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Dense multi-offset reflection tomography John Brittan* and Jerry Yuan, PGS Marine Geophysical Summary non-hyperbolic residual curves). In addition, Gray et al. (2001) note that the system of equations solved in most In seismic reflection tomography, the velocity model of the reflection tomography algorithms is simultaneously over- subsurface is updated by back-projecting travel-time determined and under-determined. residuals along ray-paths. The travel-time residuals are picked from the seismic data itself and the methodology The fundamental under-determination is due to the used to gather these picks is a fundamental part of any velocity/depth ambiguity (which the pick parameterisation velocity inversion workflow. In particular, the density at will not address); whilst the fundamental over- which the residuals are picked in the four-dimensional data determination is a result of many cells of the velocity space (inline, crossline, offset and depth/time) appears to model being updated by many different ray paths. This have a significant effect on the precision of the velocity over-determination, in principle, is what leads to the updates that are output from the tomographic inversion. increase in precision of the velocity model determined from Dense, single-offset picking samples the residuals in the dense picks, however this effect will be dependent on the data space very finely but does not necessarily represent distribution of this density in the multi-dimensional space their true values with great accuracy. Dense, multi-offset in which the picks are parameterised. For example, picking offers a similarly fine sampling but with greater employing dense single-picks will increase the sampling in adherence to the true residual value. These two the inline and crossline directions while leaving the offset methodologies are compared and contrasted on a complex direction well sampled (as the fitted curve will give a synthetic dataset. residual value at each offset) but relatively inaccurate. In contrast, employing sparse multi-offset picks will increase the accuracy of the sampling in the offset direction; Introduction however the sampling in the inline and crossline directions will remain sparse. Reflection tomography is a global optimisation methodology used in velocity model building for pre-stack The effect of this different sampling was shown on a depth migration (Stork, 1992; Kosloff et al., 1996). It relatively simple synthetic dataset by Etgen (2004). By commonly uses the residual depth from common-image- comparing the inversion of a sparse set of multi-offset gathers (CIG) as input data. Given an offset between a shot picks with a dense set of single-offset picks over a common and receiver pair, ray paths are generated from the 2-D model, it was shown that, even with severe shot/receiver to an image point, and then velocities will be regularization (smoothing) using the dense single picks updated in an iterative manner along the ray paths until the gave a better result than the sparse multi-offset picks. In residual moveout is flattened. other words, in this model, the over-determination in the CDP direction was more useful in recovering the true One of the fundamental choices that must be made with a velocity model than the over-determination in the offset reflection tomography algorithm is how to pick the residual direction. It is possible however, that for a different model depths or times for each pre-stack gather. As discussed by (e.g. containing a large but heterogeneous anomaly) that Jones (2003), velocity model building techniques may this situation may be reversed. Ideally, it would seem that utilize picks from either migrated or un-migrated data and utilising dense multi-offset picks (i.e. accurate over- these picks may be on single offsets (e.g. stacks, near or far determination in all spatial directions) should give the offsets) or on multiple offsets within the gather. The optimum result for all models. However, such picking is in technique we have chosen to use in this paper is based on general costly and difficult to QC. In this paper we residual depth picks from common image gathers. Single describe a methodology for undertaking such picking, and offset picking methods (including those which fit a the application of this methodology to a complex 2-D hyperbola to the depth residual on each gather) offer a fast synthetic dataset. and robust method of supplying a dense set of picks to the tomographic update. However, Jones (2003) suggested that: Methodology (i) dense picks only increase the precision of the velocity model, not its accuracy (which is effectively determined by In this study we have compared the results of a reflection the shot and receiver sampling of seismic acquisition); (ii) tomography algorithm using dense single offset picks and single offset picks cannot resolve the same level of sub- dense multi-offset picks on a common, complex 2-D surface complexity as multi-offset picks (as the single synthetic model. The model used was the BP synthetic offset pick, or fitted hyperbola, cannot accurately represent dataset supplied for the 2004 EAGE workshop on the Dense multi-offset reflection tomography ‘Estimation of accurate velocity macro-models in complex generate ray paths from the picked depth residuals. In structures’. This model included a number of small-scale order to speed up the convergence, the tomography velocity and density heterogeneities that provided a stern algorithm is designed to simultaneously update velocities test for any reflection tomography algorithm. and depths. In this software design, we use grid-based tomography; although horizons picked from the depth migrated common-offset sections serve as part of the input for ray tracing, the velocity and depth will be updated on a cell-by-cell basis. This allows for a robust and realistic tomographic inversion. . Figure 1: Using a 3-D visualisation system to quality control the automatic RMO picks. The left-hand side shows the stack data, the right-hand side shows selected gathers and the underlying colour map is the picked residual moveout (blue indicates