Isotropic and anisotropic velocity model building for subsalt seismic imaging

Isotropic and anisotropic velocity model building for subsalt seismic imaging T. Matava 1, R. Keys 1, D. Foster 2, and D. Ashabranner 1 Abstract Basin simulators have been used previously for deriving subsalt velocity models with the use of a correlation to relate effective stress to velocity. We build on this and the work of others to use physical models to relate porosity to velocity for migrating seismic data. This process yields a physically realizable isotropic velocity model that is consistent with the geologic model and matches the tomographic velocity model above salt and in regions where the tomographic velocity estimate is accurate. We then use a geomechanical simulator to model the stress distribution in an around allochthonous salt where material properties between salt and sediment change. Our stress model is the basis for an anisotropic velocity model using Murnaghan s theory for finite elastic deformation. This formulation, with bounds placed on the elastic coefficients, leads to significant imaging improvements adjacent to salt. Introduction Issues with seismic reflection imaging in and around large velocity contrasts, such as those presented by allochthonous and autochthonous salt, are well known. Past approaches to address these difficulties have involved improvements in seismic acquisition (e.g., wide azimuth or coil surveys) and imaging algorithms (e.g., reverse time migration or RTM). We propose that significant improvement in subsalt images may be obtained through additional geologic control in the subsalt migration velocity model. In this paper we show how to use an integrated basin simulation of a geologic model to develop isotropic and anisotropic velocity volumes for subsalt imaging. The first reported use of velocity models derived from a geologic interpretation for subsalt imaging was by Albertin et al. (22). They used a basin model to generate a present-day effective-stress volume and an empirical relationship between velocity and effective stress derived from well data (Petmecky et al., 28) to create a velocity volume. More recently, De Prisco et al. (214) and Szydlik et al. (215) used methods presented by Brevik et al. (214) to build both isotropic and anisotropic subsalt velocity models with porosity, permeability, and effective stress derived from basin models. In each of these cases, the basin model is a tool that uses a geologic model to create a velocity model for the subsalt region where tomography is either significantly limited or cannot be applied. Isotropic velocity-model building Three-dimensional integrated basin simulators, such as those described by Moeckel et al. (1997) or Hantschel and Kauerauf (29), are tools designed to forward model pressure, temperature, and porosity using a geologic model for sediment type, sedimentation rate, and basin architecture. These simulators use a one-dimensional vertical compaction law to calculate a change in porosity with a change in effective stress that has the form 1 ConocoPhillips. 2 University of Texas Institute for Geophysics. dφ =Cdσ eff =C ( dσ lith dp pore ), (1) where φ is porosity, σ is stress (effective and lithostatic), and P pore is the pore pressure. Compressibility is defined as C = φ σ eff and, in this case, is the irreversible change in porosity associated with compaction. Values for compressibilities of sediments in a compacting margin environment are typically one to two orders of magnitude greater than compressibilities associated with reversible processes in the same sediments (e.g., reflection seismic wave propagation). High values for sediment compressibility combined with low permeability result in overpressure in which pore fluids carry a portion of the sediment load. Conservation laws for mass and momentum are used to derive balanced equations that describe the pore pressure and stress evolution in the basin. Porosity changes with burial depth due to sediment loading constitute a source term for fluids in the mass and momentum laws. We assume a single-phase fluid with Terzaghi coupling (Terzaghi and Peck, 1948) between lithostatic stress and pore pressure (equation 1). Equation 1 and lithostatic loading histories through geologic time, combined with mass and momentum balances on the liquid, allow calculation of the pore pressure and effective stress for the volume. Additionally, a host of other parameters may be calculated, such as bulk density and bulk modulus as well as the regional flow field in a basin. Hantschel and Kauerauf (29) provide complete details of integrated basin modeling to quantify a petroleum system. We use a geologic interpretation of a three-dimensional seismic volume to forward model porosity changes due to sedimentation type, sedimentation rate, and basin architecture. Porosity is a fundamental variable because of the relationship between porosity, effective stress, and permeability. Allochthonous salt may be treated either as a constant-age sedimentary layer with bounding surfaces or as facies within a sedimentary layer. In the first case, salt also may be inflated or deflated either geometrically or due to changes in vertical loading. It is our experience that the best seismic images are obtained when the salt is treated as sediment but is inflated or deflated through time. Calibration of a basin model to create a velocity volume is performed similarly to basin-model calibration for oil and gas exploration; however, emphasis is placed on porosity, pore pressure, and lithostatic load. Wireline data and control points are used to calibrate porosity. Control points are pseudowells in which a vertical velocity profile is inverted for porosity and used as if it were a calibration well. Pressure on the fluid phase is calibrated with both wireline data and pressure measurements where available. Coupling between the porosity and effective stress through the compressibility of the sediments (equation 1) http://dx.doi.org/1.119/tle353xxx.1. 936 THE LEADING EDGE March 216

