Calibration of Pre-Stack Simultaneous Impedance Inversion using Rock Physics Scott Singleton and Rob Keirstead, Rock Solid Images Log Conditioning and Rock Physics Modeling Summary Geophysical Well Log Analysis: One of the first steps in This paper is the third part in a reservoir characterization integrating a well into a seismic study is to prepare the log series. Its objective is to demonstrate the necessity of curves over the full well-bore. This includes calculations of understanding the rock property responses of a reservoir so the standard petrophysical volumetric curves for porosity, that the project results can correctly interpreted. fluid, and minerals. In addition, special emphasis is placed on robust calculation of density, Vp, and Vs where measured data is missing or determined to be in error. The first step is to check and correct acoustic and density well log curves. For the current study a combination of Raymer for density and Greenburg-Castagna for Vs were applied in the shallow zone above the reservoir. Within the turbidite reservoir section a laminated sand fluid substitution was used to understand its behavior as fluid content varies, and a matrix substitution to understand its behavior as sand content varies. Synthetic gathers were calculated for all models using both ray traced and full waveform algorithms. These exercises showed that AVO analysis could be used to detect fluid changes in the seismic data but not for detecting sand content changes. Rock physics crossplots, however, could make this distinction. The seismic inversion was calibrated to acoustic impedance (AI), shear impedance (SI), and Poisson s Ratio (PR) well log curves and clearly revealed that acoustic anomalies seen in this prospect were the result of sand content changes and not the result of fluid saturation changes. Introduction This paper represents the third installment in a sequence of reservoir characterization articles that follow a workflow whose ultimate goal is to understand and predict the rock properties of a reservoir away from well control. The first article described a method to detect anomalous seismic attenuation (Singleton, 2008). This was important because the seismic data exhibited a steep fall-off in amplitude which was caused by high attenuation in and above the reservoir interval. The second article dealt with the seismic gathers that were input into the inversion process (Singleton, 2009). It is of the utmost importance that the quality of data input into a simultaneous pre-stack inversion be as high as possible. Errors in seismic gathers (low S/N, resolution loss from excessive NMO stretch, non-flat reflectors, offset amplitude problems, etc.) are broadcast straight into the inversion impedance volumes, so this is a critical step in geophysical reservoir characterization. This paper discusses the final step in reservoir characterization calibration of the rock property response from well logs to that of the seismic inversion, and modeling of the reservoir so that we understand the effects of rock property changes away from well control. In the subject well, the measured density was poor in the upper section of the well (above 2680 m) and was mostly replaced (see Singleton, 2008, for log plot). A Raymer model (Raymer, et al., 1980) replaced the density in the shallowest section of the well, a soft sand model (Dvorkin and Nur, 1996) replaced density within the faulted block (1945-2480 m), and then Raymer was used again until 2680 m, below which the measured density was used. The compressional velocity was mostly reliable through the entire well with some minor exceptions. Vp edits were made using a soft sand model and were verified by calibration to the seismic. The shear velocity was estimated from the Greenberg-Castagna model (Greenberg and Castagna, 1992) from the top of the well to 2680 m; below this level the measured shear was unedited. The reservoir zone is the Nise Formation and it consists of a thinly laminated turbidite sequence (Figure 1). As these laminations are below the vertical resolution of the logging tools, special care must be taken in the analysis (Mavko, 2007). Calculation of effective porosity and water saturation is challenging with this rock type. Fortunately the reservoir zone possesses quality measured resistivity and acoustic/elastic curves, though lacks high resolution resistivity curves that can assist thin-bed analysis. Only two minor spikes were removed from the bulk density curve, Vp and Vs were unedited. Mineral and fluid volumes in the reservoir zone were calibrated to core and FMI (Formation Micro Imager) analysis. Fluid Substitution: We then modeled different fluid saturation scenarios in order to determine the range of potential rock property responses in the Nise Formation away from well control. Specifically, we tested the 100% brine saturated case and a higher oil saturation case, here 80% oil and 20% brine (Figure 1). The Gassmann method (Gassmann, 1951; Biot, 1956; Mavko, et al, 1998) can be problematic in sub-resolution sand laminations because it assumes homogenous rock and that substitution occurs uniformly over the entire interval rather than only in sands (Mavko, 2007). Because of this, the fluid effect in the reservoir interval will tend to be exaggerated (Walls, et al., 2008). The Thomas-Yin method provides a solution to this 1815
