等效偏移距偏移方法在声波反射成像测井中的应用研究_英文_

等效偏移距偏移在声波反射成像测井中的应用研究_英文_ in Application of the equivalent offset migration method acoustic log re,ection imaging* ?1,21,21,21,2 1,2Zhang Tiexuan, Tao Guo, Li Junjun, Wang Bing, and Wang Hua Abstract: Borehole acoustic reflection logging can provide high resolution images of near- borehole geological structure. However, the conventional seismic migration and imaging methods are not effective because the reflected waves are interfered with the dominant borehole-guided modes and there are only eight receiving channels per shot available for stacking. In this paper, we apply an equivalent offset migration method based on wave scattering theory to process the acoustic reflection imaging log data from both numerical modeling and recorded field data. The result shows that, compared with the routine post-stack depth migration method, the equivalent offset migration method results in higher stack fold and is more effective for near-borehole structural imaging with low SNR acoustic reflection log data. Keywords: acoustic reflection logging, common scatter point gather, signal processing, near- borehole structure imaging resolution of the surface seismic can be investigated in Introduction this way (Tang et al., 2007; Wang et al. 1998). Therefore, the acoustic reflection image log has signi,cant potential applications for finding concealed reservoirs. The acoustic imaging technique was developed in the With the signals recorded with modern acoustic 1980’s and has improved with the advances of logging logging tools, the acoustic reflection image can be instruments and processing methods in recent years generated with multiple step data processing similar to (Hornby 1989). By utilizing the wave energy radiating surface seismic surveys. First, a compressional velocity into the formation from the borehole, the acoustic model of the vicinity of the borehole is created using reflection image log can detect the wave fields reflected the compressional head waves. Then, to extract the from near-borehole fractures or small structures. With re,ected energy, the traditional sonic arrivals including advanced cross dipole transmitter and receiver array P and S head waves and Stoneley waves must be and azimuthally distributed receiver elements on the filtered out of the waveforms for each shot. The ,ltered downhole tools, the azimuthal directions of the reflected traces are input to depth migration which positions the waves can also be identified. The geological structures re,ections in their correct spatial location using the about 1 to 10 m away from the borehole and beyond the Manuscript received by the Editor November October 29, 2009; revised manuscript received November 16, 2009. *This work was supported by the National Natural Science Foundation of China (Grant No. 50674098), the 863 Program (Grant No. 2006AA06Z207 & 2006AA06Z213), and the 973 Program (Grant No. 2007CB209601). 1. State Key Laboratory of Petroleum Resource and Prospecting, China University of Petroleum, Beijing, 102249, China. 2. Beijing Key Laboratory of Geodetection and Information Technology, China University of Petroleum, Beijing, 102249, China. ?Corresponding author (Tao Guo, email: taoguo@vip.sina.com). The equivalent offset migration method velocity model. designed offset range. The CSP gather contains all of the A typical modern acoustic logging tool may have reflection energy in the CMP gather and the scattered a receiver array of 8 to 13 stations (e.g., the Acoustic energy coming from the reflection point. Thus, it more Reflection Image Logging Tool developed by Dagang effectively extracts the information from the seismic Logging Services of PetroChina has a receiver array signals. As Bancroft et al. (1998) pointed out, the CSP of eight stations, while Schlumberger’s SonicScanner gather stack is a complete Kirchhoff prestack migrated has a receiver array of 13 stations). Compared with section, whereas the CMP stack still requires poststack other seismic signals, the reflected waves from an migration. A number of researchers have applied the acoustic logging tool contain the interference from the EOM method for cases of low SNR seismic data and dominant borehole guided modes and there are only 8 have proved that it is especially useful for processing to 13 receiving channels per shot available for stacking. relatively weak seismic wave signals (Wang et al., 2000; These unique features of acoustic reflection waves may Wang et al., 2007; Yin et al., 2007). cause the conventional seismic migration and imaging In this paper, we investigate the applicability of EOM methods to fail in