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P-wave fracture prediction algorithm using pre-stack data with limited azimuth distribution: A case study in the TZ45 area, Tarim Basin, China

P-wave fracture prediction algorithm using pre-stack data with limited azimuth distribution: A... of seismic waves varies with offset and azimuth (AVOZ). A noise attenuation fracture inversion algorithm is presented for fracture detection based on P-wave AVOZ. The conventional inversion method always fails when applied to limited azimuth data because of the existence of noise. In our inversion algorithm, special attention is paid to suppressing the noise during inversion, to overcome the limitation of the conventional inversion method on limited azimuth data. Numerical models are employed to illustrate the effectiveness of the method. The inversion algorithm is then applied to Tazhong 45 area fi eld data which is acquired under limited azimuth distribution. Compared with cores and fullbore formation microimage (FMI), the inverted results (fracture density and orientation) are reasonable, suggesting that the inversion algorithm is feasible for fracture prediction in the Tarim Basin. Tarim Basin, azimuthal anisotropy, AVOZ inversion, fracture detection Key words: in anisotropic media. Mallick et al (1998), Schoenberg et al 1 Introduction (1999) and Gray and Head (2000) used a law of amplitude The exploration area has been proven very large in the versus azimuth to study fracture mediums. Shen et al Tarim Basin in China, about 2,100 km in the Tabei area (2002) proposed a method of using attributes such as AVO and 7,300 km in the Tazhong area. The proven reserves (amplitude versus offset) and FVO (frequency versus offset) in carbonate reservoirs discovered in the Tazhong area are to detect fracture orientation in a carbonate reservoir located estimated to be 4.8×10 tonnes in the past three years. in the Maporal Field in the Barinas Basin of southwestern The key technical problem is how to predict and Venezuela. Luo and Evan (2004) presented an amplitude- characterize this type of reservoirs. The storage spaces are based multiazimuth approach for mapping fractures. Al- mostly secondary, of which about 99% porosity is from Marzoug et al (2006) estimated small azimuthal variations fractures and dissolution caves or holes (Sun et al, 2011a). in P-wave velocity (maximum 5%) and a larger variation in How to predict fracture development is a question which azimuthal AVO at the reservoir (larger than 100%) in two confronts us. Saudi Arabian fi eld studies. It is known that vertically aligned fractures in a reservoir A well established technique used in fracture prediction could induce P-wave seismic anisotropy. P-wave contains is based on Ruger’s equation (Ruger, 1998), which describes plenty of fracture information which involves amplitude the reflection amplitude variation with offset and azimuth variation versus azimuth, variation of azimuthal travel (AVOZ). This conventional fracture detection method requires time and velocity (Crampin et al, 1980; Ruger 1996; 1998; the use of wide azimuth data (Wang et al, 2006; Zelewski et Grechka et al, 1999; Tsvankin, 2001). A lot of work has been al, 2009), because for azimuthally limited data, the existence done on fracture detection based on P-wave features. Neidell of noise will make the solution unstable. However, as and Cook (1986) applied P-wave data to predict fractures Ordovician carbonate reservoirs in the Tarim Oilfi eld underlie based on differential stacking velocity. Then amplitude a big desert, poor surface conditions lead to very high seismic versus offset (AVO) was used to study fractured reservoirs. acquisition cost, and the pre-stack data is azimuth limited due Ruger (1998) gave the law of P-wave amplitude variation to cost factors. Thus early fracture detection research always fails. It is a challenge if we make use of the current data with * Corresponding author. email: szd@cup.edu.cn, samzdsun@yahoo.com limited azimuth distribution. Received March 18, 2011 The algorithm we introduce in this paper is the P-wave Pet.Sci.(2011)8:422-432 423 fracture prediction algorithm using pre-stack data with limited represents the anisotropic term in the reflection coefficient azimuthal distribution, where a noise attenuation method is gradient and is also the fracture density to be inverted. employed. Then it is applied to the Tazhong 45 area, where A conventional inversion method based on Eq. (2) can be the data is acquired under limited azimuthal distribution. given by further derivation: Before the inversion is conducted, the data is processed using the flow which could retain the integrity of the amplitude ­ Ri ( ,II ) C C cos sin i 1 2 variation information, where the multiples are excluded, the 2 22 2C sinII cos sin iC  sinI sin i signal to noise ratio is enhanced and the amplitude preserved ani 2 C B cos I migration is employed. The inversion results are proven to be (3) 2 s reliable and are in good agreement with the geological data. ani CB sin 2I 3 s Moreover, it is feasible to detect effective fractures (higher ani 2 C B sin I anisotropy, fi lled with liquid or gas), which suggests that the 4 s algorithm presented in this paper is feasible and effective. where C , C , C and C are four unknowns, assuming the fold 1 2 3 4 2 The algorithm of 3D pre-stack inversion of the common refl ection point (CRP) is n, then Eq. (2) can be expressed as: The Ruger P-wave refl ection coeffi cient equation (Ruger, 1998) is (4) AXB 1 ' Z Ri (,I ) where A denotes the matrix of n rows and 4 columns; X 2 Z is the column vector which contains C , C , C , and C ; B 1 2 3 4 ­½ '' DE§· 2 G is the seismic reflection amplitude (without noise). Then °° ¨¸ the conventional fracture inversion method is to calculate DD G °° ©¹ 1°° sin i the unknown X. Wide azimuth data are needed in order to ®¾ ªº (1) §· °° 2E 2 overcome the noise interference as the existence of noise «» ' G  2 ' J cosII ( ) ¨¸ s °° makes the solution unstable. «» ©¹ °° ¬¼ ¯¿ In order to make use of the limited azimuth data to ­½ D 4 conduct the inversion, a special algorithm is needed to ' H cos II (  ) 1°° suppress the noise interference. We introduce the noise part D sin ii tan ®¾ V 22 N to the conventional equation (Eq. (4)), then Eq. (4) is °° ' G sin I ( I ) cosII ( ) ¯¿ ss transformed to: V V ' J where' H , ' G and denote the Thomsen parameters; α (5) AX BN and β are