75th EAGE Conference & Exhibition incorporating SPE EUROPEC 2013 London, UK, 10-13 June 2013

Tu-07-14Quantifying Uncertainty in Final Seismic DepthImage Using Structural Uncertainty Analysis -Case Study Offshore NigeriaL.P. Letki* (WesternGeco*), H. Ben-Hadj-Ali (Total E&P) & P. Desegaulx(Total E&P Nigeria)

SUMMARYImportant decisions, such as drilling decisions and economic evaluations, are often based on interpretationof one seismic image of the target area. The assumptions made when creating this specific image areusually well-known; however, the uncertainty associated remains unquantified. This work presents a casestudy of the application of structural uncertainty analysis (SUA). Starting from a final depth imagingimage, SUA has been used to quantify the uncertainty in the positioning of the target horizons, targetsurface and thus positioning of the well trajectories due to the TTI model uncertainty only. This isachieved by generating 500 models that equally satisfy the data, and, by then repositioning the targetsusing map migration. Finally, statistics and displays are generated to estimate and visualise the structuraluncertainty.

75th EAGE Conference & Exhibition incorporating SPE EUROPEC 2013 London, UK, 10-13 June 2013

Introduction

Important decisions, such as drilling decisions and economic evaluations, are often based on interpretation of one seismic image of the target area. The assumptions made when creating this specific image are usually well-known; however, the uncertainty associated remains unquantified. The structural uncertainty workflow, as presented in Osypov et al (2011), enables one to quantify and map this uncertainty for a prestack depth-migrated image. This work presents a case study of the application of structural uncertainty analysis (SUA) performed by WesternGeco for Total in 2012. The starting point of the SUA is a final depth imaging image, created using the final tilted transverse isotropy (TTI) model. Several key horizons have been interpreted on this volume as well as a small target surface. There are two planned well trajectories: a vertical well close to the identified target surface area and a deviated well (Figure 1). SUA has been used to quantify the uncertainty in the positioning of the target horizons, target surface and thus positioning of the well trajectories due to the TTI model uncertainty only. Several other uncertainty components exist and are not considered in this study.

Figure 1 Initial depth-migrated image with two interpreted target horizons (in blue and red), a target surface (yellow), and the two planned well trajectories (light blue).

Uncertainty tomography: Method and results

The starting point of the method is the model uncertainty. The seismic data available cannot completely constrain the TTI model used to migrate the data and, therefore, several models exist that verify the data in a similar manner. In the context of seismic tomography, this means that a number of models lead to the same global level of residual moveout (RMO) in the migrated prestack volume. The components of the model that are not constrained by the data―or tomographic operator in this case―constitute the tomography null space. In other words, two TTI models from the tomography null space will lead to the same level of residual moveout in the migrated gathers, but the image (and depth of target events) will be different. The aim of the structural uncertainty analysis workflow (Figure 2) is to sample the tomography null space; that is, to derive a representative number of equivalent TTI models, and then to quantify the effect on the final image and on the location of the target horizons. The workflow used for the uncertainty tomography is as follows:

The final TTI model of the depth imaging project is the starting model of a tomographic update. The gathers, migrated using this starting model, are used to pick the residual moveout information and build the tomographic operator. This tomographic update leads to a new reference model. The common image point (CIP) gathers are demigrated using the initial model and remigrated using this new reference model using the Gaussian packet migration (GPM) algorithm. These new gathers are used to pick the residual moveout information and build the tomographic operator of the uncertainty tomography. Note that this tomographic update is not a standard tomographic update, but uses the same algorithm and prior information as the uncertainty tomography. The new reference model is the reference model for the uncertainty analysis.

75th EAGE Conference & Exhibition incorporating SPE EUROPEC 2013 London, UK, 10-13 June 2013

A set of prior perturbation models is derived by combining random perturbations of velocity, epsilon, and delta with prior information and a steering filter. The prior information contains spatially and depth-variant standard deviations for velocity, epsilon, and delta, ensuring that the perturbations are geologically plausible. The steering filter is based on the structural dip of the area and ensures that the model perturbations are structurally consistent.

A set of posterior perturbation models is derived by projecting the prior perturbation model on the tomographic operator. This will ensure that all models now satisfy the data and lead to the same global level of residual moveout on the migrated gathers.

The posterior perturbation models are added to the reference model to create a set of TTI models (referred to as SUA models in this work). In the present case study, 500 SUA models were generated.

After performing the uncertainty tomography, the main quality control is to verify that the gathers are still flat within the limits of the data uncertainty; in other words, to check that the residual moveout level is globally preserved when migrating the seismic data using the SUA models. An important point is that this is a global criterion: the moveout of individual events will change and, in certain areas, it will increase; in other areas, it will decrease. After map migration of the key horizons, three SUA models were identified and the gathers were remigrated using the GPM workflow and these updated models. Note that two of the selected models lead to extreme positions (shallowest and deepest) of the key horizons in the uncertainty analysis. CIP picking was performed on the remigrated gathers and the gamma statistics compared with the initial model and the new reference model.

