76th EAGE Conference & Exhibition 2014 Amsterdam RAI, The Netherlands, 16-19 June 2014

We E104 10Geomechanical Velocity Model BuildingA. Rodriguez-Herrera* (Schlumberger), O. Zdraveva (WesternGeco) & N.Koutsabeloulis (Schlumberger)

SUMMARYWe show that geomechanically-induced orthorhombic velocity predictions are consistent with wide-azimuth anisotropic seismic data observations in the Gulf of Mexico. We predict anisotropic velocityperturbations around a salt dome by means of 3D geomechanicamodeling and the application of rock-physics predictions. Ultimately, geomechanically predicted seismic velocities may therefore be used invelocity model building and imaging workflows and are expected to improve seismic images in areas withcomplex salt tectonics including the Gulf of Mexico, the North Sea, offshore West Africa and offshoreBrazil.

76th EAGE Conference & Exhibition 2014 Amsterdam RAI, The Netherlands, 16-19 June 2014

Introduction In recent years, many efforts have been dedicated to improving the imaging of complex subsurface structures. Alongside better velocity models, more accurate migration algorithms and multiple attenuation techniques, new wide-azimuth seismic acquisition schemes aim at improving our ability to image steeply dipping and overhanging salt-bodies, as well as sub-salt reflectors. These applications have converged towards the joint application of wide azimuthal ray-coverage and imaging algorithms running on anisotropic velocity models (Zdraveva et al., 2012). As the complexity of the velocity model increases (e.g. symmetry classes) so does the task of attaining all parameters involved in describing such a model, and due to the intrinsic limitations of the imaging process, this cannot be achieved by velocity analysis of appropriate seismic gathers alone. Expanding the work of Sengupta, et al. (2008, 2009) and Bachrach, et al. (2008), we aim at incorporating additional constraints into velocity models, which arise from the expected geomechanical conditions for subsurface sediments lying in the vicinity of salt bodies. These are not incorporated a priori, but by simulating and solving for the particular geomechanical characteristics of their natural settings and the manner in which these would imprint themselves over the velocity field. Ultimately, this process should result in improved images of salt flanks and sub-salt reflectors, as well as increase the fidelity of seismic amplitudes. In this paper, we take a first step in this direction and show that geomechanically-induced orthorhombic velocity predictions are consistent with wide-azimuth anisotropic seismic data observations in the Gulf of Mexico.

Dataset: Gulf of Mexico wide-azimuth seismic survey The processing of a wide-azimuth seismic survey in the southern Green Canyon area in the Gulf of Mexico revealed azimuthal anisotropy patterns, mainly, in the vicinity of the allochthonous salt bodies at the Sigsbee escarpment (see Fig. 1). Having originally employed a transversely isotropic velocity model to image the salt structure, azimuthal velocity variations were mostly neglected and consequently reflected themselves as inaccuracies in the final seismic image. In this study, stress perturbations around the salt dome are presented as the cause of the observed velocity anomalies. These stress perturbations in the vicinity of salt are well-known, and can be modelled using finite element stress analysis (e.g. Fredrich et al., 2003). Applying stress sensitive velocity models, the excess stress (or strain) due to the presence of the salt body can be transformed to anisotropic velocity perturbations. Such a workflow has been demonstrated by Sengupta, et al. (2008, 2009) and Bachrach, et al. (2008).

Figure 1 Map of study area at the edge of the Sigsbee escarpment in the Gulf of Mexico (http://bit.ly/It2WjB), and bathymetry surrounding the area of interest (Far right).

Geomechanical modeling A spatial discretization is firstly defined over the seismic volume of interest and guided by available horizon interpretations. For the purpose of subsurface stress simulations, a spatial description of mechanical properties needs to be assigned to the entire model. Such distribution is constructed based on the latest P-wave velocity, Vp, after several tomographic iterations. S-wave velocity, Vs, is computed from using Castagna et al. (1985), and density is computed using a Gardner velocity-

76th EAGE Conference & Exhibition 2014 Amsterdam RAI, The Netherlands, 16-19 June 2014

density relationship. In a next step, dynamic Young’s modulus, E, and Poisson’s ratio, ν, are computed, and transformed to static elastic properties using Gulf of Mexico appropriate correlation functions. As an example, the resulting three-dimensional distributions of Vp and E are displayed in figures 2(a) and 2(b), respectively. Note that the trends follow the expectation of an increase of E with depth, indicating the rock is becoming stiffer due to compaction during burial.