P-wave velocity and S-wave velocity, respectively; is the acquisition azimuth of the survey line; is the Through the singular value decomposition (SVD) method, fracture direction; i denotes the incidence angle; Z U D is the matrix A in Eq. (5) can be expressed as: the vertical P-wave impedance; and G U E denotes the vertical shear modulus. (6) A UWV When the incidence angle is not large, is sin ii tan relatively small, the third term in Eq. (1) can be neglected. where U is the orthogonal matrix of n rows and 4 columns; Then Eq. (1) can be given by: W is the diagonal matrix with 4 rows and 4 columns, and of which the diagonal elements are positive or 0; V is the iso ani 2 Ri ( ,I ) P ªº B B co s(I I ) sin i (2) ¬¼ orthogonal matrix with 4 rows and 4 columns. Calculating the generalized inverse by the SVD method, we obtain: with TT 1 ' Z X AA A B N (7) 2 Z T  1T T  1T VW U B VW U N ª º 12 '' DE§ · G iso By using Eq. (7), the effective signal can be separated B «  » ¨ ¸ 2 DD G « » from noise. Concretely, it is to multiply N with a small © ¹ ¬ ¼ number or to divide it by a large number, then the noise part will approach 0. The infl uence of noise on the inversion result ªº 12 § E · ani V B «» ' G 2 ' J can be limited, which enables us to use the limited azimuth ¨ ¸ 2 D «» © ¹ data to perform the inversion (Sun et al, 2011b). ¬¼ where P represents the reflection coefficient of the vertical 3 The feasibility of the inversion method iso incident wave; B is the isotropic term in the reflection ani coefficient gradient which is azimuthally invariant; B Fig. 1(a) represents a wide azimuth acquisition system 424 Pet.Sci.(2011)8:422-432 (top) and a limited azimuth acquisition system (bottom). On Further, based on the conventional method, for the data with the top part of Fig. 1(a), the spots and receivers distribute in a certain extent of noise, full azimuth data could be used to the range of 360 degree azimuth, while at the bottom part of calculate anisotropy, as is shown in the middle of Fig. 1(b). Fig. 1(a), spots and receivers cover a limited part of the whole However, from the bottom of Fig. 1(b) we can conclude that azimuth range. anisotropy could not be inverted properly from the limited We divide Fig. 1(b) into three parts: the top part, the azimuth data based on the conventional method (inside the middle part and the bottom part. The colored diagrams red ellipse there is no anisotropy). However, if we introduce ani represent inversion results of the fracture density (B in Eq. the noise suppression method into the inversion process, (2), red highest, green lowest), while the black and white the fracture density which is relatively uniform from left to diagrams represent the seismogram CMP gathers with ‘full right can be shown (the right map). Therefore, by the noise azimuth’ or ‘limited azimuth’ marked at the bottom. As it is attenuation method discussed, we can calculate anisotropy shown on the top part of Fig. 1(b), for data without noise, on the basis of the limited azimuth distribution data, which the inversion results of the full azimuth data and the limited could help us to make use of existing limited azimuth data azimuth data are the same, and both of them show the correct and possibly save some costs in some acquisition layout (Sun results (weak, strong, weak, strong feature from left to right). et al, 2011b). ILINE_NO XLINE_NO 1 0.35 50 53 56 59 0.50 Without noise Without noise 0.25 0.20 0.15 0.10 0.05 880 0 -0.05 1500 900 -0.10 -0.15 940 -0.20 -0.25 rec_y -0.3 980 -0.35 sou_x 3500 4000 4500 5000 5500 6000 6500 sou_y -500 Full azimuth Limited azimuth -1000 ILINE_NO -1500 0.14 XLINE_NO 1 50 53 56 59 0.12 -2000 0.10 With noise 820 0.08 0.06 Full azimuth acquisition 0.04 0.02 880 0 -0.02 -0.04 -0.06 1500 940 -0.08 960 -0.10 -0.12 -0.14 rec_y sou_x Full azimuth 3500 4000 4500 5000 5500 6000 ILINE_NO ILINE_NO sou_y -500 1.4 XLINE_NO 1 0.9 XLINE_NO 1 50 53 56 59 0.8 1.2 50 53 56 59 0.7 -1000 1.0 With noise 0.6 0.8 0.5 820 -1500 0.6 Noise attenuation 0.4 0.3 0.4 0.2 -2000 method 860 0.2 0.1 0 880 0 -0.1 -0.2 -0.2 900 Limited azimuth acquisition -0.4 -0.3 -0.4 -0.6 940 -0.5 940 -0.8 -0.6 960 -1.0 -0.7 -0.8 -1.2 -0.9 -1.4 Limited azimuth (a) (b) Fig. 1 Numerical examples illustrating difference between wide azimuth and limited azimuth on azimuthal AVO inversion, showing the effectiveness of the new method in noise suppression shown in Fig. 2. From Fig. 2, some conclusions are drawn. 4 Data processing before inversion Firstly, both of the two acquisition systems have wide ranges of offsets, but the fold of second acquisition system is higher 4.1 Geometry of 3D fi eld data than that of the fi rst one, and both of the two have unequal Data quality has been improved as the 3D acquisition fold for different offsets. Secondly, the second acquisition system is optimized year by year ever since 2002 in the system has a relatively larger and more uniform range of Tazhong area. Two designing methods are frequently used, azimuth than the first one, but the azimuth range for both those are, 10 lines, 30 shots and 216 traces (every 5 lines), of them is mainly centralized in the lateral direction, for and 12 lines, 36 shots and 216 traces (every 6 lines). Now the vertical direction, the offsets are smaller, and the fold is we analyze the azimuth distribution of acquisition lines and lower, the azimuth distribution is not uniform and the range the fold of different offsets, and the analytical results are of the fold is limited (Sun and Wang, 2008). Time, ms Time, ms Time, ms Amplitude Amplitude Amplitude Time, ms Amplitude Time, ms Pet.Sci.