Seismic reservoir characterization using the multiattribute rotation scheme: Case study in the South Falkland Basin Pedro Alvarez 1, Bruce Farrer 2, and Doyin Oyetunji 1 Downloaded 08/15/16 to 50.207.209.154. Redistribution subject to SEG license or copyright; see Terms of Use at http://library.seg.org/ Abstract Estimating information about reservoir properties from seismic data is a key challenge in exploration and in the appraisal and production of hydrocarbons. We discuss how to perform quantitative reservoir characterization by integrating well-log and seismic-inversion data through the application of the multiattribute rotation scheme (MARS). This method is a hybrid rock-physics/statistical approach that uses a global search algorithm to estimate a customized transform for each geologic setting in order to predict petrophysical properties from elastic attributes. The transform is computed using measured and/or rock-physics-modeled well-log information and is posteriorly applied to seismically derived elastic attributes to predict the spatial distribution of petrophysical reservoir properties. This workflow was applied on the Darwin Field, located in the South Falkland Basin, which consists of two adjacent tilted fault blocks: Darwin East, which contains the discovery well 61/17-1, and Darwin West, which remains untested. The resulting rock-property volumes (water saturation, clay content, and total porosity) characterize the heterogeneity of the reservoir and were used to delineate the extension of the proven reservoir and to delineate other potential plays in the area. In addition, these property volumes can be used as inputs for static model generation and reserve estimation, as well as to optimize the exploration and exploitation plan for the area. Geologic setting The South Falkland Basin is located along the southern margin of the South American plate (Figure 1). The basin was initially formed during the late Jurassic/early Cretaceous as a result of a separation between Antarctica and South America. After rifting, the South Falkland Basin developed as a passive-margin bordering the expanding Weddell Sea. The passive margin setting continued throughout the Cretaceous period into the early Tertiary. During the early to mid Tertiary, differential movements between the South American plate and Antarctica led to the development of the Scotia Sea spreading center. The opening of the Scotia Sea led to the partial subduction of the Weddell Sea plate and a loading of the South American plate creating a foreland basin in the vicinity of the South Falkland Basin. Continued opening of the Scotia Sea resulted in northward shortening and progressive inversion of the foreland basin. Major tectonic activity ceased by the late Miocene. During the early Cretaceous, a broad and shallow marine shelf developed. Hinterland erosion and shelfward transportation of older quartzite-dominated bedrock formed linear, laterally continuous sand bodies across the shelf. Periodic drops in base level led to the development of slope and basin floor fans as sandrich sediments were flushed out from the shelf into deeper water. Principal source rocks were formed from late-jurassic to early- Cretaceous sediments, with poor oceanic circulation and water stratification leading to the development of anoxic marine shales. The opening of the South Atlantic eventually allowed marine circulation, halting the deposition of the early-cretaceous source intervals by the late Aptian. Base level rose during the late Cretaceous, drowning the hinterland and replacing the coarse sediment supply with fine pelagic sedimentation. The passive structural setting remained in place until the opening of the Scotia Sea in the mid Tertiary, generating multiple trapping geometries through loading of the South American Plate and the development of a fold and thrust belt associated with the northward shortening. The Darwin structure comprises two adjacent tilted fault blocks: Darwin East, which contains the discovery well 61/17-1, and Darwin West, which remains untested (Farrer and Rudling, 2015) (Figure 2). The reservoir encountered in the discovery well is interpreted to be a quartz-rich shallow marine sandstone with some feldspar, lithic fragments, and clays. Net pay in the discovery well Figure 1. Location map of the studied area. Figure 2. 3D view of the Darwin structure showing the location of the discovery well 61/17-1. 1 Rock Solid Images. 2 Borders & Southern Petroleum Plc. http://dx.doi.org/10.1190/tle35080669.1. August 2016 THE LEADING EDGE 669