ensures consistency between the rock-physics model for the sediment type, sedimentation rate, and basin architecture. We also do not attempt to estimate the presence of variables, such as smectite, to model additional water source terms during phase transitions. Finally, we typically use only three to five sediment types in our model to calibrate between the seabed and deepest source rocks in the basin. An approximation for the differential effective medium (DEM) rock-physics model is used to calculate the velocity from basin-model porosity, pore pressure, and shale volumes. This model represents the rock as a mixture of ellipsoidal sand and shale pores. The model has the advantage that calculations are efficient, compared to the numerical DEM algorithm, and it is physically based (i.e., the elastic moduli always satisfy the Voigt- Reuss bound required for a real elastic material). The bulk modulus K is the unique solution of the equation calibrated models in shorter times. Reducing the cycle time means that the cause-effect on the images is fresh in the minds of those involved in the project, which further reduces the number of iterations to produce a final image (typically less than 1 in most extensional settings). Improvements in an isotropic image from the subsalt Wilcox Play in the Gulf of Mexico are shown in Figure 2. This isotropic image qualitatively shows better delineation of subsalt reflectors in the target area and an improved image of basement structure. An additional impact of this reprocessing program is shown in Figure 3, which displays changes in the structure of the reservoir against allochthonous salt. These changes are because the initial K 1 f K o K = K o 1 K 1 φ ( ) f K p o, (2) where K o is the grain bulk modulus, K f is the pore fluid bulk modulus, and φ denotes porosity. The shear modulus, G is calculated from grain shear modulus G o and φ with ( ) q o G =G o 1 φ. (3) Exponents p o and q o depend on the shape or aspect ratio of dry ellipsoidal sand and shale pores. Formulae for these exponents are given by Keys and Xu (22). Equations 2 and 3 are the basis for our elastic, isotropic moduli, which are used to calculate velocity of the sediments. Velocities derived from tomography in the suprasalt section and outboard of allochthonous salt are an important component to imaging the seismic volume. The tomographic velocity volume is most reliable in suprasalt minibasins and south of the Sygsbee Escarpment where salt is absent. Vertical control points, or psuedowells, are used to obtain consistency between tomographic and basin-model-derived velocity volumes. These control points are calculated by inverting a tomographic velocity profile for porosity using the DEM model, (Figure 1). In practice, several psuedowell control points (< 12) are used throughout the model to supplement drilled wells for calibration. Control points are updated as the tomographic volume evolves. Further, the velocity volume derived from the basin model initializes and constrains subsequent tomography revisions. In summary, methods used to build isotropic velocity models are physically based and designed to yield consistent results between tomography and basin modeling velocity volumes. Tomography is used in the shallow suprasalt section and merged with the DEM velocity to yield an enhanced velocity volume, particularly for the subsalt part of the volume. Control points in the form of psuedowells allow a direct comparison of tomographic and basin-modeling results and aid in obtaining a consistent velocity volume. Relying on physical models instead of correlations yields Figure 1. A DEM-calculated porosity profile (black dots) from the tomographic velocity model compared with the basin model porosity (red line) at a particular control point. Horizontal lines are stratigraphic tops included in the basin model. The basin model matches the general trend of the velocity model; however, the velocity model shows low porosity (fast sediments) at approximately 4 km, suggesting that a fast wave may be affecting the overall velocity model at this location. Similarly, the basin model suggests too low porosity at approximately 9 km. Resolving these issues with physical models (rather than correlations) brings together geologic and geophysical models and increased understanding of the processes occurring in the basin. Figure 2. A comparison between (a) the initial image and (b) the final image after reprocessing. The final image followed a workflow outlined in the text, which combined tomographic velocities and basin-modeling velocities to produce a final image. March 216 THE LEADING EDGE 937