(2011)8:422-432 425 10L 30S 216T (every 5L) 10L 30S 216T (every 5L) Fold Fold 49-59 43-48 43-48 31-36 37-42 31-36 19-24 25-30 19-24 7-12 12L 36S 216T (every 6L) 12L 36S 216T (every 6L) Fold 4200 3325 Fold 51-58 4180 51-58 37-43 37-43 23-29 23-29 8-14 0-14 Fig. 2 Analysis of fold and azimuth of CRP gathers in the Tazhong 3D seismic acquisition system (L is short for line, S-shot, T-trace) From processing fl ow (Fig. 3), we can see the results are 4.2 Problems in the 3D seismic data divided into two types: conventional processing fl ow without The Tazhong area is characterized by loose dunes in pre-stack migration (left part) and processing fl ow with pre- surface, large variation of sand layer thickness. Additionally, stack migration (right part). Fracture inversion will be carried Ordovician carbonate reservoirs are characterized by high out based on the data from the two flows respectively, in seismic wave velocity and deep burial with the depth ranging order to test the effect of migration on inversion. Now, we from 4,000 to 7,000 m. Besides, fractures, dissolution pores present some key steps in the processing fl ow: and caves are highly developed, thus this area shows strong 1) Noise attenuation. Different noise attenuation methods heterogeneity and anisotropy. are used considering different noise sources and types. Due to the complex geological conditions, seismic data Spherical divergence compensation is applied to improve S/N. have following characteristics. First, folds in the conventional 2) Surface consistent processing. Surface-consistent acquisition system are unequal with high folds in the middle amplitude compensation, surface-consistent static correction, offsets and low in the edge. Second, the azimuth distribution surface-consistent wavelet shaping and surface-consistent is limited, where the coverage range of azimuth is less than de-convolution are included. Surface consistent amplitude 60 degrees. Third, due to the deep burial, low velocity in the compensation eliminates imbalance of energy resulted surface and various interferences, the data has low sighal/ from different explosion and receiving conditions. Surface noise (S/N). Considering the data features in the Tazhong consistent wavelet shaping and surface consistent de- area, we present processing fl ow before inversion, including convolution focus on removing inconsistency of the energy some key processing methods. in space, instability of waveform and differences between wavelet and phase from different shots, as well as suppressing 4.3 Processing fl ow of the 3D data noise to improve data quality. Considering the complexity of seismic data in the 3) Forming super gathers. When seismic data from the Tazhong area, data processing is especially important before conventional acquisition is used in inversion, they always lack anisotropic inversion. Amplitude preserved processing enough folds, and the azimuth distribution is also limited. is the prerequisite of inversion. The key to the amplitude Forming super gathers can increase folds and the azimuth preservation data processing is to eliminate the interference range of the azimuth gathers and S/N will be improved. brought about by the non-geological factors in order to keep 4) Defining azimuth and forming azimuth gathers. The the integrity of the seismic data. Only reliable seismic data data is divided into groups according to their azimuth and can provide true amplitude variation information for the offset range and then the azimuth angle of each gather is fracture inversion. defi ned to form azimuth gathers. 426 Pet.Sci.(2011)8:422-432 5) Pre-stack 4D noise attenuation. According to the primary wave and multiples are separated based on their unpredictability of random noise and the predictability of different energy positions. Radon Transform is a type of effective signal in the F-XYZ domain, a prediction operator ‘subtraction method’ when it is used in multiples elimination. is applied to the seismic data to suppress noise, and then the First, data are transformed into the Radon domain and the data is transformed back into the time-space domain. As a method of velocity removal is used to separate multiples, and result, noise is suppressed and S/N is improved. then the data are transformed to the time-space domain and 6) Multiples elimination. In the Radon domain, the multiples are removed from the effective signal. 3D observation system define Field static correction Geometric diffusion compensation Noise eliminating Surface consistent compensation Produce azimuth gathers NMO Velocity analysis Stack Pre-stack time migration Noise eliminating Pre-stack 4D noise eliminating Multiple attenuation Multiple attenuation Residual static correction & NMO Residual static correction & NMO Inversion Inversion Fig. 3 Pre-stack processing fl ows of 3D seismic data obtained in the Tazhong carbonate reservoir and 44.3-59.3 degrees. For each sector, the azimuth angle is 5 Analysis of azimuth gathers before defi ned as the middle angles, which are, 7.15, 21.8, 36.8 and inversion 51.8 degrees, so that each azimuth gather in the Tazhong45 3D seismic data in the Tazhong45 area is distributed in the area contains four azimuths. azimuth range of 0-59.3 degrees. The azimuth is divided into After a series of processing steps, common reflection four sectors: 0-14.3 degrees, 14.3-29.3 degrees, 29.3-44.3 428 Pet.Sci.(2011)8:422-432 0.0 4n/55m 4 n/ 5 5m TZ86 ZG171 0.2 TZ861 TZ452 ZG162-1H 1n/30m ZG18 ZG26 TZ451 ZG162 0.4 TZ88 TZ45 ZG16 0.6 ZG14-1 ZG14 ZG163 ZG161 0.8 ZG15 TZ63 2n/47m ZG15-2 ZG15-1H 1.0 Fig. 5 Fracture density and direction inverted in the TZ45 area. The area with higher crack density mostly centers on the region close to well TZ452. Fracture density increases from southeast to northwest from well TZ88 to well ZG17 (from FMI data, the fracture angles corresponding to each offset are 7.15, 21.8, 36.8, and linear density of well TZ88 equals to 0.06, well TZ86 shows 51.8 degrees. As it is shown in Fig. 7, the amplitudes in 36.8 0.09 and well ZG17 shows 0.17 ). The fractures which are of degrees for each of the azimuth gather are higher, thus there high conductivity identifi ed by the FMI well logging data of is a certain amount of anisotropy in these azimuth gathers. well TZ88 account for 43% in the whole number of fractures In Fig. 8, the inversion results (fracture density and in this well, while fractures of high conductivity of well TZ86 direction) across well ZG16 and the FMI data of well ZG16 account for 78%, and those of well ZG17 account for 86%. are compared. The fracture density section is on the left Based on the core data, well TZ49 and well TZ63 are all side of Fig. 8(a), and the right one is part of the FMI image fully fi lled, the fi lling degree decreases to well TZ45 and well between the horizons on top of the Lianglitage II Member TZ451, half fi lled fractures account for 56.3% and 62.5% in and 10 ms downward from it, the FMI image shows effective the two wells above respectively. For well TZ86, the fi lling fracture (dark cosine lines, which represent the highly degree is the lowest, the half filled and unfilled fracture conductive fractures). The fi gure on the left side of Fig. 8(b) account for 63%. Therefore, from FMI logging data and core