is 67.8 m, with porosity up to 30%, averaging 22% (Figure 3), and an average permeability of 337 md. The reservoir consists of an early-cretaceous sand unit that extends across the two fault blocks and is clearly represented on 3D seismic by amplitude conformance to structure and a class 3 AVO response (Farrer and Rudling, 2015). Fluid samples recovered from the well confirmed the presence of a high-yield gas condensate (148 to 152 stb/mmscf). Current management assessment indicates that the Darwin field has a prospective liquid recoverable resource in excess of 360 MMBO. Well-log conditioning based on rock-physics modeling Proper well-log conditioning is a fundamental part of seismic reservoir characterization. Rock-physics diagnostics (RPD) provide robust tools for determining site-specific rock-physics models, which relate reservoir properties such as porosity, clay content, and water saturation to elastic rock properties. To ensure that a good-quality suite of well logs is used in this study, we applied RPD on the 61/17-1 well-log data. The first part of this analysis involved carrying out detailed petrophysical analyses of the logs to determine the reservoir properties (lithology, porosity, and fluid content; see Figure 3). This was followed by RPD to establish the rock-physics models that best fit the 61/17-1 well-log data. The elastic data were then corrected by replacing problematic measured data with values derived from the rock-physics modeling to give a reliable well-log suite. Lithology interpretation was performed using linear gamma ray complemented with a neutron/density crossplotting approach, while the water saturation was estimated using Archie s equations. In the P-wave velocity versus porosity domain, the soft sediment model (Dvorkin and Nur, 1996) proved robust in the clay-rich interval, while the stiff sediment model was more appropriate for the Darwin sands. A weighted average of the soft and stiff sand models was used Figure 3. From left to right: Caliper, deep resistivity, neutron/density, lithology, porosity, fluid saturation, measured depth, density, V P, and V S, respectively. The red elastic curves are the original logs, while the black curves are the final conditioned logs. Rock-physics-model curves are in blue. Rock-physics-modeled V P was estimated from density where it was required using a weighted average between the soft sediment and stiff sediment model. Rockphysics-modeled V S was predicted using Greenberg-Castagna s relationship. Notice that, in general, a very good agreement was found between the raw (red) and model (blue) data, which validates the quality of the measure data and the selected rock-physics models. As a result, in only a few intervals (less than 10% the analysis window), the rock-physics-modeled data were used to correct bad measurements. for intermediate lithology. Greenberg and Castagna s relationship (1992) provided the best fit in the P-wave velocity versus S-wave velocity domain and was used for the V S prediction. Figure 3 shows the 61/17-1 well-log data before and after conditioning and the curves predicted by the rock-physics modeling at in situ porosity, mineralogy, and gas saturation. Overall, the data quality is good, with a high correlation between measured and modeled data. Mismatches between the measured and final conditioned logs within the zone of interest are the result of subtle depth shifts in the raw data. Prestack simultaneous inversion Prestack simultaneous seismic inversion has been performed to convert prestack seismic data to elastic layer properties and to obtain their volume distribution throughout the Darwin area. The main benefit of working with inversion data is that elastic properties are directly connected to reservoir properties, which are the ultimate goal of all our predictions. The prestack simultaneous seismic-inversion method that was used has been described by Tonellot et al. (2001). This is a model-based inversion in which a global objective function is minimized in order to compute an optimal model for P-wave impedance (I P ), S-wave impedance (I S ), and density, which best explains all the angle stacks and the geologic knowledge introduced through a priori low-frequency model information of these properties. Input data consists of (1) partial seismic angle stacks, (2) conditioned well data, (3) interpreted seismic horizons and faults, and (4) seismic interval velocities. Partial angle stacks were built using seismic gathers that were conditioned using the approach described by Singleton (2009) as an input, where signal-to-noise ratio, offsetdependent frequency loss, and gather alignment were the