velocities, which were too fast, pushed the basement horizons too deep. Reprocessing slowed these velocities, decreased the depth to basement, and shallowed the dip of the horizon into the threeway trap against salt. Additionally, the geometry of the horizon that subcropped into salt changes during reprocessing. These imaging results are important from a petroleum system perspective. The section shown in Figure 2 includes the entire petroleum system from source to trap. This image allows interpretation of not only the trap but also away from the trap where fluids, presumed to have been expelled from a source rock, migrate both laterally and vertically to a reservoir. Improved images in both reflector continuity and depth increases our confidence in the petroleum system, which is presented as reduced prospect risk. Indeed, these improved images and the significantly different structural maps imply large changes to the petroleum system for the area in terms of fluid-quality prediction, volume of hydrocarbons available to trap, and equity negotiations (Figure 3). geomechanical simulation of our basin model to predict stress perturbations from an isotropic reference model and estimate velocity anisotropy and anisotropic imaging parameters. Specifically, we used the theory of finite elastic deformation developed by Murnaghan (1937) to calculate the impact of stress on velocity. Murnaghan derived an expansion of the strain energy density with respect to strain perturbations. Neglecting perturbations in strain of third order and beyond, this expansion yields the following approximation for the stress dependent elastic stiffness: Anisotropic velocity-model building The sixth-order tensor C ijklmn in equation 4 is the third-order elasticity (TOE) coefficient. For an isotropic reference medium, there are five nonzero TOE coefficients, of which three are independent. Common practice uses core measurements to estimate the required coefficients, but these measurements have both considerable variability and significant uncertainty due to the complexity of the laboratory measurements. Although there is large uncertainty in the TOE coefficients, we can still derive useful bounds for them. From the experimental observation that P-wave and S-wave velocity increases in the Seismic velocities are influenced by stress, and the presence of salt can produce stress-induced anisotropy in the velocity field. Geomechanical models have demonstrated the impact of stress halos and arching around rugose salt bodies on velocity anisotropy (Bachrach and Sengupta, 28; Fredrich et al., 23). Their model results suggest that these stress arches and halos extend hundreds of meters in the sediment away from the salt body. Poroelastoplastic modeling (Nikolinakou et al., 212) shows that stress-induced effects can extend kilometers away from salt bodies. We used a C ijkl = C ijkl +C ijklmn emn, (4) where Cijkl is the stress dependent stiffness tensor, C ijkl is the reference, unstrained isotropic stiffness tensor, and emn is the strain tensor that is related to the stress, σij through Hooke s law σ ij = C ijkl ekl. (5) Figure 3. A basemap showing the interpreted Wilcox reflector for (a) the initial image and (b) the final reprocessed image shown in Figure 2. In this case, the Wilcox is subcropped by allochthonous salt on the bottom left half of the figure. Reprocessing decreased the velocity in the subsalt section. Slower velocities significantly decreased the depth of the Wilcox horizon both at the subcrop to salt as well as in the center of the basin. Additionally, the area of closure at the subcrop changed significantly. The lower dip of the Wilcox into salt evident in the reprocessed image resulted in higher mean resources assigned to the prospect. 938 THE LEADING EDGE March 216

direction of an applied force (Nur and Simmons, 1969), it can be shown that the independent TOE coefficients, in Voigt notation, satisfy the bounds sion to be positive and require tension to be negative. We constrain the TOE coefficient C 111 to be proportional to the reference stiffness coefficient C 11 and choose the remaining coefficients to satisfy the symmetry conditions and bounds in equations 6 and 7. Using equations 4 and 5 with these TOE coefficients and the stress perturbations from the basin simulator, we obtain a stress-dependent elastic-stiffness tensor that is guaranteed to produce an anisotropic velocity model for which P-wave and S-wave velocities increase in the direction of increasing stress. We use this stress-dependent stiffness tensor to calculate the Thomsen delta and epsilon anisotropic imaging parameters. Typically, for subsalt imaging projects, δ is determined from a VSP or checkshot well data; however, wells may be located quite a distance from the area of interest. In theory, the ε parameter may be determined by flattening imaged gathers near the wells. In practice, ε is chosen to be proportional to δ. Once determined, these one-dimensional, depth-dependent anisotropic parameters are extended laterally from the seabed over large distances and are fixed, even though velocities are updated during model building. In our process, δ and ε are updated by the stress modeling and change as the three-dimensional stress varies laterally. Figure 4 shows a standard model for δ. Figure 5 shows the stress estimate for δ. The seismic images for these two anisotropic models are shown in Figures 6 and 7, respectively. Both of these images are produced by a 3D prestack reverse time migration (RTM) algorithm. Overall, the stress-induced anisotropic model improves the coherency of reflectors in the deeper section. Notice that the positioning of events is shifted between these two sections. This