is the amplifi ed result of Fig. 5 near well ZG16, and the right data we draw the conclusion that the filling degree of the fi gure is the statistical FMI rose diagram. fractures decreases from southeast to northwest and from From the fracture density section (left of Fig. 8(a)), we can southwest to northeast, which indicates effective fractures see that the fracture density is quite high between the top of increase from southeast to northwest. Therefore, the inversion the Lianglitage II Member and the horizon 10 ms downward result is in good agreement with the geological background in from it. The FMI image (right of Fig. 8(a)) and its rose this area. diagram show that the fracture direction is 35 degrees north To further illustrate the effectiveness of the inversion by east. The amplifi ed result near well ZG16 (left of Fig. 8(b)) method, the azimuth gathers across well ZG16, the inverted show that the fracture direction is in good agreement with the results (fracture dens ity and direction) across well ZG16 and FMI data. From the azimuth gathers across well ZG16, the the FMI data from this well are compared. inverted results (fracture density and direction) across well The prestack azimuth gathers across well ZG16 (inline ZG16 and the FMI data from this well, we can conclude that 1206, crossline1004) are extracted. The offsets extracted the inversion results are consistent with the well data, which are 2,575, 2,585 and 2,595 m respectively, and the azimuth suggests that the inversion method is reliable and applicable. T1700 T1700 T1600 T1600 T1500 T1500 T1400 T1400 T1300 T1300 T1200 T1200 T1100 T1100 T1000 T1000 T900 T900 T800 T800 T700 T700 T600 T600 Pet.Sci.(2011)8:422-432 429 Fracture density and filling features in grain limestone member 3.8% N=1 22% 14% 38.5% N=9 N=29 N=10 Length of the core 8.9 m 0.17 86% 61.5% 78% ZG17 N=16 TZ86 1.91 0.09 N=7 TZ49 43% TZ452 ZG18 57% 1.22 TZ451 0.0% 0.46 0.0% TZ88 TZ45 ZG16 0.0% 0.77 0.17 0.01 Length of the core 14.7 m 0.0% Length of the core 32.42 m 100% N=18 Length of the core 11.73 m 43.8% 0% 37.5% N=7 56.3% N=3 N=9 N=1 62.5% legend N=5 100% Oil and gas wells Oil and gas show wells Dry hole TZ63 0.42 Fracture linear density of the core 0.22 0.27 Fracture linear density of FMI 0.0% 0.0% No cores or FMI 0 m / 10000 m Unfilled fracture (%) Semi-filled fracture (%) Length of the core 9.04 m 100.0% N=2 Completely filled fracture (%) 100. 0 N=2 Fracture of high resistivity (%) Fracture of high conductivity (%) Linear fracture density and fi lling features in grain limestone member Fig. 6 2575 2585 2595 7.15 21.8 36.8 51.8 7.15 21.8 36.8 51.8 7.15 21.8 36.8 51.8 –500 –1000 –1500 –2000 Fig. 7 Azimuth gathers across well ZG16 6.2 Effects of migration on inversion Figs. 9 and 10 show the inversion results (fracture density and direction) of top of the Lianglitage II Member. The left The fracture prediction algorithm is applied to two sets of data (data that went through migration and data that did not), part of each figure represents the inverted fracture density, and the results include two parameters: fracture density and while the right part represents the fracture direction. It can be fracture direction (Figs. 9 and 10). found that inversion results using the ordinary data which has L700 L800 L700 L900 L800 L1000 L900 L1100 L1000 L1200 L1100 L1300 L1200 L1300 L1400 L1500 L1400 L1600 L1500 L1700 L1600 L1700 Time, ms Amplitude 430 Pet.Sci.(2011)8:422-432 T900 T950 T1000 T1100 T1200 ZG16 Top of Lianglitage II 6146 Member Downward 10 ms from the top of Lianglitage II Member (a) Comparison of the inverted fracture density section and FMI data 330 30 ZG16 270 90 0 0.4 0.8 1.2 1.6 240 120 (b) The amplifi ed inverted result near well ZG16 and the rose diagram obtained from FMI Comparison between the inverted result and FMI Fig. 8 not gone through migration can not refl ect the information of which is signifi cant to inversion. Because of the complexity of the geological conditions and seismic data in the Tazhong fractures, while the data after pre-stack migration can. This area, migration should be included in the processing fl ow. is because migration can provide the true amplitude variation 432 Pet.Sci.(2011)8:422-432 anisotropic media. Geophysics. 1998. 63(3): 935-947 References Sch oenberg M A, Dean S and Sayers C M. Azimuth dependent turning Al- Marzoug A, Neves F A, Kim J J and Nebrija E. P-wave anisotropy of seismic waves reflected from fractured reservoirs. Geophysics. from azimuthal AVO and velocity estimates using 3D seismic data 1999. 64(4): 1160-1171 from Saudi Arabia. Geophysics. 2006. 71(2): E7-E11She n F, Sierra J, Burns D R and Toksöz M N. Azimuthal offset- Cra mpin S, McGonigle R and Bamford D. Estimating crack parameters dependent attributes applied to fracture detection in a carbonate from observations of P-wave velocity anisotropy. Geophysics. 1980. reservoir. Geophysics. 2002. 67(2): 355-364 45(3): 345-360 Sun Z D and Wang Y Y. P-wave fracture prediction algorithm using Gra y D and Head K. Fracture detection in Manderson Field: A 3-D prestack data with limited azimuthal distribution. 2008. Research AVAZ case history. The Leading Edge. 2000. 19(11): 1214-1221 Report Vol. 1 of Laboratory for Integration of Geology and Gre chka V, Tsvankin I and Cohen J K. Generalized Dix equation and Geophysics, China University of Petroleum. 13-23 analytic treatment of normal-moveout velocity for anisotropic media. Sun Z D, Jia C, Zhou X, et al. Carbonate research in China-technologies Geophysical Prospecting. 1999. 47(2): 117-148 meeting tough challenges. 2011a. EAGE, 73rd annual meeting, Luo M and Evan B J. An amplitude-based multiazimuth approach to Expanded Abstract mapping fractures using P-wave 3D seismic data. Geophysics. 2004. Sun Z D, Xiao X and Wang Z M. P-wave fracture prediction algorithm 69(3): 690-698 using prestack data with limited azimuthal distribution. 2011b. Lyn n H B, Simon K M and Bates C R. Correlation between P-wave EAGE, 73rd annual meeting, Expanded Abstract AVOA and S-wave traveltime anisotropy in a naturally fractured gas Tsv ankin I D. Seismic Signatures and Analysis of Reflection Data in reservoir. The Leading Edge. 1996. 15(8): 931-935 Anisotropic Media. Pergamon Press. 2001 Mal lick S, Craft K L, Meister L J, et al. Determination of the principal Wan g D Y, Lu C P, Dong W J, et al. Fracture analysis for carbonate directions of azimuthal anisotropy from P-wave seismic data. reservoirs using 3D seismic P-wave data: Middle East case study. Geophysics. 1998. 63: 692-706 Paper SPE 101596 presented at Abu Dhabi International Petroleum Nei dell N S and Cook E E. Seismic method for identifying low velocity Exhibition and Conference, 5-8 November 2006, Abu Dhabi, UAE subsurface zones. US Patent. 1986. 4571710 Zel ewski G, Lu C P, Tsenn M, et al. P-wave seismic azimuthal Rug er A. Reflection coefficient and azimuthal AVO analysis in anisotropy for detection and prediction of fractures in a Middle anisotropic media. Ph.D Thesis. 1996. Colorado School of Mines, Eastern carbonate reservoir. 2009. International Petroleum Leadville, Colorado Technology Conference, 13903 Rug er A. Variation of P-wave reflectivity with offset and azimuth in (Edited by Sun Yanhua) http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Petroleum Science Springer Journals