processing the acoustic logging for acoustic reflection imaging by processing both signals for delineating the near borehole structural synthetic data and field log data and then compare the features. For instance, only four to six stack fold can be results with conventional poststack migration. achieved to suppress the noise for an array of acoustic reflection waves when the common midpoint (CMP) The principle of acoustic re, ectiongathers are formed for NMO. In addition, the acoustic reflection signals inevitably suffer from borehole- image logging guided mode interference leading to very low SNR compared with input traces in surface seismic migration operations (Chabot et al., 2002; Tao et al., 2008a and From the full-wave signals received by the acoustic 2008b). logging tools, the acoustic reflection image logging B a n c r o f t e t a l . ( 1 9 9 8 ) f o r m a l l y i n t r o d u c e d a n technique is designed to detect the wave energy radiated equivalent offset migration method (EOM). The method from the transmitter as compressional and shear wave forms common scatter point (CSP) gathers and applies leaky modes into the formation away from the borehole a simplified Kirchhoff migration on the CSP gathers. and are reflected by the near-borehole structure. By This method gains computational efficiency by forming utilizing and analyzing the scattered energy from these the CSP gathers with high fold and large offsets. reflections received by the acoustic logging tool, this The EOM is based on wave scattering theory. It uses technique can image the near-borehole geological equivalent offset to map data into CSP gathers in the structure. T Wellbore signal R1 R2Reflection R3 signal R4 T-transmitter Bed interface R-receiver Fig.1b Imaging a near-borehole bedding boundary using acoustic re,ections from the lower (tool below bed) and upper (tool above Fig.1a Schematic map of acoustic bed) sides of the boundary. re,ection image logging. Zhang et al. The equivalent offset migration concept The EOM was introduced based on the double square root equation of seismic wave travel time (Bancroft et al., 1998). By adopting the principle of prestack Kirchhoff integral migration, it constructs common scatter point (CSP) gathers by sorting the input seismic traces in a designed offset range based on the points where the seismic energy is scattered. The process of forming the CSP gathers is equivalent to the process of prestack migration and can be divided into three major steps. The first step is to convert the input traces to the CSP gathers; the second step is to perform simple Kirchhoff migration on the CSP gathers, including noise elimination, filtering, and moveout correction; and the final step is to stack the corrected gathers (Wang et al., 2007). The process of forming CSP gathers is schematically Fig.1c A ,eld data processing example from ARI.shown in Figure 2a. Assume that the acoustic wave Displayed in this figure are the gamma ray log (left panel), the raw is emitted from the point S at (0, x - h) to a scattering waveform data of the acoustic reflection image log (middle panel), point at CSP (d, 0) somewhere in the subsurface and the and the final image of the geologic structural near the borehole (right scattered wave from that point is received at point R (0, panel). x + h). Let the projection of CSP on the borehole axis be the origin of the coordinates, O (0, 0) and M (0, x) be F i g u r e 1 i l l u s t r a t e s w h y t h e b o r e h o l e a c o u s t i c the mid-point between S and R. Assuming the medium m e a s u r e m e n t c a n o b t a i n t h e g e o l o g i c s t r u c t u r a l velocity is v, the travel time for the seismic wave can be information away from the borehole. Figure 1a depicts written as an acoustic reflection image tool across an inclined bed with a steeply dipping angle intersecting the 2 2 22h – x + d x + h + d vertical borehole. As the acoustic source on the tool is () ( ) (1) + t = , energized, it generates acoustic waves propagating along v v and around a borehole that can be classified into two 1 where h is the half distance between S and R ; d = tv categories, according to their propagation direction. The 0 2first is the waves that travel directly along the borehole, and t is the two-way zero-offset travel time from the 0 including the (refracted) compressional head wave, the CSP to the borehole projection point. Now convert (refracted) shear head wave, and the Stoneley wave, equation (1) from the depth to the time domain: i.e., the classic borehole mode arrivals. The waves of the second category are the acoustic energy that radiates 2 