occurs because, on the conventional section, tomographic updates of velocity optimally flatten the gathers. When a different δ and ε are used, the gathers will not be completely flat, so an additional iteration of tomography is required. Prior to the tomographic update the location of salt bodies are reinterpreted. Additional depth images are shown in Figure 8 11. In Figures 8 and 1, the 1D model for δ and ε is used; in Figures 9 and 11, the stress induced anisotropic model is used. Figure 4. Standard model for the Thomsen anisotropic parameter δ. Figure 5. Stress-induced anisotropic model for the Thomsen aniso- Figure 6. Seismic image using the 1D anisotropic model. This is a Figure 7. Seismic image using the stress dependent anisotropic 1 C111 < C112 < C111 2 < C155 < C144 along with the symmetry conditions of C144 = and C155 = (C 111 C112 4 (6) (7) (C 112 C123 2 ) ). As a sign convention, we take compres- Blue indicates no anisotropy, δ =. This figure shows the model for δ adjusted for water bottom depth; δ varies only in the depth direction. The value of ε for this application is twice the value of δ. Data courtesy of PGS. prestack depth-migrated image using the δ shown in Figure 4. The value of ε is twice the value of δ. This image is produced by a 3D prestack RTM algorithm. Data courtesy of PGS. Special Section: S u b s a l t i m a g i n g tropic parameter δ. The color blue indicates no anisotropy, δ =. Because of stress variations, the model for δ varies laterally. The blue areas are salt bodies which are isotropic. For stress-induced anisotropy, the ε parameter is, to first order, equal to δ. model. This is a prestack depth-migrated image using stress dependent ε and δ shown in Figure 5. This image is produced by a 3D prestack RTM algorithm. Data courtesy of PGS. March 216 THE LEADING EDGE 939

Each of these examples shows improved imaging in the deeper section below the salt bodies using the stress-induced parameters. Also, the base-of-salt reflection is more visible. These image improvements enable more detailed mapping of the subsalt structures. Stress-induced velocity anisotropy around large rugose salt bodies is modeled using TOE theory and static stress modeling. This application is useful for providing the conventional anisotropic parameters δ and ε. Standard estimates of these parameters tend to vary only with respect to depth. The stress-induced anisotropic parameters vary laterally and correlate to stress variations around salt bodies. It seems intuitive that if velocities vary laterally, the anisotropic parameters should vary laterally as well. The seismic images derived from the stress-induced anisotropic parameters show improved coherency deeper in the section than in the conventional model. Subsalt reflectors and base-of-salt reflections are better imaged with the stress-induced anisotropic parameters. The improvement of the images is evidence that a laterally varying anisotropic model is more accurate than the standard 1D mode for these parameters. In summary, we have shown the improvements that are possible in subsalt seismic images when tomographic velocity volumes are modified with geologically derived velocity models. We build on the previous work by showing how physically based models, using a constitutive relationship that relates porosity to effective stress, can be used to constrain the isotropic material properties of the sediments. A DEM model which converts a forward model for porosity into an isotropic velocity model is the basis for this new isotropic velocity model. Key to this workflow is a geologic interpretation of the reimaged seismic data. Because we used physically based models for the isotropic portion of imaging, we are able to extend these imaging improvements with anisotropic stress fields available from the basin model to develop anisotropic velocity models. These models represent a second-order effect on the isotropic velocity volume but the improvements on image quality are still significant. The edges of salt become better defined and deep sediment, often considered basement, are resolved better and allow a more accurate geologic interpretation of the seismic data. We have shown that by using physically based models we are able to produce geologically and geophysically consistent seismic volumes. A byproduct of these reimaging programs is a petroleum-system view of prospects and plays that is developed at the same time as the reimaging program, which is typically early in the exploration program. This means the petroleum systems analysis of the play, including trap size and position, Figure 8. Seismic image using the 1D anisotropic model. This is a Figure 9. Seismic image using the stress-dependent anisotropic Figure 1. This is a prestack depth migrated image using the one- Figure 11. Seismic image using the stress-dependent anisotropic Summary prestack depth-migrated image using the one-dimensional model for δ and ε. This image is produced by a 3D prestack RTM algorithm. Data courtesy of PGS. dimensional model for ε and δ. This image is produced by a 3D prestack RTM algorithm. Data courtesy of PGS. 94 THE LEADING EDGE March 216 model. This is a prestack depth-migrated image using the stress dependent ε and δ. This image is produced by a 3D prestack RTM algorithm. Data courtesy of PGS. model. This is a prestack depth-migrated image using the stress dependent ε and δ. This image is produced by a 3D prestack RTM algorithm. Data courtesy of PGS.