P-wave fracture prediction algorithm using pre-stack data with limited azimuth distribution: A case study in the TZ45 area, Tarim Basin, China

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Springer Journals
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Copyright © 2011 by China University of Petroleum (Beijing) and Springer-Verlag Berlin Heidelberg
Subject
Earth Sciences; Mineral Resources; Industrial Chemistry/Chemical Engineering; Industrial and Production Engineering; Energy Economics
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1672-5107
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1995-8226
DOI
10.1007/s12182-011-0160-y
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Abstract

of seismic waves varies with offset and azimuth (AVOZ). A noise attenuation fracture inversion algorithm is presented for fracture detection based on P-wave AVOZ. The conventional inversion method always fails when applied to limited azimuth data because of the existence of noise. In our inversion algorithm, special attention is paid to suppressing the noise during inversion, to overcome the limitation of the conventional inversion method on limited azimuth data. Numerical models are employed to illustrate the effectiveness of the method. The inversion algorithm is then applied to Tazhong 45 area fi eld data which is acquired under limited azimuth distribution. Compared with cores and fullbore formation microimage (FMI), the inverted results (fracture density and orientation) are reasonable, suggesting that the inversion algorithm is feasible for fracture prediction in the Tarim Basin. Tarim Basin, azimuthal anisotropy, AVOZ inversion, fracture detection Key words: in anisotropic media. Mallick et al (1998), Schoenberg et al 1 Introduction (1999) and Gray and Head (2000) used a law of amplitude The exploration area has been proven very large in the versus azimuth to study fracture mediums. Shen et al Tarim Basin in China, about 2,100 km in the Tabei area (2002) proposed a method of using attributes such as AVO and 7,300 km in the Tazhong area. The proven reserves (amplitude versus offset) and FVO (frequency versus offset) in carbonate reservoirs discovered in the Tazhong area are to detect fracture orientation in a carbonate reservoir located estimated to be 4.8×10 tonnes in the past three years. in the Maporal Field in the Barinas Basin of southwestern The key technical problem is how to predict and Venezuela. Luo and Evan (2004) presented an amplitude- characterize this type of reservoirs. The storage spaces are based multiazimuth approach for mapping fractures. Al- mostly secondary, of which about 99% porosity is from Marzoug et al (2006) estimated small azimuthal variations fractures and dissolution caves or holes (Sun et al, 2011a). in P-wave velocity (maximum 5%) and a larger variation in How to predict fracture development is a question which azimuthal AVO at the reservoir (larger than 100%) in two confronts us. Saudi Arabian fi eld studies. It is known that vertically aligned fractures in a reservoir A well established technique used in fracture prediction could induce P-wave seismic anisotropy. P-wave contains is based on Ruger’s equation (Ruger, 1998), which describes plenty of fracture information which involves amplitude the reflection amplitude variation with offset and azimuth variation versus azimuth, variation of azimuthal travel (AVOZ). This conventional fracture detection method requires time and velocity (Crampin et al, 1980; Ruger 1996; 1998; the use of wide azimuth data (Wang et al, 2006; Zelewski et Grechka et al, 1999; Tsvankin, 2001). A lot of work has been al, 2009), because for azimuthally limited data, the existence done on fracture detection based on P-wave features. Neidell of noise will make the solution unstable. However, as and Cook (1986) applied P-wave data to predict fractures Ordovician carbonate reservoirs in the Tarim Oilfi eld underlie based on differential stacking velocity. Then amplitude a big desert, poor surface conditions lead to very high seismic versus offset (AVO) was used to study fractured reservoirs. acquisition cost, and the pre-stack data is azimuth limited due Ruger (1998) gave the law of P-wave amplitude variation to cost factors. Thus early fracture detection research always fails. It is a challenge if we make use of the current data with * Corresponding author. email: szd@cup.edu.cn, samzdsun@yahoo.com limited azimuth distribution. Received March 18, 2011 The algorithm we introduce in this paper is the P-wave Pet.Sci.(2011)8:422-432 423 fracture prediction algorithm using pre-stack data with limited represents the anisotropic term in the reflection coefficient azimuthal distribution, where a noise attenuation method is gradient and is also the fracture density to be inverted. employed. Then it is applied to the Tazhong 45 area, where A conventional inversion method based on Eq. (2) can be the data is acquired under limited azimuthal distribution. given by further derivation: Before the inversion is conducted, the data is processed using the flow which could retain the integrity of the amplitude ­ Ri ( ,II ) C C cos sin i 1 2 variation information, where the multiples are excluded, the 2 22 2C sinII cos sin iC  sinI sin i signal to noise ratio is enhanced and the amplitude preserved ani 2 C B cos I migration is employed. The inversion results are proven to be (3) 2 s reliable and are in good agreement with the geological data. ani CB sin 2I 3 s Moreover, it is feasible to detect effective fractures (higher ani 2 C B sin I