Figure 1: Log and synthetics plot. Panels from left to right are lithology (panel 1), fluid saturation (panel 2), panel 3: in-situ AI (black), 80% oil AI (green), wet AI (blue); PR (same colors as in AI) (panel 4), ray trace synthetic gather (panel 5), full waveform synthetic gather (panel 6), conditioned seismic gather (panel 7). problem based on the Thomas-Stieber-Yin-Marion model for the porosity of thinly bedded sands and shale, which assumes that all rocks in the interval can be constructed by mixing high porosity sand and low porosity shale (Mavko, et al., 2009). Using this model the equation for porosity in a laminated sequence of shale and dirty sand is: [ φ cleansand ( 1 φ shale ) V dispshale ] + ( NG) φ shale φ = NG 1 where net-to-gross, NG, is the thickness fraction of sand layers. The Thomas-Yin method uses known values for sand properties to perform conventional Gassmann fluid substitution in the sand layers and then recomputes the Vp, Vs, and density of the new average laminated rock using Backus averaging. However, because we do not have reliable data for the sand properties in the Nise Formation we used a slightly different model to substitute fluids. Our laminated sand fluid substitution algorithm makes a fractional adjustment to the Gassmann results based on shale content (Walls, et al., 2008). For example, if the log resolution shale content for a single data point is 60%, in reality meaning 60% shale laminations and 40% sand laminations, the change in velocity after fluid substitution will be 40% of the Gassmann results because it assumes fluid substitution should only occur in sand layers (Figures 1 and 2). Calculations comparing the Thomas-Yin method to our method were performed in an area where the sand rock Figure 2: AI vs. PR rock physics crossplot showing the decrease in AI and PR due to laminated fluid substitution (arrows). Green is 80% oil and black is wet conditions. Dotted line at an AI ~ 4380 indicates an effective cutoff for discrimination of in-situ and 80% oil conditions. properties were known and the results were within 3%-5%. We believe this is a tolerable margin of error for geophysical purposes. Matrix Modeling: To further understand potential seismic responses away from well control, we modeled variations in mineralogy within the reservoir zone. A soft sand model was fit to the 100% brine saturated fluid substitution results 1816
and the rock properties were perturbed based on this model. Following this, the in situ fluids were substituted back into the rock using our laminated sand fluid substitution method. Two cases were generated, one adding 20% more shale to the reservoir and one subtracting 10% shale from the reservoir (Figure 3). The results show minimal change in the Vp / density space for either case. This is because the decrease in clay content will serve to increase Vp and density (harder sand rock fabric) but there is also more capacity for hydrocarbon fluids, so when the in situ fluids are substituted back into the cleaner formation there is a compensating drop in velocity and density. Shear velocity is unaffected by fluid content so it remains high in the cleaner case, resulting in a decrease in Poisson s ratio. of normal-incident reverberations that are typically seen in the North Sea (Singleton, 2009). The fluid and matrix cases show substantial differences between the ray traced and full waveform solutions. Increases in hydrocarbon saturation cause higher amplitude near and far offsets in the pure, ray traced solution, resulting in larger negative intercept and gradient. This essentially moves the response from AVO Class II to Class III (Figure 4). This response is identical on the full waveform solution (Figure 5). The matrix response on the pure, ray traced solution is almost perpendicular to the fluid response, moving to higher negative gradients but decreasing the negative intercept and flipping it to a positive intercept (Figure 4). This is a shift to harder rock fabric and thus from AVO Class II to Class IIP. Unfortunately, the full waveform solution has trouble Fluid effect Matrix effect Figure 3: AI vs. PR rock physics crossplot showing the decrease in PR due to an increase in sand content (arrow). Orange is +10% sand and black is -20% sand. Horizontal dotted line at an AI ~ 4380 indicates an effective cutoff for discrimination of in-situ and 80% oil conditions from Figure 2. Vertical line is a cutoff for in-situ conditions at PR=0.39. Synthetics: Ray trace and full waveform synthetics were calculated for all fluid and matrix cases discussed above. The full waveform synthetic algorithm used here was described in Singleton (2008) and is based on the Kennett elastic solution (Kennett, 1974; Kennett and Kerry, 1979) which contains all wave propagation effects, such as multiples, transmission losses, and attenuation. It is readily apparent that the ray trace and full waveform synthetic solutions differ considerably in the reservoir zone (Figure 1). The pure, ray traced solution shows the reservoir top reflector to be an AVO Class II (Figure 4). However, the full waveform solution shows a flat amplitude trough response in the first half of the gather, then increasing in amplitude in the last half of the gather. This seems to be a hybrid AVO Class III/IV response (Figure 5). Although odd in its character, it matches the seismic gather quite well except for anomalous high amplitude near offsets, which were shown to be the result Figure 4: Intercept vs. Gradient crossplot of ray trace synthetic AVO character of the reservoir top reflector showing the effects of fluid and matrix changes. Fluid effect Figure 5: Intercept vs. Gradient crossplot of full waveform synthetic AVO character of the reservoir top reflector showing the effects of fluid and matrix changes. 1817