mobility, and fluid quality, are developed early when flexibility usually remains in the program s direction. For example, insight gained with this early knowledge of the petroleum system ranges from the drilling order of prospects to equity negotiations and constitutes a significant competitive advantage to those who implement such a program correctly. Acknowledgments A host of geoscientists contributed their time and effort on imaging projects using methods presented in this paper. Their contributions included much ingenuity and insight. For their efforts we thank J. Chang, M. Clavaud, B. Foster, E. Frugier, J. Law, Z. Li, G. Neupane, J. Western, and Y. Zeng. We appreciate Y. Zhang for reviewing and improving this article. We thank the ConocoPhillips Company for supporting this work and PGS and CGG seismic companies for permission to publish the seismic images. Corresponding author: tim.matava@conocophillips.com References Albertin, M. L., S. Petmecky, and P. Vinson, 22, An integrated approach to overburden characterization and drillability assessment: 22 SEG Summer Research Workshop on Geopressure. Bachrach, R., and M. Sengupta, 28, Using geomechanical modeling and wide-azimuth data to quantify stress effects and anisotropy near salt bodies in the Gulf of Mexico: 78th Annual International Meeting, SEG, Expanded Abstracts, 212 216, http://dx.doi.org/1.119/1.35479. Brevik, I., T. Szydlik, M. P. Corver, G. De Prisco, C. Stadtler, and H. K. Helgesen, 214, Geophysical basin modeling, part I: Generation of high quality velocity and density cubes for seismic imaging and gravity field modeling in complex geology settings: 84th Annual International Meeting, SEG, Expanded Abstracts, 4733 4737, http://dx.doi.org/1.119/segam214-444.1. De Prisco, G., M. P. Corver, I. Brevik, H. K. Helgesen, D. Thanoon, R. Bacharach, K. Osypov, R. E. F. Pepper, and T. Hantschel, 214, Geophysical basin modelingeffective stress, temperature and pore pressure uncertainty: 76th EAGE Conference and Exhibition-Workshops. Fredrich, J. T., D. Coblentz, A. F. Fossum, and B. J. Thorne, 23, Stress perturbations adjacent to salt bodies in the deepwater Gulf of Mexico: SPE conference paper 84554-MS, http://dx.doi.org/1.2118/84554-ms. Hantschel, T., and A.-I. Kauerauf, 29, Fundamentals of basin and petroleum systems modeling: Springer Science & Business Media. Keys, R. G., and S. Xu, 22, An approximation for the Xu-White velocity model: Geophysics, 67, no. 5, 146 1414, http://dx.doi.org/1.119/1.1512786. Moeckel, G. P., D. P. Schmitt, A. A. Walsh, and C. T. Tan, 1997, 3D integrated basin simulation and visualization: 1997 AAPG Annual Convention. Murnaghan, F. D., 1937, Finite deformations of an elastic solid: American Journal of Mathematics, 59, no. 2, 235 26, http://dx.doi.org/1.237/237145. Nikolinakou, M.-A., G. Luo, M. R. Hudec, and P. B. Flemings, 212, Geomechanical modeling of stresses adjacent to salt bodies: Part 2 Poroelastoplasticity and coupled overpressures: AAPG Bulletin, 96, no. 1, 65 85, http://dx.doi. org/1.136/411111143. Nur, A., and G. Simmons, 1969, Stress-induced velocity anisotropy in rock: An experimental study: Journal of Geophysical Research, 74, no. 27, 6667 6674, http:// dx.doi.org/1.129/jb74i27p6667. Petmecky, R. S., M.-L. Albertin, and N. Burke, 28, New velocity model building techniques to reduce sub-salt exploration risk: 78th Annual International Meeting, SEG, Expanded Abstracts, 2772-2776, http://dx.doi.org/1.119/1.363921. Szydlik, T., H. K. Helgesen, I. Brevik, G. De Prisco, S. A. Clark, O. K. Leirfall, K. Duffaut, C. Stadtler, and M. Cogan, 215, Geophysical basin modeling: Methodology and application in deepwater Gulf of Mexico: Interpretation, 3, no. 3, SZ49 SZ58, http://dx.doi.org/1.119/int-215-1.1. Terzaghi, K., and R. B. Peck, 1948, Soil Mechanics in Engineering Practice: J. Wiley and Sons. March 216 THE LEADING EDGE 941