over- moved out arrivals). The dense, single-offset picking methodology used an Figure 2: Using the 3-D visualisation system to pick dense, multi- automatic residual move-out (RMO) scanning technique. offset residual moveout. The green surface is a guide horizon used In this technique, every sample on each common image to aid the picking; the red spheres are the positions of manual picks and the yellow points represent the picks auto-picked by the gather is scanned along a moveout equation defined by a visualisation system. power exponent (e.g. 2 for a parabolic curve) and a number of trial coefficients of fit. The coefficient that gives the highest semblance is applied to data at the sample. Once Data examples the entire dataset has been scanned the residual moveout volume can be analysed (Figure 1) and smoothed. Figure 3 shows example image gathers from the right-hand end of the example dataset. At this end of the dataset, the The dense, multi-offset picking methodology utilises the velocity anomalies within the model are small and laterally capabilities of a high-end 3-D visualisation system. A discontinuous, which makes a suitable test for a grid-based horizon of interest is picked on the migrated and stacked reflection tomography algorithm. The gathers in Figure data volume, and the zero-offset depth of this horizon is 3(a) have been depth migrated using a starting model used as a guide to pick the depth residuals on the pre-stack derived from a pre-stack time migration of the data. It can data. (This guide horizon is the green surface in Figure 2). be seen that at all depths below 1km, the initial velocity Pre-stack migrated data is loaded into the visualisation model is incorrect and all events have some residual system in the form of crossline/offset volumes and depth moveout. On many gathers in this dataset, below residuals surfaces are chosen using a combination of approximately 2km, the residual moveout becomes very manual and automatic picks (Figure 2). The surfaces can difficult to characterise accurately using a single parabolic be analysed and smoothed interactively within the curve. A number of horizons were picked using the two visualisation system. methodologies described above and the resulting depth residuals were input into the reflection tomography The picks from both methodologies were input into a algorithm. Figure 3(b) shows the same gathers migrated common reflection tomography inversion algorithm. This with the velocity field derived using the dense, multi-offset algorithm uses a modified anisotropic ray tracing code to depth residual picks. Figure 3(c) shows the same gathers Dense multi-offset reflection tomography using the dense single-offset depth residual picks. It is clear that the dense, single-offset pick result is close to the (a) multi-offset pick result, however, particularly at depth, the flattening is inferior. It is also possible that, in a real survey situation, the remaining move-out on the single- offset pick gathers would be attributed to the presence of anisotropy (the model used here was purely isotropic). A comparison of the velocity models derived using the two picking methodologies shows that only the dense, multi- offset picking has the resolution to image the small, laterally discontinuous velocity anomalies (Figure 4). These results also appear to confirm the observation by Etgen (2004) that the horizontal resolution of reflection tomography is greater than the vertical resolution (the anomalies have a true vertical extent of approximately 100m). (b) Conclusions In this paper we present a methodology that utilises a 3-D high-end visualisation system to provide dense, multi-offset depth residual picks to a reflection tomography algorithm. Comparisons on a complex 2-D synthetic model suggest that possibly as a result of the over-determination in the inversion using dense multi-offset picks, a more accurate result is achieved than that using dense, single-offset depth residual picks. References Etgen, J., 2004. What can migration velocity analysis resolve? 66th EAGE Conference and exhibition – abstracts (c) for workshop on “Estimation of accurate velocity macro- models in complex structures”. Gray, S.H., Etgen, J., Dellinger, J. and Whitmore, D., 2001. Seismic migration problems and solutions. Geophysics, 66, 1622-1640. Jones, I.F, 2003. A review of 3-D PreSDM model building techniques. First Break, 21, 3, 45-58. Kosloff, D., Sherwood, J., Koren, Z., MacHet, E. and Falkovitz, Y., 1996, Velocity and interface depth determination by tomography of depth migrated gathers. Geophysics, 61, 1511-1523. Stork, C., 1992, Reflection tomography in the postmigrated domain. Geophysics, 57, 680-692. Acknowledgements Figure 3: Gathers from the right-hand side of the esxample dataset We would like to thank BP for providing the synthetic after depth migration with the (a) initial velocity model (b) velocity dataset. The authors would also like to thank Joel Starr, model derived from dense, multi-offset depth residual picks and (c) Shelton Ma, Peter Wijnen, Trong Tang, Chris Taylor, Dave velocity model derived from dense, single-offset depth residual King, Sandy Carroll and Jostein Lima for their assistance picks. and PGS Marine Geophysical for permission to publish this paper. Dense multi-offset reflection tomography (a) 1km (b) 1km (c) 1km Figure 4: A comparison of the velocity model derived using tomographic inversion of the synthetic dataset using (a) dense, multi-offset depth residuals; (b) dense, single-offset depth redsiduals and (c) the difference between the two models. Note the compressed velocity scale on the difference plot and that only a small sub-section of each model is shown. The white arrows on (a) indicate the location of small low velocity anomalies in the subsurface. These anomalies of are limited lateral (<1000m) and vertical (100-200m) extent. It is clear that only the velocity model derived using dense, multi-offset depth residuals is able to resolve these features adequately, although the result is constrained by the inherent limit on the vertical resolution of seismic reflection tomography.

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