issues addressed in the conditioning. Synthetic seismograms were generated using the conditioned well-log data to make well ties for seismic to well-log calibration and estimate wavelets from each angle stack. The well data, seismic horizons, and seismic interval velocities were used to generate I P, I S, and density low-frequency background models, which add the low-frequency component that is not present in the seismic data. Inversion parameters, such as I P, I S, and density standard deviations, lateral correlation distance, wavelet amplitude scale factors, noise level of the input angle stack, and number of iterations, were determined by performing trial inversions at the Darwin reservoir and then comparing results to well-log information upscaled to seismic resolution. A comparison between synthetic partial angle stacks (created using the final I P, I S, and density volumes), and the input partial angle stacks yield residuals that mainly contain incoherent noise, which implies that the AVO information of the main events of the seismic data have been explained by our optimal I P, I S, and density model. 670 THE LEADING EDGE August 2016
Figure 4. Cross-sections through the I P (top left) and Poisson s ratio (top right) cubes derived from the inversion, passing through the discovery well (61/17-1). Well-logderived values of I P, and Poisson s ratio, upscaled to seismic resolution, and markers related to the top and base of the reservoir are plotted on each section. Bottom left: Full-stack (0 40 degree) measured seismic section showing the full-stack synthetic seismogram at the well location. Bottom right: Top structure map showing the line along which the sections are extracted. Figure 4 show a west-east cross-section through the I P and Poisson s ratio cubes derived from the inversion, passing through the discovery well (61/17-1). The well-logmeasured values of I P, and Poisson s ratio, upscaled to seismic resolution, are plotted on each section along with the well tops indicating the position of the top and base of the reservoir. Figure 4 also shows the measured full-stack (0 40 ) seismic section and the full-stack synthetic seismogram at well location. Note that at the discovery well location, the reservoir section is fully resolved by the seismic data; however, the main reservoir unit thins from west to east implying the presence of tuning effect in the amplitude data in the east, which is diminished by the use of the impedance attributes (Latimer et al., 2000). Overall, a good match was obtained between the seismic and well-log derived I P and Poisson s ratio attributes, which is an important quality control of the elastic attributes obtained from the seismic inversion, especially because only low-pass-filtered log information was incorporated into the seismic inversion during the low-frequency model step. Multiattribute rotation scheme: Method and theory The multiattribute rotation scheme (MARS) uses a numerical solution, based on a global search algorithm, to estimate a transform to predict petrophysical properties from elastic attributes. The transform is computed from well-log-derived elastic attributes and petrophysical properties, and is posteriorly applied to seismically derived elastic attributes to predict the spatial distribution of petrophysical reservoir properties. MARS estimates a new Figure 5. (a) Sketch of a crossplot of two attributes color coded by a target property. Dashed gray lines represent new attributes estimated via axis rotation, and the blue line represents the attribute τ that shows the maximum correlation coefficient with the target petrophysical property. (b) Example of a crossplot between the angles of rotation and the correlation coefficients calculated at each of these angle. MARS uses an exhaustive evaluation of all possible n-dimensional spaces (formed by n attributes) and angles to find an attribute τ that exhibits the global maximum correlation with the target petrophysical property. attribute τ in the direction of maximum change of a target property in an n-dimensional Euclidean space formed by an n number of attributes. The method sequentially searches for the maximum correlation between the target property and all the possible attributes that can be estimated via an axis rotation of the basis that forms the aforementioned space (Alvarez et al., 2015). Figure 5 shows a sketch illustrating the methodology. Equation 1 shows the mathematical expression for the attribute τ for the specific case of two dimensions: τ = A1 SF A1 sin(θ i ) + A2 SF A2 cos(θ i ), (1) where A1 and A2 are elastic attributes; SF A1 and SF A2 are scale factors, which are applied to equalize the order of magnitude of August 2016 THE LEADING EDGE 671
