿ÜÑ▲ê Üô、Ö▲ê «ぜÜ¿ÜÑ、¢á ó ïÜçëñ½ñÖÖ▲ñ óÖâÜë½íîóÜÖÖ▲ñ öñêÖÜ¿ÜÇóó» ___________________________________________________________________________  123 Then (6) can be rewritten as kkkAarctgB  . 7. MPS12 ( )f  is determined using the expression (3). 8. The predictive parameters are calculated basing on the obtained values 12 ( )f , They are later used for conclusions about reservoir properties of the observed formation.  Fig. 2. The flowchart for the prediction of reser-voir properties of sedimentary formation  Currently, the proposed algorithm is implemented on a computer and the research of its effectiveness is carried out on the model of layered absorbing envi-ronments.  References 1. ごçíÖôñÖ¡Üç ゑ.ぢ., ゑ▲¿ñÇ¢íÖóÖ だ.ぞ., だë¿Üç だ.ゑ. ó Ñë. ぱí£ÜôíïöÜöÖ▲ú íÖí¿ó£ ïñúï½óôñï¡óê ïóÇÖí¿Üç ó ñÇÜ äëó½ñÖñÖóñ ç £íÑíôíê äëÜÇÖÜ£í ÇñÜ¿ÜÇóôñï¡ÜÇÜ ëí£ëñ£í// ごÖÖÜçíîóÜÖÖ▲ñ ½ñöÜÑ▲ ó öñêÖÜ¿ÜÇóó ÖñâöñÇí£ÜäÜóï¡Üç▲ê. – どÜ½ï¡μ ぴぞどご. –2000. –ï. 6β–74. β. んçñëßÜê ん.ゎ., どëíäñ£Öó¡Üçí ぞ.ん. だöëí¢ñÖó　 ó äëñ¿Ü½¿ñÖó　 ä¿Üï¡óê çÜ¿Ö äëó ÖÜë½í¿áÖÜ½ äí-ÑñÖóó Öí ÇëíÖóî▲// ぱó£ó¡í £ñ½¿ó. –1972. –ヽλ. γ. ぢöñîÜç で.ぞ. んÖí¿ó£ çÜ¿ÖÜç▲ê äÜ¿ñú Ñ¿　 äëÜÇÖÜ£óëÜçíÖó　 ÇñÜ¿ÜÇóôñï¡ÜÇÜ ëí£ëñ£í. – ぜ.μ ぞñÑëí, 1λκλ. –1γ5ï.  ぢだでどづだぎぞごぎ ご んぞんずごげ ぱんげだゑぼび ぢだづどづぎどだゑ がごぱぱばげごだぞぞだざ ぢずんげぜぼ どぎづぜだÄぜごででごだぞぞだゎだ がごだがん どíëíïÜçí ず.ぢ., げó½óÖ ゑ.ぢ. どÜ½ï¡óú äÜ¿óöñêÖóôñï¡óú ÜÖóçñëïóöñö 6γ4050, づÜïïó　, Ç. どÜ½ï¡, äë–ö ずñÖóÖí, γ0 E-mail: Tarasova.luda31@mail.ru  ゑçñÑñÖóñ がóââÜ£óÜÖÖ▲ú ëñ¢ó½ öñë½Ü~½óïïóÜÖÖÜÇÜ äëñÜßëí£Üçíöñ¿　 ~ÖñëÇóó êíëí¡öñëó£Üñöï　 ïëíçÖó-öñ¿áÖÜ ½í¿▲½ó ä¿ÜöÖÜïö　½ó öÜ¡Üç J ó ïëíçÖó-öñ¿áÖÜ ÖñßÜ¿áüó½ Üö¡¿ÜÖñÖóñ½ äíëí½ñöëÜç ä¿í£-½▲ Üö öñë½ÜÑóÖí½óôñï¡ÜÇÜ ëíçÖÜçñïó　. ÄöÜ ÜßÜ-ï¿Üç¿ñÖÜ ½í¿▲½ó óÜÖÖ▲½ó ä¿ÜöÖÜïö　½ó öÜ¡í £í ïôñö äÜçñëêÖÜïöÖÜú óÜÖó£íîóó ó, ïÜÜöçñöïöçñÖÖÜ, ½í¿Üú ¡Ü½äñÖïíîóñú äëÜïöëíÖïöçñÖÖÜÇÜ £íë　Ñí ç ½ñ¢~¿ñ¡öëÜÑÖÜ½ £í£Üëñ. ぞí çÜ¿áöí½äñëÖÜú êíëí¡-öñëóïöó¡ñ öñë½Ü~½óïïóÜÖÖÜÇÜ äëñÜßëí£Üçíöñ¿　 ~ÖñëÇóó (ゑんび どÄぢ) ç ÖñÑÜ¡Ü½äñÖïóëÜçíÖÖÜ½ ëñ¢ó½ñ, ¡ÜÇÑí êó½óôñï¡óú äÜöñÖîóí¿ ä¿í£½▲ ßÜ¿áüñ ëíßÜö▲ ç▲êÜÑí ~½óööñëí たE>FE, äÜ　ç¿　ñö-ï　 ÜôíïöÜ¡ Öíï▲àñÖó　 öÜ¡í (¡çí£óÖíï▲àñÖó　) (ëóï. 1, öÜô¡í A). ぢÜï¿ñÑÖññ Öí£çíÖóñ ÜäëñÑñ¿　ñö-ï　 öñ½, ôöÜ ~öÜö öÜ¡ ½Ü¢ñö ß▲öá £í½ñöÖÜ ½ñÖáüñ öÜ¡í ~½óïïóó ï ~½óööñëí J<<JEe [1].  づóï. 1. でêñ½íöóôñï¡Üñ ó£Üßëí¢ñÖóñ ゑんび どÄぢ ó ëíïäëñÑñ¿ñÖó　 äíëí½ñöëÜç ä¿í£½▲ (öÜô¡í A – ÑóââÜ£óÜÖÖ▲ú ëñ¢ó½)  ゑんび 　ç¿　ñöï　 óÖöñÇëí¿áÖÜú êíëí¡öñëóïöó¡Üú ¡ÜÖâóÇÜëíîóú äíëí½ñöëÜç ä¿í£½▲ ó äÜ~öÜ½Ü äëí-çó¿áÖÜïöá ½ÜÑñ¿ñú ÑóââÜ£óÜÖÖÜÇÜ ëñ¢ó½í ÖñÜß-êÜÑó½Ü äÜÑöçñë¢Ñíöá ïëíçÖñÖóñ½ ï ~¡ïäñëó½ñÖ-

The algorithm for predicting reservoir properties of rocks basing on the information properties of the mutual phase spectrum of reflected seismic waves

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The algorithm for predicting reservoir properties of rocks basing on the information properties of the mutual phase spectrum of reflected seismic waves

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