Figure 2 Structural and property model for geomechanical calculations. Seismic interpretations are used to model the geometry of the salt dome. (a) P-wave velocity, Vp, is used to compute (b) Young’s modulus, E, using rock-physics transforms. See text for detail. Inside the salt body, due to salt creep over geological timescales, deviatoric stresses are continuously suppressed and the overall stress state tends towards isotropic, i.e. the three principal stresses at a given location are equal. This leads to variety complex stress states that can result around salt bodies, ranging from lithostatic stress-fields acting on the salt body’s interface with juxtaposed sedimentary layers, stress transfer mechanisms due to plasticity and mechanical perturbations related to active diapirism. Treating the current conditions as the steady-state of the salt’s long term stress path, we assign the salt body with homogeneous mechanical properties that would result in isotropic stresses under equilibrium conditions. We use a finite element simulator (Koutsabeloulis and Hope, 1998) to predict subsurface stress scenarios honoring the stress-strain relationships defined over each element and obtained from mapping seismically-derived mechanical properties onto the computational mesh (Herwanger and Koutsabeloulis, 2011). For this particular study, we imposed a tectonically relaxed background stress field by means of appropriate boundary conditions and therefore leaving all stresses beyond the Poisson’s effect attributable to salt-induced perturbations. Although it could be plausible to use boundary conditions that mimic observed tectonic stresses (different magnitudes of horizontal stresses acting on the boundaries of the model), the approach was to prescribe the least amount of information causing azimuthal stress anisotropy. It consists in a parsimonious attempt to discern the signal caused by the presence and geometry of the salt body from any user-defined input.

Salt induced orthorhombic velocity variations The geomechanical account to salt-induced velocity anomalies rests on the sensitivity of seismic wave velocities to rock strain/stress (e.g. Birch, 1966; Nur and Simmons, 1969; Johnson and Rasolofosaon, 1996). In broad terms, a mechanical compression (compressive strain / increase in compressive stress) causes an increase in P-wave velocity in the direction in which the compression occurs. The opposite is true for dilation, causing a decrease in P-wave velocity in the direction in which dilation occurs. Making use of a rock-physics model that encapsulates such velocity−strain relationships (Thruston 1974; Prioul et al., 2004), predicted excess strains (tensors) can be transformed into anisotropic velocity perturbations in every cell of the model. We define excess strains as those arising when computing the component-wise difference of strain fields between a model with salt and without salt (see Fig. 3).

76th EAGE Conference & Exhibition 2014 Amsterdam RAI, The Netherlands, 16-19 June 2014

Figure 3 Principal components of the excess strain tensors across the volume of interest: Predicted (a) minimum (b) intermediate and (c) maximum principal excess strain field. Note that at the same spatial location, rocks can be subjected to both compressional and dilatational forces simultaneously. The relationship between salt-induced excess strains on predicted velocity perturbations is depicted in Figure 4. Along with the magnitude (colours) of the minimum and maximum principal values of excess strain, it is also possible to observe the direction in which the strain occurs (see Fig. 4a). For P-waves traveling parallel to the maximum principal excess strains, in this case orthogonal to the salt interface, a speedup is predicted (see Fig. 4b). For P-waves traveling parallel to the minimum principal excess strains, in this case tangential to the salt interface, a slowdown is predicted (see Fig. 4c). For both minimum and maximum principal strain directions lying approximately on the horizontal plane, as can be the case for diapiric structures, the model would yield an orthorhombic velocity model with strong azimuthal P-wave anisotropy.

Figure 4 (a) Predicted excess strain in a horizontal plane at a depth of 4500m (14650ft) below sea level. Note the compression in directions orthogonal to the salt, and dilation in directions parallel to the salt. (b) and (c) Velocity perturbations along the principal directions of the excess strain. (b) In directions for which compression occurs, velocity increases (speedup), and (c) for directions in which dilation occurs, a velocity decrease (slowdown) is predicted.

Prediction of seismic attributes As means to substantiate the model’s validity, we show a comparison between seismic data observations and geomechanical velocity model predictions. The comparisons show that the observed azimuthal velocity variations strongly agree with the expected (simulated) patterns, confirming, at least, that a main driver for azimuthal anisotropy is indeed of a geomechanical nature. As shown in Fig. 5, we compare interval velocity errors measured by statistical analysis of γ (Al-Yahia, 1986) as a function of observation azimuth with predicted velocity perturbations for the same observation azimuths (45°, 15° and 75° from North). Predicted velocity perturbations for single processing azimuths are approximated as the average predicted velocity perturbations over an offset-angle range from -50° to +50°. Most of the major positive and negative anomalies are similar in shape between observations and predictions. Additionally, the decrease of velocity perturbations with distance from salt is also similar between observations and predictions.

76th EAGE Conference & Exhibition 2014 Amsterdam RAI, The Netherlands, 16-19 June 2014

Figure 5 Observed (top row) and predicted (bottom row) velocity perturbations at different (source-receiver) azimuths. The arrow in each sub-plot indicates the azimuths: 45° (a,d), 15° (b,e) and 75° (c, f). Negative values (red) indicate that the velocity model is too fast and positive values (blue) indicate that the velocity model is too slow, where maximum and minimum velocity errors are approximately ±3%.

Conclusions

We have geomechanically derived a velocity perturbation model which is able to reproduce a series of observed velocity anomalies around a salt structure in the Gulf of Mexico. This study represents another step towards the use of geomechanical concepts in the improving subsurface imaging techniques, primarily, in the generation of complex velocity models. Future efforts should include the automated generation of subsurface stress models and the “implicit” use of geomechanics for velocity model updating, for example, by identifying efficient iterative schemes that can intelligently and independently select when to carry out a geomechanical velocity updating step.

Acknowledgements We thank Schlumberger management for permission to use the GoM data included in this work and many colleagues at Schlumberger/WesternGeco for their contribution to this work.

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