Figure 2 Example CIP gathers remigrated using new reference model (left) and a selected SUA model (right); the level of residual moveout is similar, but the depth of individual events has changed. The gamma histograms and maps show that the level of RMO for the SUA updates is slightly higher than the level of RMO for the new reference model. This may be due to the definition of the null space and/or to uncertainties in the demigration, remigration process. To quantify the difference in residual moveout, cumulative fraction gamma statistics are compared. These statistics represent the fraction of picks with an associated absolute gamma below a reference gamma as function of the reference gamma. If the curve moves in the top left direction, the global level of residual moveout is reduced. These statistics allow us to compare on a single graph the global residual moveout level of the initial model, the new reference model, and the three selected SUA models. Error corridors are also included. These correspond to a systematic error in gamma of 0.5%, 1%, 1.5%, and 2%. The results presented in Figure 3 show that the selected SUA models preserve the global RMO level within 0.5% absolute error in gamma. The same analysis performed on 1-km windows shows that the RMO level is preserved within 1% absolute error in gamma in the shallow window and less than 0.5% in the deeper windows. The analysis also shows that the three selected SUA models are equivalent in terms of residual moveout.

75th EAGE Conference & Exhibition incorporating SPE EUROPEC 2013 London, UK, 10-13 June 2013

Figure 3 Cumulative fraction gamma statistics (all picks within water bottom and water bottom + 4 km).

Structural uncertainty analysis results

To quantify the impact of the model uncertainty on the seismic image, key structures (such as horizons and specific target surface) are repositioned using the generated 500 SUA models, using map demigration with the initial model, followed by map remigration using the SUA models. This leads to 500 different positions for the target horizons/surface. These results are then analysed to derive statistics and quantify the level of uncertainty. 100 models were selected from the 500 models generated by the uncertainty tomography to derive statistics from the map migration results. As no well constraints were included in the tomography, this selection was based on the well misties at the two most reliable wells. For each of the 500 SUA models, the well mistie for the remigrated target horizon is calculated at the two well locations. The models are then ranked by average absolute mistie. The first 100 models are selected to quantify the uncertainty level in the seismic image. These models have an average absolute mistie of less than 10 m and individual absolute misties less than 15 m. For each target horizon, the analysis leads to 100 possible locations of the horizon. The results are visualised and quantified using:

Envelope horizons (representing, for each X/Y location, the shallowest and deepest position of the target horizon) (Figure 4a).

Mean position of the horizon and associated vertical standard deviation. Point displacement vector statistics, enabling us to visualise both vertical and lateral uncertainty. Probability volume (Figure 4b).

A map view of the repositioned target surface is also a good indicator of the lateral uncertainty. (Figure 4c) Finally, another way to visualise the impact of structural uncertainty on the well planning is to look at the problem from another point of view and reposition the well trajectories on the initial image. This was done for two well trajectories and results can be visualised as a set of possible trajectories and associated probability volume. (Figure 4d)

75th EAGE Conference & Exhibition incorporating SPE EUROPEC 2013 London, UK, 10-13 June 2013

Figure 4 Structural uncertainty analysis results (a – top left) 100 positions for 1 target horizon, with envelope (red) and original horizon (light blue). (b – top right) Probability volume for a target horizon. (c – Bottom left) map view of the repositioned target surface. (d – Bottom right) Repositioned well trajectory with probability volume of target surface and calculated effective radius of uncertainty.

Conclusion

To quantify the uncertainty in the seismic image due to model uncertainty, uncertainty tomography was used to generate 500 models that equally satisfy the data. The level of residual moveout is globally preserved within the limit of 0.5% absolute error in gamma. From the 500 models, the key horizons, target surface, and well trajectories were repositioned using map migration. Out of the 500 models, 100 models were selected based on the average mistie of the target horizon at two existing well locations. Statistics and displays were generated to estimate and visualise the structural uncertainty.

Acknowledgements

The authors thank Total and WesternGeco for giving the permission to publish this work. The authors also thank the following people for their generous help and assistance: Konstantin Osypov, Arturo Ramirez, Abdelhak Menari, and David Hill, as well as all the project team.

References

Osypov, K., O'Briain, M., Whitfield, P., Nichols, D., Douillard, A., Sexton, P., Jousselin, P. [2011] Quantifying Structural Uncertainty in Anisotropic Model Building and Depth Imaging - Hild Case Study. 73rd EAGE Conference & Exhibition, Extended Abstracts.