Tuning effect on fluid properties estimated from AVO inversion

RC P2.6 Tuning effect on fluid properties estimated from AVO inversion. Maria Rojas* and De-hua Han. University of Houston Summary AVO seismic signatures present in seismic data could be affected by several factors; one of those is the tuning or thin-bed effect. We propose a methodology to infer from seismic amplitudes and fluid properties, the presence of thin bed effect. This methodology includes: forward modeling, normal incidence amplitude and gradient estimation using Zoeppritz’s equations, a method to obt ain P-S zero-offset reflectivities from acoustic impedances and AVO inversion techniques based on Biot-Gassmann theory. We tested the methodology for 25 rock property models from different environments under two situations: with and without thin-bed effect. For almost 96% of the rock models with tuning effect, the fluid bulk modulus (Kf) was negative and 80% of the models without tuning effect, Kf was positive. On the other hand, rock models without tuning effect and Kf negative, showed saturated bulk modulus (Ksat) approximating Reuss bound and Kdry /µdry ratio lower than 0.6. Introduction In seismic exploration, reservoir fluid characterization represents the primary objective, hence numerous technologies have been developed to extract from seismic data the fluid and rock properties; one of the most used technologies is known as AVO inversion. bulk modulus to identify fluid properties, assuming Kdry = λdry which leads constant C (Vp 2dry /Vs 2dry ) equal to 2.33. Unfortunately, seismic amplitudes not only come from different pore-fluids or contrast in impedance but also come from diverse problems and pitfalls, such as the effect of thin bed, which is going to be addressed in this work. Tuning effect can be defined in a simple way as the interference of the energy from the top and base reflections of a bed. Since every day discovery of a blocky reservoir, thick enough to avoid tuning effect is a challenging task, we want to define one of the many and important unknowns pertaining to this issue, as follows: Is it possible to infer a possible tuning indicator if the seismic amplitudes and the fluid properties are substantially different from those that we will expect without tuning condition? In order to answer that question, we are going to test the sensitivity and response of different AVO inversion techniques under non-tuning condition and then under tuning condition in order to search for proper indicators. To accomplish that task, several tools are going to be used: forward modeling, Zoeppritz’s equations, AVO inversion and Gassmann’s equations. Dataset Recently, several methods have been proposed in order to extract the fluid properties of the reservoir based on AVO inversion: Hilterman (2001) and Russell (2001) illustrated a technique based on Biot-Gassmann theory to extract the fluid term (ρ f) from the P (IP ) and S (IS) acoustic impedances. ρ f = I P2 − CI S2 (1) where IP and IS are the P-wave and S-wave impedance contrast respectively and C is the constant used to differentiate fluid term which depends on the available well-log data. Goodway (2001) proposed the lambda-mu-rho technique based on two attributes Lambda-rho (λρ) and Mu-Rho (µρ) (Lamé impedances), which are obtained from AVO by using C = 2. In this method the fluid term is lambda-rho (λρ). Batzle et al., (2001) proposed to use the saturated SEG/Houston 2005 Annual Meeting Twenty-five (25) rock-property models (Table 1) represent the input data from different environments (Class I, II, III and IV). The rock-property models include P-wave, S-wave velocities and densities for shale and sands. The objective is to test the methodology for reservoirs with different shales/sands impedances ratio. Some of the rock-property models were taken from Castagna (1994) and from measurements in deep-water environments. Technical approach In order to carry out the AVO inversion to extract the fluid properties of the reservoir, several tasks are included in our technical approach: 1465 RC P2.6 Tuning effect on fluid properties ρ (sand) 2140 2300 2010 2410 2250 2450 2590 2050 2020 2100 2090 2060 2080 2090 1960 2320 2090 1990 2000 2040 2070 2100 2100 2180 2200 Table 1. Rock property models. Velocities are given in m/s and densities in Kg/m3. Examples of a synthetic gather with and without tuning effect are shown in Figure 2. 