C031 Quantifying Structural Uncertainty in Anisotropic Depth Imaging - Gulf of Mexico Case Study

Transcription

1 C031 Quantifying Structural Uncertainty in Anisotropic Depth Imaging - Gulf of Mexico Case Study K. Osypov* (WesternGeco), D. Nichols (WesternGeco), Y. Yang (WesternGeco), F. Qiao (WesternGeco), M. O'Briain (WesternGeco) & O. Zdraveva (WesternGeco) SUMMARY Quantifying structural uncertainty in the process of anisotropic model building is of paramount importance, especially in volumetrics estimation and drilling risk analysis. The modern concept of geophysical model building is based on integration of various data types and constraining by knowledge databases and targeted numerical modeling. Tomographic inversion of common-image-point gathers is the main engine for building the earth model. However, this inversion alone is very ambiguous, especially in the presence of anisotropy. Therefore, it is necessary to add well information and other measurements like electromagnetics and gravity in a simultaneous joint inversion process. Furthermore, geological knowledge, basin and geomechanical modeling, and lithoclassification are important constraints for model building. This novel methodology using uncertainty analysis delivers an entire suite of models that fit all available data equally well, allowing the user to select the most geologically plausible solution. In other words, uncertainty analysis has the capability to provide a new paradigm for model building. A case study for the Walker Ridge area of the Gulf of Mexico is presented in this paper.

2 Introduction In the past, the goal of seismic imaging was to focus the data and provide a high-quality subsurface image. In the last decade, more emphasis has been placed on delivering a proper depth image that is as close as possible to the actual subsurface structure. To achieve this goal, it is no longer enough to simply focus the data; one now must use a realistic anisotropic earth model to perform such imaging. It is well known that surface seismic data alone cannot uniquely resolve all the parameters of an anisotropic subsurface. What is less well appreciated is that we often cannot resolve all the parameters of the model, even if we have well data (Bakulin et al., 2009a). It is very important for interpreters working with migrated data to understand the impact of the uncertainty in the estimates of the velocity model and the anisotropy on the structure. This applies not only to the depth of data for a depth migration, but also the lateral positioning of events in the image. All this impacts significantly the reserves estimates and the decisions for exploration and developments based on risks and financial ramifications. Therefore, there is a strong need to provide error measures with any model and imaging process that can provide a quantitative measurement of the uncertainty associated with the resultant structural positioning. Additionally, uncertainty analysis is a tool for building geologically consistent models and for optimizing well ties at the final stage of model building. Methodology The workflow starts with building the initial anisotropy model calibrated with available well data and steered between wells with given geological structural interpretation. The second step is multiscale non-linear tomography as described by Woodward et al. (2008). This is an iterative process involving migrating the data, picking common-image-point (CIP) gathers and dips, ray tracing, and solving a huge, but sparse system of linear equations. Uncertainty analysis is applied after the last non-linear iteration of tomography when the solution has converged and driven the flatness of the gathers to the acceptable value. Thus, the third step of the workflow is Lanczos decomposition of the anisotropic tomographic operator as per Osypov et al. (2008a, b). Then, in the fourth step, random models generated for a given prior covariance are orthogonalized with respect to obtained eigenvectors, i.e., performing null-space projection (Bakulin et al., 2009b). Next, in the fifth step, the models are validated by checking the predicted residual moveout. This moveout should remain in the allowed tolerance level, which is the key idea behind the null-space projection method. Finally, in the sixth step, we perform map migrations of horizons of interest for the set of obtained perturbations in velocity and the anisotropic parameters ε and δ. The resulting set of target horizon instances is statistically analyzed and structural uncertainty estimates are derived. Optionally, if well data are available, we select the models that tie wells based on the least-squares criterion. The methodology is to some extent dependent on the constraints provided by prior information such as well data and assumptions about the model properties and scale of smoothness. To accommodate this, it is necessary to run through the analysis described above several times with varying geologic scenarios for prior information. Based on this sensitivity analysis, structural uncertainty can be calibrated by available mistie information. Having performed the iterative eigendecomposition once, the model builder can now choose from various model scenarios that satisfy other constraints (e.g., geomechanics or rock physics) or fit other data (MT, gravity, and others). Case study