showing any change in intercept as a result of the harder rock fabric and only shows the increase in hydrocarbon accommodation space (e.g. fluid effect) (Figure 5). These results clearly show that while the pure, theoretical ray trace solution shows the effects of both fluid and matrix changes, the real world is somewhat more complex. Full waveform results show us that the AVO effects of fluid changes are detectable but changes in sand percentage are not. To properly quantify fluid and matrix changes, we need to move into the prestack inversion domain with rock physics providing the calibration. Compounding this unfortunate situation is the areal distribution of reservoir section containing sand volume greater than that encountered at the well location (Figure 7). Enhanced sand volume preferentially occurs to the west of the well location, at the edge of the anticlinal structure and on its flanks (this is also seen in Figure 6). Unfortunately, on the anticlinal flank the reservoir section above the flat spot (oil/water contact) is less than half as thick as on the top of the anticline. This leads to speculation that the enhanced amplitudes on the anticline flanks are due to tuning distortions. Regardless of tuning issues, the reservoir section is too thin on the flanks to be considered economic, especially given the results in this paper. Figure 6: PR inversion volume and AI/PR crossplot. Crossplot geobody capture zone is defined by a maximum PR of 0.39 and is separated into polygons of 0.36-0.38 and 0.39. Dotted lines show AI cutoff of ~4380 and PR cutoff of 0.39 (Figures 2 and 3). On the PR section, the PR log is shown in color, VSH on left and SW on right. Inversion Calibration A simultaneous prestack inversion had been previously performed on this data set using the IFP model-based inversion algorithm (Singleton, 2008; 2009; Tonellot, et. al., 2001; 2002). For the current study, Poisson s Ratio was calculated from the acoustic and shear impedance volumes and cross-plotted to determine rock property relationships (Figure 6). The inversion crossplot bears a striking relationship to Figure 3, with all low PR data points falling above the AI cutoff value of ~4380. This provides strong evidence that reservoir changes within the project area are due to variations in sand content rather than changes in fluid saturation. Figure 7: 3D visualization of geobodies captured using the polygons in Figure 6. Voxel color identifies the captured polygon. Well is shown in red on right. Horizon at base of reservoir zone (O/W contact) shown in partial transparency. Conclusions Rock physics calibration of prestack inversion results has demonstrated that anomalous acoustic anomalies in this reservoir are due to increases in sand content rather than increases in hydrocarbon fluid saturation. While this may be unfortunate news to the exploration leaseholder, it demonstrates the value of an integrated rock physics approach to exploration and reservoir characterization. Acknowledgements We wish to thank Statoil for allowing the use their data and to present it in this abstract. This well was originally processed by Miguel Ascanio and Jack Dvorkin in close collaboration with Statoil partners. Rone Shu developed and programmed the laminated sand fluid substitution algorithm. We also thank the sponsors of the RSI Lithology and Fluid Prediction (LFP) Consortium (phases 1 and 2) for their support of this work. 1818
EDITED REFERENCES Note: This reference list is a copy-edited version of the reference list submitted by the author. Reference lists for the 2009 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. REFERENCES Biot, M.A., 1956, Theory of propagation of elastic waves in a fluid saturated porous solid. II. Higher-frequency range: Journal of the Acoustical Society of America, 28, 168 178. Dvorkin, J., and A. Nur, 1996, Elasticity of high-porosity sandstones: Theory for two North Sea datasets: Geophysics, 61, 1363 1370. Gassmann, F., 1951, Uber die elastizitat poroser medien: Vier. der Natur Gesellschaft, 96, 1 23. Greenberg, M. L., and J. P. Castagna, 1992, Shear-wave velocity estimation in porous rocks: Theoretical formulation, preliminary verification and applications: Geophysical Prospecting, 40, 195 209. Kennett, B. L. N, 1974, Reflections, rays, and reverberations: Bulletin of the Seismological Society of America, 64, 1685 1696. Kennett, B. L. N., and N. J. Kerry, 1979, Seismic waves in a stratified half space: Geophysical Journal of the Royal Astronomical Society, 57, 557 583. Mavko, G., 2007, Rock physics issues in laminated sands: Rock Solid Images LFP2 Consortium Report. Mavko, G., T. Mukerji, and J. Dvorkin, 1998, The rock physics handbook: Cambridge University Press., 2009, The rock physics handbook, 2nd ed.: Cambridge University Press. Raymer, L. L., E. R. Hunt, and J. S. Gardner, 1980, An improved sonic transit time-to-porosity transform: 21st Annual Logging Symposium, SPWLA, paper P. Singleton, S., 2008, The use of seismic attenuation to aid simultaneous impedance inversion in geophysical reservoir characterization: The Leading Edge, 27, 398 407., 2009, personal communication. Tonellot, T., D. Mace, and V. Richard, 2001, Joint stratigraphic inversion of angle-limited stacks: 71st Annual International Meeting, SEG, Expanded Abstracts, 227 230., 2002, 3D quantitative AVA: Joint versus sequential stratigraphic inversion of angle-limited stacks: 72nd Annual International Meeting, SEG, Expanded Abstracts, 253 256. Walls, J., R. Shu, and G. Mavko, 2008, Laminated sand fluid substitution, ultra deep water GOM: Rock Solid Images LFP2 Consortium Report. 1819