2 2 2 1 1 { [{ [away from the borehole and reflects back to the borehole h – x + t v x + h + t v ()( )| 0 | | 0 | 22 J J [ [ from the boundaries of geological structures. These (2) t = + , v v waves are called reflected arrivals (Tang, 2004). As shown in Figure 1b in a vertical well, the acoustic energy and introduce the equivalent offset hto convert the e strikes the lower or upper side of the bed (depending on double square root equation (2) to a single square root whether the tool is below or above the bed) and reflects equation: back to the receiver as secondary arrivals. After wave 2 field separation, stacking, and migration, these reflected 1 { [ 2 h+ v twaves can be processed to image the formation structural | |e 0 2 J [ (3) feature away from the borehole. An example of a field . t = 2 v data processing result from our software ARI (Acoustic Reflection Imager) is shown in Figure 1c. Equation (3) could be re-written as: The equivalent offset migration method 2can be written as: 4h 2 2 e (4) .t = t + 0 2 v(6) I ? , y, h= W ? , y, x, h D t+ t? , y, x, h dx,() ()() e s r ƒE q u a t i o n ( 4 ) s h o w s t h a t t h e C S P t r a v e l t i m e equation is a hyperbolic equation. As is illustrated in where I is the imaging result, τ is the seismic wave Figure 2, equation (4) means that the acoustic wave is the travel travel time, y is the CSP spatial location, tr travel time along the source S to a scattering point to time from detection point to imaging point, h is half receiver point R is equivalent to the two-way travel the source-receiver offset, W is the weight function time from the co-located source and receiver at the 1 is the angle between the W = (cos 8 + cos 8 ) , 8s r sequivalent offset to the scattering point. Substituting 2 equation (2) into equation (3), we can express the incident line and the vertical axis, θis the angle between r equivalent offset has e the reflection line and the vertical axis, and D is the temporal difference of the input data. The relationship 2 2 4 x h 2 2 2 between τ, he, and tis: 0 h= xh– .(5) e 2vt () 24h 2 2 e (7) .? = t + 0 2 Equation (5) shows that the equivalent offset his a e v time-dependent function and the data samples of the Compared with conventional prestack migration, equivalent offset in the CSP gathers are contained in the EOM with CSP gathers not only has relatively the input acoustic reflection data with different spacing. high signal to noise ratio but is also capable of further This implies that the equivalent offset values for the o p e r a t i o n s l i k e v e l o c i t y a n a l y s i s , r e s i d u a l s t a t i c CSP gathers can be calculated by equation (5) from the correction (Bancroft et al., 1998) and providing a higher different spacing and travel time of reflection waves in SNR migrated section. Therefore, the EOM method the input traces from the image log data. is very useful for the processing of acoustic reflection B a s e d o n t h e K i r c h o f f p r e s t a c k t i m e m i g r a t i o n imaging data with low SNR. equation (Docherty, 1991), the CSP migration equation R R ( 0, x+ h ) S tR h he tS he M (0,x ) CSP t0 CSP x CSP O ( 0, 0) (d,0) S ( 0, x-h) Fig.2b The ray paths for equivalent offset andFig.2a Schematic diagram of the travel time prestack migration. calculation for a scatter point at a given The solid line refers to the equivalent offset ray path and depth. the dashed line refers to the prestack migration ray path. reflection log data with our finite difference simulation The results of applying EOM to is shown in Figure 3. There is a near-borehole infinite theoretical modeling planar interface (the vertical red line in the figure) parallel to the vertical wellbore. The parameters of the model are: wellbore diameter is 0.2 m, distance between Model 1: A near-borehole formation interfacethe interface and well axis is 5 m, borehole fluid velocity is 1500 m/s, and the near-bore medium velocity is 3000 parallel to the wellbore m/s. The first simple model used for generating the acoustic Zhang et al. on the equivalent offset is shown in Figure 4a. Figure 4b shows the waveforms after moveout correction. It can be Medium velocity 4500m/s Medium velocity Borehole seen that the arrival time alignment has been achieved. (5m away from 3000m/s fluid the borehole) Figure 4c shows the stacked trace. velocity 2. Multiple scattering points on the interface: These 1500m/s CSP gathers, denoted as CSP1,CSP2 and CSP3… on the interface, are formed by sorting the raw acoustic CSP3 r e f l e c t i o n w a v e f o r m s o f c o m m o n - s o u r c e r e c o r d s CSP2 based on the equivalent offset