0.45 0.4 0.5 0.5 Interface shale/gas sand 0.55 Time (s) Vp (shale) Vs (shale) ρ (shale) Vp (sand) Vs (sand) 2770 1520 2290 3080 2340 4060 2180 2580 3620 2580 3050 1690 2340 2910 1850 3210 1600 2390 3960 2800 2770 1270 2450 2690 1590 2750 1260 2430 3190 1980 3600 1850 2630 4910 3300 1940 770 2100 1540 980 2670 1130 2290 2070 1290 2100 1030 2100 1680 1150 2590 1390 2300 1860 1160 2380 940 2270 2250 1300 2740 1390 2060 2840 1760 2310 940 1900 3040 1920 2870 1300 2270 2930 1790 2770 1520 2300 4050 2380 2900 1330 2290 2540 1620 2476 963 2230 1861 1105 2593 1052 2250 2084 1221 2706 1138 2290 2295 1347 2825 1228 2310 2457 1445 2926 1305 2340 2606 1543 3062 1408 2350 2841 1678 3225 1532 2360 2936 1764 3332 1613 2370 3118 1876 Time (s) # 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 0.6 0.7 Interface shale/gas sand 0.6 0.65 0.7 Tuning effect 0.8 0.75 0.9 0.8 1 0 (a) 100 200 300 400 Offset(m) 500 600 700 0 (b) 100 200 300 400 500 600 700 Offset (m) Figure 2. Synthetic CDP gather for a model with two layers over a half-space. a) No tuning effect, b) With tuning effect. 2. Estimation of Intercept and Gradient Estimates of normal incidence amplitude (A) and gradient (B) are going to be made from a linear fit. However, amplitudes were calculated based on the Zoeppritz’s equations. 1. Forward Modeling To form synthetic CMP gathers rock-property models are assumed to generate reflectivity series, which is to be convolved with a 30Hz Ricker wavelet. The layer model to be used is a two-layer model over a half space (Figure 1). Setting offset equal to depth, I restrict the incidence angle to be lower than 30 degrees (Table 2). 0m 0s Time Offset 700 m SHAL E 700m GAS SHAL E 1s Figure 1. Layer model used to generate synthetic gather. A gas sand layer is encased in two shale sequences. (Vertical and horizontal scales are not the same). Parameter Thickness of layer 1 Thickness of layer 2 Offset max. Sampling interval Time interval Value 700 m Variable 700 m 20 m 0.001 s RC (θ ) = A + B sin 2 θ (2) 3. AVO Inversion To find the fluid term or pore-fluid discriminant from seismic data, we will use a method based on a linear approximation of the Zoeppritz’s equations to invert from intercept and gradient estimations, P and S zero offset reflectivities. This method assumes (Mavko et al. 1998): • Small contrasts in material properties across the boundaries. • • Angles of incidence less than 30° approx. Vp/Vs ratio is equal to 2. To obtain the impedances, we invert knowing that zero offset P-S reflectivities could be approximated as, RP 0 = A A−B RS 0 = 2 (3) Knowing the relationship of P-reflectivity (RP0) and Sreflectivity (RS0) with acoustic impedances, we get: Table 2. Parameters used in forward modeling. SEG/Houston 2005 Annual Meeting 1466 RC P2.6 Tuning effect on fluid properties  1 + RP 0   I P (i +1) = I P (i )   1 − RP 0   1 + RS 0   I S (i +1) = I S (i )   1 − RS 0  (4) Once impedances are calculated, the next step is calculating the fluid indicator based on the approach proposed by Batzle and Han (2001). For this technique ρ∆K is the fluid indicator, which could be found from P-wave and S-wave velocities. IP2 = ρ (Kdry + 4 µ + ∆K ) 3 2 IS = ρµ (5) Then, to obtain the fluid term, we subtract the above equations, and we look for a constant C such that ρ (Kdry + (4/3)µ) = ρµ. Constant C is defined as following: C= K dry µ 2 + V  4 λdry = + 2 =  P  3 µ  VS  dry (6) Figure 4. Intercept and gradient values calculated for gas sands under tuning and non-tuning condition. Finally, if Kdry = µ, then C = 2.33. I P2 − (2.33)I S2 = ρ∆K (7) Using the approximation proposed by Batzle and Han (2001) of the Gassmann equations, we substitute ∆K for G (φ) Kf, to calculate the fluid bulk modulus. ρK f = I P2 − ( 2 . 33 ) I S2 G (φ ) (8) where G (φ) is the gain function and represent the dry frame properties of the rock. Applying tuning condition The layer thickness of the gas sand is decreased to analyze the effect on seismic amplitudes and fluid properties from 100m to 1 m. Applying the above methodology to 25 rock models is shown in Table 1. We calculate A (intercept) and B (gradient) with and without tuning effect. As we expected, tuning effect magnify the seismic amplitude, therefore we could expect a significant change in the fluid properties of the rock under tuning condition. Applying the methodology proposed, fluid bulk modulus is calculated for both situations. SEG/Houston 2005 Annual Meeting Figure 5. Calculated fluid bulk modulus for both situations. Note that most of the rock models show negative values for tuning condition and positive values for non-tuning condition. 