Figure 6. Input well-log data for the MARS analysis. From left to right: V P, V S, density, V clay, V calcite, S w, and ϕ t. Red curves show the original logs, while black curves show versions upscaled to seismic resolution, which were obtained by low-pass filtering the input well logs. the attributes; and θ i, is the angle where the maximum correlation is reached. The final step in this workflow is to scale the attribute τ to units of the target property. This is done using equation 2, where, the coefficients m and c, can be estimated by fitting a line between τ and the actual petrophysical property. Target Property = m τ + c. (2) Multiple elastic attributes such as I P, I S, P-to-S velocity ratio (V P /V S ), the product of density and Lamé s parameters (λρ and μρ) (Goodway et al., 1997), Poisson s ratio (σ), the product of density by bulk modulus (K ρ), the product of density and dynamic Young s modulus (Eρ), Poisson dampening factor (PDF) (Mazumdar, 2007), elastic impedance (Connolly, 1999), PS elastic impedance (Gonzalez et al., 2003), etc. can be used in the MARS assessment. Because different attribute combinations produce different results, this methodology uses an exhaustive evaluation of all possible n-dimensional spaces (formed by n attributes) and angles to find an attribute that represents the global maximum correlation with the target petrophysical property. The total number of attribute spaces (N s ) to be evaluated in a MARS run is given by = ( ), (3) where N A is the total number of elastic attributes to be used and N D is the dimension of the attribute spaces to be evaluated. Multiattribute rotation scheme: Well-log calibration Figure 6 shows the well-log data used as an input for the MARS application. These data consist of fundamental elastic properties (V P, V S, and density) and target petrophysical properties, such as water saturation (S w ), total porosity (ϕ t ) and clay volume (V clay ) logs. Since the final goal of MARS is to predict petrophysical properties using seismically derived elastic attributes, the first step applied consists of filtering the input logs to seismic resolution (black logs in Figure 6). In this way, all the transforms that are estimated from the MARS analysis can be directly applied to seismically derived elastic attributes. The MARS algorithm was run three times, using for each case the target properties S w, V clay, and ϕ t. For each run, MARS evaluated all 2D combinations of the 64 elastic attributes shown in Table 1 resulting in the assessment of 2016 independent bidimensional spaces (see equation 3). In this table, each number represents a single attribute, which is obtained after applying the mathematical operation shown in the leftmost column to the elastic attribute shown in the uppermost row. For example, the number 21 represents the attribute 1 λρ. The purpose of applying a mathematical operation (such as square root, power, inverse, logarithm, etc.) to attributes is to be able to model physical phenomena that exhibit nonlinear behavior. This is a mathematical 672 THE LEADING EDGE August 2016
Table 1. Evaluated attributes. Each number represents a single attribute, which is obtained after applying the 1/λρ versus 1/κρ attribute space (identified with the index 21 and 56, respec- mathematical operation show in the leftmost column to the attribute show in the uppermost row. For example, the number 21 represents the attribute 1/λρ. Because I S2 = μρ and μ 1/2 =I S, these attributes have not been used in the tively), and at an angle of θ i equal to analysis. -61, the attribute has the global maximum correlation to S w curve (see Figure 8b). This indicates that a linear projection in this attribute space at that specific angle yields the optimal seismic inversion attribute with the highest sensitivity to the S w variations. Once the optimal parameters to be used in equations 1 and 2 to estimate S w from elastic attributes have been found (Figure 8a), these were then applied to the well-log data to test the validity of the transform. A comparison between the actual and predicted S w is shown in Figures 8c, 8d, and 8e. The first two figures show the comparison between the actual and predicted S w in the optimal crossplot space identified from the MARS analysis (1/λρ versus 1/κρ). In these figures, the gray arrows, orthogonal to the blue lines, indicate the maximum direction of change of S w in this attribute space. Figure 8e shows the comparison between the actual and predicted S