anisotropy, fi lled with liquid or gas), which suggests that the 4 s algorithm presented in this paper is feasible and effective. where C , C , C and C are four unknowns, assuming the fold 1 2 3 4 2 The algorithm of 3D pre-stack inversion of the common refl ection point (CRP) is n, then Eq. (2) can be expressed as: The Ruger P-wave refl ection coeffi cient equation (Ruger, 1998) is (4) AXB 1 ' Z Ri (,I ) where A denotes the matrix of n rows and 4 columns; X 2 Z is the column vector which contains C , C , C , and C ; B 1 2 3 4 ­½ '' DE§· 2 G is the seismic reflection amplitude (without noise). Then °° ¨¸ the conventional fracture inversion method is to calculate DD G °° ©¹ 1°° sin i the unknown X. Wide azimuth data are needed in order to ®¾ ªº (1) §· °° 2E 2 overcome the noise interference as the existence of noise «» ' G  2 ' J cosII ( ) ¨¸ s °° makes the solution unstable. «» ©¹ °° ¬¼ ¯¿ In order to make use of the limited azimuth data to ­½ D 4 conduct the inversion, a special algorithm is needed to ' H cos II (  ) 1°° suppress the noise interference. We introduce the noise part D sin ii tan ®¾ V 22 N to the conventional equation (Eq. (4)), then Eq. (4) is °° ' G sin I ( I ) cosII ( ) ¯¿ ss transformed to: V V ' J where' H , ' G and denote the Thomsen parameters; α (5) AX BN and β are P-wave velocity and S-wave velocity, respectively; is the acquisition azimuth of the survey line; is the Through the singular value decomposition (SVD) method, fracture direction; i denotes the incidence angle; Z U D is the matrix A in Eq. (5) can be expressed as: the vertical P-wave impedance; and G U E denotes the vertical shear modulus. (6) A UWV When the incidence angle is not large, is sin ii tan relatively small, the third term in Eq. (1) can be neglected. where U is the orthogonal matrix of n rows and 4 columns; Then Eq. (1) can be given by: W is the diagonal matrix with 4 rows and 4 columns, and of which the diagonal elements are positive or 0; V is the iso ani 2 Ri ( ,I ) P ªº B B co s(I I ) sin i (2) ¬¼ orthogonal matrix with 4 rows and 4 columns. Calculating the generalized inverse by the SVD method, we obtain: with TT 1 ' Z X AA A B N (7) 2 Z T  1T T  1T VW U B VW U N ª º 12 '' DE§ · G iso By using Eq. (7), the effective signal can be separated B «  » ¨ ¸ 2 DD G « » from noise. Concretely, it is to multiply N with a small © ¹ ¬ ¼ number or to divide it by a large number, then the noise part will approach 0. The infl uence of noise on the inversion result ªº 12 § E · ani V B «» ' G 2 ' J can be limited, which enables us to use the limited azimuth ¨ ¸ 2 D «» © ¹ data to perform the inversion (Sun et al, 2011b). ¬¼ where P represents the reflection coefficient of the vertical 3 The feasibility of the inversion method iso incident wave; B is the isotropic term in the reflection ani coefficient gradient which is azimuthally invariant; B Fig. 1(a) represents a wide azimuth acquisition system 424 Pet.Sci.(2011)8:422-432 (top) and a limited azimuth acquisition system (bottom). On Further, based on the conventional method, for the data with the top part of Fig. 1(a), the spots and receivers distribute in a certain extent of noise, full azimuth data could be used to the range of 360 degree azimuth, while at the bottom part of calculate anisotropy, as is shown in the middle of Fig. 1(b). Fig. 1(a), spots and receivers cover a limited part of the whole However, from the bottom of Fig. 1(b) we can conclude that azimuth range. anisotropy could not be inverted properly from the limited We divide Fig. 1(b) into three parts: the top part, the azimuth data based on the conventional method (inside the middle part and the bottom part. The colored diagrams red ellipse there is no anisotropy). However, if we introduce ani represent inversion results of the fracture density (B in Eq. the noise suppression method into the inversion process, (2), red highest, green lowest), while the black and white the fracture density which is relatively uniform from left to diagrams represent the seismogram CMP gathers with ‘full right can be shown (the right map). Therefore, by the noise azimuth’ or ‘limited azimuth’ marked at the bottom. As it is attenuation method discussed, we can calculate anisotropy shown on the top part of Fig. 1(b), for data without noise, on the basis of the limited azimuth distribution data, which the inversion results of the full azimuth data and the limited could help us to make use of existing limited azimuth data azimuth data are the same, and both of them show the correct and possibly save some costs in some acquisition layout (Sun results (weak, strong, weak, strong feature from left to right). et al, 2011b). ILINE_NO XLINE_NO 1 0.35 50 53 56 59 0.50 Without noise Without noise 0.25 0.20 0.15 0.10 0.05 880 0 -0.05 1500 900 -0.10 -0.15 940 -0.20 -0.25 rec_y -0.3 980 -0.35 sou_x 3500 4000 4500 5000 5500 6000 6500 sou_y -500 Full azimuth Limited azimuth -1000 ILINE_NO -1500 0.14 XLINE_NO 1 50 53 56 59 0.12 -2000 0.10 With noise 820 0.08 0.06 Full azimuth acquisition 0.04 0.02 880 0 -0.02 -0.04 -0.06 1500 940 -0.08 960 -0.10 -0.12 -0.14 rec_y sou_x Full azimuth 3500 4000 4500 5000 5500 6000 ILINE_NO ILINE_NO sou_y -500 1.4 XLINE_NO 1 0.9 XLINE_NO 1 50 53 56 59 0.8 1.2 50 53 56 59 0.7 -1000 1.0 With noise 0.6 0.8 0.5 820 -1500 0.6 Noise attenuation 0.4 0.3 0.4 0.2 -2000 method 860 0.2 0.1 0 880 0 -0.1 -0.2 -0.2 900 Limited azimuth acquisition -0.4 -0.3 -0.4 -0.6 940 -0.5 940 -0.8 -0.6 960 -1.0 -0.7 -0.8 -1.2 -0.9 -1.4 Limited azimuth (a) (b) Fig. 1 Numerical examples illustrating difference between wide azimuth and limited azimuth on azimuthal AVO inversion, showing the effectiveness of the new method in noise suppression shown in Fig. 2. From Fig. 2, some conclusions are drawn. 4 Data processing before inversion Firstly, both of the two acquisition systems have wide ranges of offsets, but the fold of second acquisition system is higher 4.1 Geometry of 3D fi eld data than that of the fi rst one, and both of the two have unequal Data quality has been improved as the 3D acquisition fold for different offsets. Secondly, the second acquisition system is optimized year by year ever since 2002 in the system has a relatively larger and more uniform range of Tazhong area. Two designing methods are frequently used, azimuth than the first one, but the azimuth range for both those are, 10 lines, 30 shots and 216 traces (every 5 lines), of them is mainly centralized in the lateral direction, for and 12 lines, 36 shots and 216 traces (every 6 lines). Now the vertical direction, the offsets are smaller, and the fold is we analyze the azimuth distribution of acquisition lines and lower, the azimuth distribution is not uniform and the range the fold of different offsets, and the analytical results are of the fold is limited (Sun and Wang, 2008). Time, ms Time, ms Time, ms Amplitude Amplitude Amplitude Time, ms Amplitude Time, ms Pet.Sci.