and are illustrated in CSP1 Figure 5. Figure 5a shows the CSP gathers prior to the -Transmitter moveout correction, Figure 5b shows the gathers after -Receiver moveout correction, and Figure 5c shows the result after stacking. It is apparent that there is no residual Fig. 3 Geological model 1 for the acoustic re,ection log data moveout left after NMO correction and the reflection by ,nite difference simulation. event is perfectly aligned at the correct position for the multiple CSP gathers. A perfect match is achieved Analysis of the processing results: between the original model and the experimental result 1.Single point: a single CSP gather denoted as CSP1 after the EOM. created by sorting the raw common-source records based 8 1.5 8 (m) (m) (m) 6 6 1 offset offset offset 2 2 Equivalent Equivalent Equivalent 4 4 0.5 0 0 0 100 300 500 700 800100 300 500 700 800 100 300 500 700 800 Time (us) Time (us) Time (us) Fig. 4a The CSP of one point. Fig. 4b The CSP after moveout correction. Fig. 4c The stacked result. 3 . M u l t i p l e s c a t t e r p o i n t s o n a 2 - D p l a n e : A s formed by a similar sorting method. These CSP gathers Fig. 5a The CSP prior toFig. 5b The CSP after moveout Fig. 5c The stacked result. schematically illustrated in Figure 6, there are discrete formed on the 2-D plane perpendicular to the interface moveout correction. correction. multiple scattering points on a 2-D plane perpendicular can be taken as cutting a cross section through the to the interface where the corresponding CSP gathers are borehole axis in the near-borehole formation and then The equivalent offset migration method mapping the data to this 2-D plane. Figure 7a shows the stepplane, Figure 7b is the section after moveout correction, Interface size CSP gathers formed from the multiple points on the 2-D Horizontal and Figure 7c demonstrates the stacked section presented in a waveform format (left) and a variable density Vertical image (right). We see clearly that the geometry and the step size position of the stacked section match with the theoretical geological model exactly. This means that the EOM isCSP well suited for processing the acoustic reflection image log data. Fig. 6 Schematic diagram for forming CSP gathers from multiple discrete points on a 2-D plane. Fig. 7a The CSP gathers Fig. 7b The section after Fig. 7c The waveform and variable density presentation formed on the 2-D plane. moveout correction. after stack. f t r- r l i t rf it i l f , shown in Figure 9 with the waveform image in Figure 9a Model 2: A deviated near-borehole interfac e i l f t t r l i . rf r and the variable density image in Figure 9b. The stacked with an angle of 5? to the borehole axis section has accurately delineated the geological featuref r i t rr i t r - l As shown in Figure 8, the interface in this case has o he nea bo eho e n e ace w h a d p ang e o 5? a d p ang e o 5? o he bo eho e ax s We pe o med exactly the same as the given geological model. similar data processing as in the previous model, i.e., o m ng he co espond ng CSP ga he s on a 2 D p ane and then stacking the signals. A ,eld acoustic re,ection imaging data example T o c o m p a r e a n d a n a l y z e t h e a p p l i c a b i l i t y a n d Horizontal step size effectiveness of the conventional poststack depth Interface m i g r a t i o n m e t h o d a n d E O M m e t h o d f o r a c o u s t i c Vertical reflection imaging, the field acoustic reflection data by step size the Acoustic Reflection Image Logging Tool developed by Dagang Logging Services of PetroChina from an CSP oil field was selected and separately processed by the two methods. The field data has a low SNR. The results Fig. 8 Geometry for Model 2. presented in a down-going waveform section are shown Zhang et al. selected and enlarged. These segments were 160 marked with a red rectangular frame and 140 60 presented for comparison in Figures 10c, 10d, 10e and 10f, respectively. It is apparent 120 from Figure 10a and the correspondent 50 segments in the enlarged pictures in Figures 100 10c and 10e that the section obtained by 40 poststack depth migration does not provide 80 clear and continuous reflection events, and Z Depth (m) 30 the diffraction wave energy could not be 60 properly focused, whereas the reflection 20 40 section using the EOM (Figure 10b and the correspondent segments in the enlarged 10 20 pictures in Figures 10d and 10f) shows a much better image with more clear and 0 0 100 300 500 700 800 100 300 500 700 800 continuous reflection events(e.g., see the Time (us) Time (us) areas marked with red lines in the enlarged Fig. 9a The stacked section in Fig. 9b Variable density plot.segment in Figure 10f), and the diffraction waveform. wave energy were properly focused. Z Depth (m) XX40 a1 XX30 (m) Depth a2 XX20 XX10 100 300 500 600 (c) The enlargement of the area (e) The enlargement of the area Time (us) inside the red box (a1) in Figure inside the red box (a2) in Figure (a) The section obtained with the 10a. poststack depth migration method. 