3 To validate the uncertainty analysis workflow described above, a 67- by 31-km test area was selected from a wide-azimuth survey over the Walker Ridge area of the Gulf of Mexico. As part of the full depth imaging processing workflow, a VTI anisotropic model for the sediments was built using multiazimuth tomography; the project was entering the salt body interpretation phases with the top of salt interpretation completed. The VTI sediment velocity model had undergone three iterations of tomography and the CIP gathers were considered to be flat. Two important wells with horizon marker information were available within the area, making further well-tie analysis possible within the uncertainty analysis workflow. To aid this analysis, two key geological horizons, Oligocene and Top Wilcox, were interpreted over the whole area from the latest sediment PSDM images. The analysis started with ray tracing through the final VTI model and was followed by Lanczos eigendecomposition of the anisotropic tomography operator as per Osypov et al. (2008a). The prior information was decided using a scale length of 48,000 ft for horizontal and 600 ft for depth. Velocity, ε, and δ were varied independently by +/- 400 ft/s, +/- 0.08, and +/- 0.04, respectively. The next step was the null-space projection of prior perturbations. 500 random models were generated for this prior covariance and were orthogonalized with respect to obtained eigenvectors. The resulting 500 model perturbations after projection are in the null-space of the topographic operator within the linear assumption. The corresponding updated models are equally probable and will result in the same CIP gather flatness. Target horizons were map-migrated for the obtained 500 updated velocity models. Statistics analyses were performed with 500 surface realizations from the previous step. One statistical product from the 500 different versions of target horizons is the standard deviation map (Figure 1). The standard deviation of 500 horizon depths at each horizontal location was calculated and plotted on the top of original target horizons. This can provide oilfield developers with a good estimation of structure uncertainty obtained by tomography-based model building processes. Figure 1 Maps of standard deviation values along the z direction for both Oligocene and Top Wilcox. The availability of well log data from two wells gave us the opportunity to analyse and use the uncertainty analysis workflow to improve on well misties. Well/horizon intersections were analyzed for Oligocene and Top Wilcox at two wells.the distributions of well/horizons intersections for one of these two wells are plotted as blue histograms with well marker in Figure 2. The model with corresponding map-migrated horizons (shown in Figure 2 at one well intersection) closest to all four well markers was selected in a least-squares sense. This optimum velocity model was used for another

4 migration. The resulting stack images indicate that well misties have been reduced, in average, from about 200 ft to 100 ft. This demonstrated that, with well data, the uncertainty analysis can help the model building process. The CIP gathers remain with the same flatness within the tolerance shown in Figure 3. The absolute depth of events changed, for instance at the level of 22,000 ft, by about 100 ft. Figure 2 Migrated imaging with horizons and well markers. The blue histograms show the distributions of 500 map-migrated horizons around the original horizons. Left panel: with original velocity model; Right panel: with perturbed velocity model. Figure 3 Common-image-point gathers around wells. Left panel: with original velocity model; Right panel: with perturbed velocity model. Conclusion The proposed methodology enables a novel approach to model building. The null-space of the anisotropic inversion as well as to examine a range of analysis allows one to reveal the non-uniqueness equivalent models providing similar fit to the data. With the uncertainty analysis, a model builder can explore a range of equivalent models and pick one that he considers more geologically plausible based on any a priori information. Also, after map migration through those models, we obtain hundreds of equally probable horizons that are used for structural uncertainty statistics in the form of P10-P50-P90 horizons and standard deviation maps. In addition, a final model and image optimizing the well ties

5 are obtained. Furthermore, imaging uncertainty analysis serves as highly valuable input to volumetrics and NPV uncertainty, drilling planning, and exploration and development risk analysis. Acknowledgements We thank Mart Smith, Robert Hubbard, Phil Whitfield, Andrey Bakulin, Ran Bachrach, and Marta Woodward for enlightening discussions and comments. References Bakulin, A., Woodward, M., Nichols, D., Zdraveva, O. and Osypov, K. [2009a] Building TTI depth models using anisotropic tomography with well information. 79th SEG Annual International Meeting, Expanded Abstracts, Bakulin, A., Nichols, D., Osypov, K., Woodward, M. and Zdraveva, O. [2009b] Anisotropic model building with uncertainty analysis. 79th SEG Annual International Meeting, Expanded Abstracts, Osypov, K., Nichols, D., Woodward, M., Yarman, C.E. and Zdraveva, O. [2008a] Tomographic velocity model building using iterative eigendecomposition. 70 th EAGE Conference& Exhibition, Extended Abstracts. Osypov, K., Nichols, D., Woodward, M., Zdraveva O. and Yarman, C.E. [2008b] Uncertainty and resolution analysis for anisotropic tomography using iterative eigendecomposition. 78th SEG Annual International Meeting, Expanded Abstracts, Woodward, M., Nichols, D., Zdraveva, O., Whitfield, P. and Johns, T. [2008] A decade of tomography. Geophysics, 73, VE5-VE11.