w information in the spatial domain, exhibiting an excellent match between the actual S w curve (estimated though a petrophysical evaluation) and the S w curve estimated from elastic attributes. A similar procedure was posteriorly applied for the target reservoir properties V clay and ϕ t. Figure 9 presents a comparison between the actual and predicted V clay and ϕ t. For these cases, a very good correlation coefficient between the actual and predicted reservoir property curves of 0.96 and 0.95 were obtained for the cases of V clay and ϕ t, respectively. Figure 7. Matrix showing the absolute value of the correlation coefficient between the S w curve and the attribute τ, for each evaluated crossplot space. The row and column indexes represent the attributes specified in Table 1. Note that this is a symmetric matrix and the color map has been set to highlight the highest correlation coefficient values; i.e., all the values in the matrix less than 0.958 are shown in blue. The attribute space and angle where the global highest correlations with the S w curve were found is highlighted. strategy used to linearize potential nonlinear relationships between the elastic attributes and the petrophysical properties, with the goal of improving the correlation between the attribute and the target petrophysical property. For the S w estimation, Figure 7 shows a matrix of the absolute value of the correlation coefficient between the S w log and the attribute, for each evaluated crossplot space. In this figure, the row and column indexes represent the attributes specified in Table 1. Note that this is a symmetric matrix, and the color map has been set to highlight the highest correlation coefficient values; i.e., all the values in the matrix less than 0.958 are shown in blue. It is worthwhile to mention that even though MARS is a deterministic approach, the final solution is not unique; as observed in Figure 7, there are several crossplot spaces that can be used to create attributes with a high correlation to the target property. As a result of this analysis, it was found that in the Multiattribute rotation scheme: Seismic application The transforms derived from the MARS analysis were applied to seismically derived elastic volumes to obtain a volume of reservoir properties. Cross-sections of the resulting volumes of S w, V clay, and ϕ t along the Darwin West and Darwin East structures are shown in Figure 10. In this figure, a good match between the seismic and well-log-derived reservoir properties can be observed. In the S w volume, the presence of fluid contacts was identified in the Darwin East and West structures, which in the time domain are offset but may line up in depth, and support the prospectivity of the Covington East prospect. In the V clay volume, there is good lateral continuity of the shallow marine reservoir rock and the cap rock, and in the porosity volume a decrease of porosity with depth in the reservoir rock can be observed, which can be explained by a compaction trend. Next, the spatial distribution of the reservoirs was mapped by crossplotting the seismically derived S w and ϕ t volumes and back-propagating the areas with the best petrophysical properties (Figure 11a). From this, geobodies were created, and their thickness was computed with the goal of creating a net pay thickness map of the reservoir (Figure 11b). The resultant map has a very good agreement with the structure and can be used for reserve estimation to optimize future well locations. Finally, as a quality control of the results, the elastic data associated August 2016 THE LEADING EDGE 673
Figure 8. (a) Parameters used in equations 1 and 2 to estimate S w from elastic attributes at seismic resolution scale. (b) Crossplot between θ and the correlation coefficients between the S w log and the set of attributes estimated via axis rotation. (c) and (d) Comparison between the actual and predicted S w log, at seismic resolution, in the crossplot space 1 λρ versus 1 κρ. Gray arrows, orthogonal to the blue lines, indicate the maximum direction of change of S w in this attribute space. (e) Comparison between the actual and predicted S w logs at seismic resolution. Figure 9. (a) and (b) Comparison between the actual and predicted total porosity log, at seismic resolution, in the optimal crossplot space identified from the MARS analysis; and (c) in the spatial domain. (d) and (e) Comparison between the actual and predicted volume of clay log, at seismic resolution, in the optimal crossplot space identified from the MARS analysis; and (f) in the spatial domain. 674 THE LEADING EDGE August 2016