10a. XX40 b1 XX30 Z Depth (m) Z b2 XX20 XX10 100 300 500 600 (d) The enlargement of the area (f) The enlargement of the area Time (us) inside the red box (b1) in Figure inside the red box (b2) in Figure (b) The migrated section obtained by 10b. applying the EOM 10b. Fig.10 The section comparison by separately applying the poststack migration method and the EOM to the downgoing wave in one well of Dagang Oil ,eld . The equivalent offset migration method Tang, X. M., Zheng, Y., and Patterson, D., 2007, Processing Conclusions array acoustic-logging data to image near-borehole geological structures: Geophysics, 72(2), E87 – E97. Tao, G., He, F. J., Wang, B., Wang, H., and Li, L. S., 2008a, By detecting high resolution reflected acoustic waves Applying the acoustic reflection image logging to the and using data acquisition and processing methods similar 3-D waveform simulation method research both in the to seismic exploration, the acoustic reflection imaging homogeneous and the heterogeneity formations: Science technique can be employed to investigate formation in China Series D: Earth Sciences, 38(1), 166 – 173. structure adjacent to the borehole, to delineate near- Tao, G., He, F. J., Yue, W. Z., and Chen, P., 2008b, borehole fracture geometry, and to image small structures Processing of array sonic logging data with multi-scale which cannot be resolved by surface seismic methods. STC technique: Petroleum Science, 5(3), 238 – 241. EOM converts the double square root equation to a Wang, N. X., Su, H., Liu, W. M., and Ou, Y., 1998, The single square root equation to focus the scattered energy reflected acoustic wave imaging analysis in the acoustic along a hyperbolic path. The key step of EOM is forming f u l l - w a v e l o g g i n g : W e l l L o g g i n g T e c h n o l o g y ( i n CSP gathers. EOM is especially useful for increasing the Chinese), 22(4), 278 – 283. stack fold and hence improving the signal-to-noise ratio Wang, Y., Zhu, Y. P., and Yang, H. Z., 2000, The research of the migrated section. on applying the common scatter point imaging to process the 3-D seismic data with low signal-noise ratio: Oil Both numerical simulation and field data results of Geophysical Prospecting, 35(1), 20 – 26. applying EOM have demonstrated that the EOM is Wang, W., Yin, J. J., Liu, X. W., Zhao, J. M., Wang, B., and superior to the conventional post-stack depth migration Huang, Y., 2007, Equivalent migration method and its method, providing a better image of clear and continuous application: Chinese Journal of Geophysics, 50(6), 1823 reflection events. This method should be very useful – 1830. for the migration and imaging of the low SNR acoustic Yin, J. J., Wang, W., Wang, B., Liu, X. W., Li, W. H., and reflection image log data and should have significant Zhao, Z. W., 2007, The research on the multiple wave potential applications in the acoustic reflection image attenuation technique based on the scatter imaging: logging. Geophysical Prospecting for Petroleum, 46(4), 319 – 323. References Bancroft, J. C., Geiger, H. D., and Margrave, G. F., 1998, Zhang Tiexuan holds a B.S. degree in Well Logging The equivalent offset method of prestack time migration: f r o m C h i n a U n i v e r s i t y o f Geophysics, 63(6 ), 2042 – 2053. Petroleum-East China and a Chabot, L, Henley, D.C., Brown, R.J. and Bancroft, Masters degree in Geological J.C., 2002, Single-well seismic imaging using the full E n g i n e e r i n g f r o m C h i n a waveform of an acoustic sonic: SEG Int’l Exposition and U n i v e r s i t y o f P e t r o l e u m - 72nd Annual Meeting,Salt Lake City, Utah. Beijing. Now she is studying Docherty, P., 1991, A brief comparison of some Kirchhoff f o r h e r P h D d e g r e e i n i n t e g r a l f o r m u l a s f o r m i g r a t i o n a n d i n v e r s i o n : g e o l o g i c a l r e s o u r c e s a n d Geophysics, 56(8), 1164 – 1169. g e o l o g i c a l e n g i n e e r i n g a t Hornby, B. E., 1989, Imaging of near-borehole structure the University of Petroleum- using full-waveform sonic data: Geophysics, 54(6), 747 Beijing. She is currently concentrating on acoustic – 757. logging and wireline formation testing and, at the Tang, X. 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