(2011)8:422-432 425 10L 30S 216T (every 5L) 10L 30S 216T (every 5L) Fold Fold 49-59 43-48 43-48 31-36 37-42 31-36 19-24 25-30 19-24 7-12 12L 36S 216T (every 6L) 12L 36S 216T (every 6L) Fold 4200 3325 Fold 51-58 4180 51-58 37-43 37-43 23-29 23-29 8-14 0-14 Fig. 2 Analysis of fold and azimuth of CRP gathers in the Tazhong 3D seismic acquisition system (L is short for line, S-shot, T-trace) From processing fl ow (Fig. 3), we can see the results are 4.2 Problems in the 3D seismic data divided into two types: conventional processing fl ow without The Tazhong area is characterized by loose dunes in pre-stack migration (left part) and processing fl ow with pre- surface, large variation of sand layer thickness. Additionally, stack migration (right part). Fracture inversion will be carried Ordovician carbonate reservoirs are characterized by high out based on the data from the two flows respectively, in seismic wave velocity and deep burial with the depth ranging order to test the effect of migration on inversion. Now, we from 4,000 to 7,000 m. Besides, fractures, dissolution pores present some key steps in the processing fl ow: and caves are highly developed, thus this area shows strong 1) Noise attenuation. Different noise attenuation methods heterogeneity and anisotropy. are used considering different noise sources and types. Due to the complex geological conditions, seismic data Spherical divergence compensation is applied to improve S/N. have following characteristics. First, folds in the conventional 2) Surface consistent processing. Surface-consistent acquisition system are unequal with high folds in the middle amplitude compensation, surface-consistent static correction, offsets and low in the edge. Second, the azimuth distribution surface-consistent wavelet shaping and surface-consistent is limited, where the coverage range of azimuth is less than de-convolution are included. Surface consistent amplitude 60 degrees. Third, due to the deep burial, low velocity in the compensation eliminates imbalance of energy resulted surface and various interferences, the data has low sighal/ from different explosion and receiving conditions. Surface noise (S/N). Considering the data features in the Tazhong consistent wavelet shaping and surface consistent de- area, we present processing fl ow before inversion, including convolution focus on removing inconsistency of the energy some key processing methods. in space, instability of waveform and differences between wavelet and phase from different shots, as well as suppressing 4.3 Processing fl ow of the 3D data noise to improve data quality. Considering the complexity of seismic data in the 3) Forming super gathers. When seismic data from the Tazhong area, data processing is especially important before conventional acquisition is used in inversion, they always lack anisotropic inversion. Amplitude preserved processing enough folds, and the azimuth distribution is also limited. is the prerequisite of inversion. The key to the amplitude Forming super gathers can increase folds and the azimuth preservation data processing is to eliminate the interference range of the azimuth gathers and S/N will be improved. brought about by the non-geological factors in order to keep 4) Defining azimuth and forming azimuth gathers. The the integrity of the seismic data. Only reliable seismic data data is divided into groups according to their azimuth and can provide true amplitude variation information for the offset range and then the azimuth angle of each gather is fracture inversion. defi ned to form azimuth gathers. 426 Pet.Sci.(2011)8:422-432 5) Pre-stack 4D noise attenuation. According to the primary wave and multiples are separated based on their unpredictability of random noise and the predictability of different energy positions. Radon Transform is a type of effective signal in the F-XYZ domain, a prediction operator ‘subtraction method’ when it is used in multiples elimination. is applied to the seismic data to suppress noise, and then the First, data are transformed into the Radon domain and the data is transformed back into the time-space domain. As a method of velocity removal is used to separate multiples, and result, noise is suppressed and S/N is improved. then the data are transformed to the time-space domain and 6) Multiples elimination. In the Radon domain, the multiples are removed from the effective signal. 3D observation system define Field static correction Geometric diffusion compensation Noise eliminating Surface consistent compensation Produce azimuth gathers NMO Velocity analysis Stack Pre-stack time migration Noise eliminating Pre-stack 4D noise eliminating Multiple attenuation Multiple attenuation Residual static correction & NMO Residual static correction & NMO Inversion Inversion Fig. 3 Pre-stack processing fl ows of 3D seismic data obtained in the Tazhong carbonate reservoir and 44.3-59.3 degrees. For each sector, the azimuth angle is 5 Analysis of azimuth gathers before defi ned as the middle angles, which are, 7.15, 21.8, 36.8 and inversion 51.8 degrees, so that each azimuth gather in the Tazhong45 3D seismic data in the Tazhong45 area is distributed in the area contains four azimuths. azimuth range of 0-59.3 degrees. The azimuth is divided into After a series of processing steps, common reflection four sectors: 0-14.3 degrees, 14.3-29.3 degrees, 29.3-44.3 428 Pet.Sci.