with the top three biggest pay sand geobodies were plotted in the I P versus Poisson s ratio attributes space (Figure 12), where it can be observed that this information plots within an area related to high porosity and high hydrocarbon saturation (low fluid compressibility) as expected according to the well-log data and rock-physics modeling. Conclusions For the Darwin field, reservoir characterization and delineation was carried out by applying the MARS methodology. Customized transforms were found from the well-log data to estimate reservoir properties from seismically derived elastic attributes. The final goal of this workflow is the application of these transforms to seismically derived attributes to generate volumes of these properties; for this reason, the quality of the results also depends on the accuracy of the seismic-inversion products. The resulting reservoir property volumes (S w, V clay, and ϕ t.) can further enhance the characterization of the heterogeneity of the reservoir, and can be applied during static model generation, reserve estimation, and to optimize the exploration, appraisal, and exploitation plan in the area. Corresponding author: pedro.alvarez@ rocksolidimages.com References Alvarez, P., F. Bolivar, M. Di Luca, and T. Salinas, 2015, Multi-attribute rotation scheme: A tool for reservoir property prediction from seismic inversion attributes: Interpretation, 3, no. 4, SAE9 SAE18, http:// dx.doi.org/10.1190/int-2015-0029.1. Connolly, P. A., 1999, Elastic impedance: The Leading Edge, 18, no. 4, 438 452, http://dx.doi.org/10.1190/1.1438307. Dvorkin, J., and A. Nur, 1996, Elasticity of high-porosity sandstones. Theory for two North Sea data sets: Geophysics, 61, no. 5, 1363 1370, http://dx.doi.org/10.1190/1.1444059. Figure 10. Cross-section (time) of the volumes of S w, V clay, and ϕ t derived from the MARS analysis along the Darwin West and Darwin East structures, together with the log information of the well 61/17-1: V clay (left) and S w (right). The location of the line is shown in the Figure 11. Figure 11. (a) Crossplot of the seismically derived S w and ϕ t volume in the interval A-B (see Figure 10). The polygons shown were used to create geobodies related to the best reservoir properties in terms of hydrocarbon saturation and porosity. (b) Net pay map of the reservoir in two-way time. Black thick lines show the main faults in the area. The red dashed line indicates the location of the cross-sections shown in Figure 10. August 2016 THE LEADING EDGE 675
Figure 12. (a) The top three biggest geobodies related to the area with the best petrophysical characteristic (low S w and high total porosity). (b), (c), and (d) Crossplot of the seismically derived I P and Poisson s ratio highlighting the points related to the top three biggest pay sand geobodies, which plot within an area related to high porosity and high hydrocarbon saturation (low fluid compressibility) as expected by the well-log data and the rock-physics modeling. Farrer, B., and C. Rudling, 2015. South Falkland Basin: Darwinian evolution: GEO ExPro, 12, no. 1, 80 83. Goodway, B., T. Chen, and J. Downton, 1997, Improved AVO fluid detection and lithology discrimination using Lamé petrophysical parameters; λρ, μρ, and λ μ fluid stack, from P- and S-inversions: 67 th Annual International Meeting, SEG, Expanded Abstracts, 183 186, http://dx.doi.org/10.1190/1. 1885795. Gonzalez, E. F., T. Mukerji, G. Mavko, and R. J. Michelena, 2003, Near and far offset P-to-S elastic impedance for discriminating fizz water from commercial gas: The Leading Edge, 22, no. 10, 1012 1015, http://dx.doi.org/10.1190/1.1623642. Greenberg, M. L., and J. P. Castagna, 1992, Shear-wave velocity estimation in porous rocks: Theoretical formulation, preliminary verification and applications: Geophysical Prospecting, 40, no. 2, 195 209, http://dx.doi.org/10.1111/j.1365-2478.1992.tb00371.x. Latimer, R., R. Davidson, and P. van Riel, 2000, An interpreter s guide to understanding and working with seismic-derived acoustic impedance data: The Leading Edge, 19, no. 3, 242 256, http:// dx.doi.org/10.1190/1.1438580. Mazumdar, P., 2007, Poisson dampening factor: The Leading Edge, 26, no. 7, 850 852, http://dx.doi.org/10.1190/1.2756862. Singleton, S., 2009, The effects of seismic data conditioning on prestack simultaneous impedance inversion: The Leading Edge, 28, no. 7, 772 781, http://dx.doi.org/10.1190/1.3167776. Tonellot, T., D. Macé, and V. Richard, 2001, Joint stratigraphic inversion of angle limited stacks: SEG Technical Program Expanded Abstracts, 2001, 227 230. 676 THE LEADING EDGE August 2016