1467 RC P2.6 Tuning effect on fluid properties Five models without tuning effect showed negative fluid bulk modulus and only one model with tuning effect showed a positive fluid bulk modulus. Dong, W. 1999. AVO detectability against tuning and stretching artifacts: Geophysics, Soc. of Expl. Geophysics 64, 494-503. For an exhaustive study of models without tuning effect but Kf<0, we use Gassmann equations in order to calculate Kdry and µdry. The results for those models were Kdry /µ ratio lower than 0.6 (Table 3). However, according to Murphy (1993) and Wang (2000), an average Kdry /µ ratio for sandstones is 0.9 and a usual approximation is Kdry =µdry . Goodway, B., 2001. AVO and Lamé constants for rock parameterization and fluid detection. Recorder Publications. 39-60. # 1 2 4 7 10 Kdry /µ 0.229 0.399 0.430 0.654 0.432 Table 3. Kdry /µ ratio for the rock-property models showing fluid bulk modulus negative for non-tuning condition. Conclusions Tuning effect is an important factor that must be considered for seismic amplitude interpretation since it affects significantly, not only the seismic amplitudes but also the fluid properties of the rock reservoir, which is the ultimate goal for exploration geophysics. On the other hand, rock physics constraints allow us to offer more quantitative description of this effect. Han, D. and Batzle, M., 2003, Gain function and hydrocarbon indicator, 73rd Ann. Internat. Mtg.: Soc. of Exp l. Geophysics, 1695-1698. Hilterman, F. J., 2001. Seismic Amplitude Interpretation. Distinguished Instructor Short Course. Distinguished Instructor Series, No. 4, Soc. Expl. Geophysics. Ostrander, W. J., 1984. Plane-wave reflection coefficients for gas sands at non-normal angles-of-incidence: Geophysics, Soc. of Expl. Geophysics, 49, 1637-1648. Russell, B. H. et al, 2003. Tutorial: Fluid-property discrimination with AVO: A Biot-Gassmann perspective: Geophysics, Soc. of Expl. Geophysics, 68, 29-39. Widess, M. B., 1973. How thin is a thin bed: Geophysics, Soc. of Expl. Geophysics, 38, 1176-1254. We proposed a simple methodology to show the impact of rock physics constraints in order to search for proper indicators of tuning effect, in this case, we found Kf < 0 for models under tuning condition and Kf > 0 for models without tuning effect. Also, we found that most of the models without tuning effect but Kf < 0 are anomalies (mostly Class I reservoirs) since their bulk moduli lie on or below Reuss bound and present considerably low Kdry /µ ratio for sandstones. Acknowledgements The authors would like to thank to the industry sponsors of “Phase III Fluid Consortium” for financial support and guidance. We would also like to thank Dr. Fred Hilterman for his helpful comments. References Batzle, M., Han, D. and Hofmann, R., 2001, Optimal hydrocarbon indicators, 71st Ann. Internat. Mtg: Soc. of Expl. Geophysics, 1697-1700. Castagna, J. 2001. AVO analysis. Recorder Publications, 29-34. SEG/Houston 2005 Annual Meeting 1468 EDITED REFERENCES Note: This reference list is a copy-edited version of the reference list submitted by the author. Reference lists for the 2005 SEG Technical Program Expanded Abstracts have been copy edited so that references provided with the online metadata for each paper will achieve a high degree of linking to cited sources that appear on the Web. Tuning effect on fluid properties estimated from AVO inversion References Batzle, M., D. Han, and R. Hofmann, 2001, Optimal hydrocarbon indicators: 71st Annual International Meeting, SEG, Expanded Abstracts, 1697–1700. Castagna, J., 2001, AVO analysis: Recorder Publications, 29–34. Dong, W., 1999, AVO detectability against tuning and stretching artifacts: Geophysics, 64, 494–503. Goodway, B., 2001, AVO and Lamé constants for rock parameterization and fluid detection: Recorder Publications, 39–60. Han, D., and M. Batzle, 2003, Gain function and hydrocarbon indicator: 73rd Annual International Meeting, SEG, Expanded Abstracts, 1695–1698. Hilterman, F. J., 2001, Seismic amplitude interpretation: SEG. Ostrander, W. J., 1984, Plane-wave reflection coefficients for gas sands at non-normal angles-of-incidence: Geophysics, 49, 1637–1648. Russell, B. H., Ken Hedlin, Fred J. Hilterman, and Lawrence R. Lines, 2003, Tutorial: Fluid-property discrimination with AVO: A Biot-Gassmann perspective: Geophysics, 68, 29–39. Widess, M. B., 1973. How thin is a thin bed?: Geophysics, 38, 1176–1254.