(2011)8:422-432 0.0 4n/55m 4 n/ 5 5m TZ86 ZG171 0.2 TZ861 TZ452 ZG162-1H 1n/30m ZG18 ZG26 TZ451 ZG162 0.4 TZ88 TZ45 ZG16 0.6 ZG14-1 ZG14 ZG163 ZG161 0.8 ZG15 TZ63 2n/47m ZG15-2 ZG15-1H 1.0 Fig. 5 Fracture density and direction inverted in the TZ45 area. The area with higher crack density mostly centers on the region close to well TZ452. Fracture density increases from southeast to northwest from well TZ88 to well ZG17 (from FMI data, the fracture angles corresponding to each offset are 7.15, 21.8, 36.8, and linear density of well TZ88 equals to 0.06, well TZ86 shows 51.8 degrees. As it is shown in Fig. 7, the amplitudes in 36.8 0.09 and well ZG17 shows 0.17 ). The fractures which are of degrees for each of the azimuth gather are higher, thus there high conductivity identifi ed by the FMI well logging data of is a certain amount of anisotropy in these azimuth gathers. well TZ88 account for 43% in the whole number of fractures In Fig. 8, the inversion results (fracture density and in this well, while fractures of high conductivity of well TZ86 direction) across well ZG16 and the FMI data of well ZG16 account for 78%, and those of well ZG17 account for 86%. are compared. The fracture density section is on the left Based on the core data, well TZ49 and well TZ63 are all side of Fig. 8(a), and the right one is part of the FMI image fully fi lled, the fi lling degree decreases to well TZ45 and well between the horizons on top of the Lianglitage II Member TZ451, half fi lled fractures account for 56.3% and 62.5% in and 10 ms downward from it, the FMI image shows effective the two wells above respectively. For well TZ86, the fi lling fracture (dark cosine lines, which represent the highly degree is the lowest, the half filled and unfilled fracture conductive fractures). The fi gure on the left side of Fig. 8(b) account for 63%. Therefore, from FMI logging data and core is the amplifi ed result of Fig. 5 near well ZG16, and the right data we draw the conclusion that the filling degree of the fi gure is the statistical FMI rose diagram. fractures decreases from southeast to northwest and from From the fracture density section (left of Fig. 8(a)), we can southwest to northeast, which indicates effective fractures see that the fracture density is quite high between the top of increase from southeast to northwest. Therefore, the inversion the Lianglitage II Member and the horizon 10 ms downward result is in good agreement with the geological background in from it. The FMI image (right of Fig. 8(a)) and its rose this area. diagram show that the fracture direction is 35 degrees north To further illustrate the effectiveness of the inversion by east. The amplifi ed result near well ZG16 (left of Fig. 8(b)) method, the azimuth gathers across well ZG16, the inverted show that the fracture direction is in good agreement with the results (fracture dens ity and direction) across well ZG16 and FMI data. From the azimuth gathers across well ZG16, the the FMI data from this well are compared. inverted results (fracture density and direction) across well The prestack azimuth gathers across well ZG16 (inline ZG16 and the FMI data from this well, we can conclude that 1206, crossline1004) are extracted. The offsets extracted the inversion results are consistent with the well data, which are 2,575, 2,585 and 2,595 m respectively, and the azimuth suggests that the inversion method is reliable and applicable. T1700 T1700 T1600 T1600 T1500 T1500 T1400 T1400 T1300 T1300 T1200 T1200 T1100 T1100 T1000 T1000 T900 T900 T800 T800 T700 T700 T600 T600 Pet.Sci.(2011)8:422-432 429 Fracture density and filling features in grain limestone member 3.8% N=1 22% 14% 38.5% N=9 N=29 N=10 Length of the core 8.9 m 0.17 86% 61.5% 78% ZG17 N=16 TZ86 1.91 0.09 N=7 TZ49 43% TZ452 ZG18 57% 1.22 TZ451 0.0% 0.46 0.0% TZ88 TZ45 ZG16 0.0% 0.77 0.17 0.01 Length of the core 14.7 m 0.0% Length of the core 32.42 m 100% N=18 Length of the core 11.73 m 43.8% 0% 37.5% N=7 56.3% N=3 N=9 N=1 62.5% legend N=5 100% Oil and gas wells Oil and gas show wells Dry hole TZ63 0.42 Fracture linear density of the core 0.22 0.27 Fracture linear density of FMI 0.0% 0.0% No cores or FMI 0 m / 10000 m Unfilled fracture (%) Semi-filled fracture (%) Length of the core 9.04 m 100.0% N=2 Completely filled fracture (%) 100. 0 N=2 Fracture of high resistivity (%) Fracture of high conductivity (%) Linear fracture density and fi lling features in grain limestone member Fig. 6 2575 2585 2595 7.15 21.8 36.8 51.8 7.15 21.8 36.8 51.8 7.15 21.8 36.8 51.8 –500 –1000 –1500 –2000 Fig. 7 Azimuth gathers across well ZG16 6.2 Effects of migration on inversion Figs. 9 and 10 show the inversion results (fracture density and direction) of top of the Lianglitage II Member. The left The fracture prediction algorithm is applied to two sets of data (data that went through migration and data that did not), part of each figure represents the inverted fracture density, and the results include two parameters: fracture density and while the right part represents the fracture direction. It can be fracture direction (Figs. 9 and 10). found that inversion results using the ordinary data which has L700 L800 L700 L900 L800 L1000 L900 L1100 L1000 L1200 L1100 L1300 L1200 L1300 L1400 L1500 L1400 L1600 L1500 L1700 L1600 L1700 Time, ms Amplitude 430 Pet.Sci.(2011)8:422-432 T900 T950 T1000 T1100 T1200 ZG16 Top of Lianglitage II 6146 Member Downward 10 ms from the top of Lianglitage II Member (a) Comparison of the inverted fracture density section and FMI data 330 30 ZG16 270 90 0 0.4 0.8 1.2 1.6 240 120 (b) The amplifi ed inverted result near well ZG16 and the rose diagram obtained from FMI Comparison between the inverted result and FMI Fig. 8 not gone through migration can not refl ect the information of which is signifi cant to inversion. Because of the complexity of the geological conditions and seismic data in the Tazhong fractures, while the data after pre-stack migration can. This area, migration should be included in the processing fl ow. is because migration can provide the true amplitude variation 432 Pet.Sci.(2011)8:422-432 anisotropic media. Geophysics. 1998. 63(3): 935-947 References Sch oenberg M A, Dean S and Sayers C M. Azimuth dependent turning Al- Marzoug A, Neves F A, Kim J J and Nebrija E. P-wave anisotropy of seismic waves reflected from fractured reservoirs. Geophysics. from azimuthal AVO and velocity estimates using 3D seismic data 1999. 64(4): 1160-1171 from Saudi Arabia. Geophysics. 2006. 71(2): E7-E11She n F, Sierra J, Burns D R and Toksöz M N. Azimuthal offset- Cra mpin S, McGonigle R and Bamford D. Estimating crack parameters dependent attributes applied to fracture detection in a carbonate from observations of P-wave velocity anisotropy. Geophysics. 1980. reservoir. Geophysics. 2002. 67(2): 355-364 45(3): 345-360 Sun Z D and Wang Y Y. P-wave fracture prediction algorithm using Gra y D and Head K. 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Published: Dec 8, 2011

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