Kinematic invariants: an efficient and flexible approach for velocity model building - CGGVERITAS. CMP, Line T Z T Z.

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1 Kinematic invariants: an efficient and flexible approach for velocity model building Patrice Guillaume, Gilles Lambaré, Olivier Leblanc, Pierre Mitouard, José Le Moigne, Jean-Philippe Montel, ony Prescott, Risto Siliqi, Nicolas Vidal, Xiaoming hang and Serge imine CGGVeritas Massy. Summary We present a fast turnaround strategy for building depth velocity models from kinematic invariants. Our approach is based on the concept of kinematic invariants describing locally coherent events by their position and slopes in the un-migrated pre-stack domain. 3D slope tomography can be based on kinematic invariants that fully characterize the events in terms of positioning and focusing. Kinematic invariants offer a versatile tool for velocity model building as they can be derived from dip and move-out picks made either in pre-stack depth migrated (presdm) or pre-stack time migrated (presm) domains, or even in the unmigrated domain. Since the invariants are in the unmigrated domain, they only need to be picked once. he classical iterative velocity update made of several iterations of RMO picking, pre-stack migration and velocity update can thus be replaced by a more efficient sequential approach involving a single presdm and a single residual move-out (RMO) picking followed by a non-linear tomographic inversion, should the quality of the initial PreSDM be appropriate for an automated volumetric picking. Introduction Estimating a depth velocity model certainly remains one of the great challenges in seismic imaging. Getting an accurate depth velocity model and reducing the turnaround time of a depth imaging project is critical. Dense volumetric automated picking of residual move-out (RMO) was an important breakthrough (Woodward et al., 1998), since it avoided time consuming horizon-based RMO picking that was used in conjunction with two-point raytracing along picked horizons. Ray shooting from a misfocused migrated event allowed back-projection of picked RMO onto the velocity model parameters located in the vicinity of the ray paths. However, several iterations of PreSDM, and dip and RMO picking were required because of the linearized velocity update (Liu and Bleistein, 1995). Feeding a non-linear depth tomography with the kinematic invariants obtained by de-migration of locally coherent events was another breakthrough (Guillaume et al., 2001). In this method, each locally coherent event is defined by its structural dip and RMO curve and the computed kinematic invariants consist in the shot and receiver positions, the two-way time and two-way time slope computed in a constant-offset un-migrated seismic cube. he kinematic invariants are velocity model independent and are similar to the observed data entering a travel-time slope tomography (Billette and Lambaré, 1998). As a result, both the time consuming presdm and picking stages have been removed from the iterative velocity updating loop and a non-linear depth tomography has emerged (figure 1). In this method, the cost function involves an assessment of the alignment of migrated facets (figure 2). initial presm, presdm RMO & Dip picking kinematic de-migration Invariants, Slope, S, R Invariants, Slope, S, R kinematic Re-migration Linear update of velocity Linear update of velocity No predicted RMO RMO minimized? Yes final PreSDM Figure 1: Velracer M non linear depth tomography Initially, the alignment was assessed considering the full set of offset facets that are associated to a single RMO curve, but the approach rapidly evolved considering the alignment of pairs of neighboring facets (figure 2), in a differential manner, which limits the bias associated to large lateral smearing of migrated facets. h i h i+1 he cost function measures the misalignment between neighboring migrated facets describing a same reflector X i to be minimized Figure 2: Velracer M initial inversion criterion More recently, as a final move towards slope tomography, the picked RMO slope information has also been demigrated (figure 6)(Chauris et al., 2002) to produce an additional invariant time slope in the un-migrated timeoffset domain, thus allowing a direct extraction of the velocity updating information from a single facet. his new step has achieved the convergence between stereotomography (Billette, Lambaré, 1998) and MVA methods. We present the upgraded Velracer M workflow (using the RMO slope) that combines the non-linear slope tomography with a robust high order RMO picking strategy that can be used in both narrow-azimuth and wide-azimuth contexts. Picking is performed in the pre-stack migrated time or depth domains, with the benefits of a better signal to noise ratio and of an easier interpretation and QC. he picked events are de-migrated to obtain all of the kinematic invariants, considering the kinematics used for the prestack migration. he invariants are inverted to update a velocity model initially built with some a priori knowledge. We present an application to an offshore Senegal dataset. 1

2 Robust automated picking in PreSM or PreSDM domains In our approach, picking of locally coherent events in the presdm or presm domain involves an automated volumetric picking of both the structural dip and the RMO (Figure 3). - Its central position and structural dip in a common offset h time or depth migrated image, - Its RMO slope at offset h in the common image point gather located at central X position. he RMO slope can be derived from the picked high-order RMO curve. CMP, Line CIP gather RMO, X, Y, Image sub-stack dip X, Y X, Y CIP Gather (h) dip = + Offset,θ Figure 3: observed elementary kinematic information High order RMO is picked in the available offset / angle migrated domain: RMO(h) =C 2 h 2 +C 4 h 4 +C 6 h 6 (h is the offset) he RMO curves are parameterized by polynomials but they are scanned and filtered spatially considering orthogonal basis functions A i (Siliqi et al., 2007). Such functions, sorted in terms of increasing complexity of the move-out curve, are shown in figure 4. Classical high order polynomial RMO(h) = C 2 h 2 + C 4 h 4 + C 6 h 6 Offset h Reconstructed C 2 Reconstructed C 2-fil (from raw A 1 & A 2 ) (from filtered A 1 & A 2 ) C 2 (noise) Figure 5a: raw and filtered C 2 high order RMO coefficients CMP, Line = + C 2 h 2 C 4 h 4 C 6 h 6 Adapted high order RMO(h) = A 1 f 1 (h) + A 2 f 2 (h) + A 3 f 3 (h) Offset h A 1 f 1 (h) A 2 f 2 (h) A 3 f 3 (h) Figure 4: classical vs. adapted polynomial RMO curves Using this orthogonal functions basis insures the preservation of the trend of the RMO curve when filtering the RMO attributes. As shown in figures 5a and 5b, the noisy part containing in particular outliers is removed. De-migrating the locally coherent events to obtain kinematic invariants As shown in blue on the right side of the figure 6, a migrated facet is characterized in a slope tomography approach by: Reconstructed C 4 Reconstructed C 4-fil (from raw A 1 & A 2 ) (from filtered A 1 & A 2 ) C 4 (noise) Figure 5b: raw and filtered C 4 high order RMO coefficients After kinematic de-migration (by specular offset ray tracing upwards from the image point in the depth case), this locally coherent event is associated to a set of kinematic invariants shown in red in figure 6 and characterized by: - A set of source and receiver positions at the surface or seabed (OBS), - wo-way time and spatial time slope m in the un-migrated common offset time domain, - Slope h in the un-migrated common midpoint gather. By using a first order aylor expansion of the presdm imaging equations in the neighborhood of the picked event, the slope h invariant can be expressed as a linear combination of the measured δrmo slope and of the ray parameters obtained from the specular de-migration (in red in figure 6)(Chauris et al. 2002). he computed kinematic invariants do not depend on the velocity model as long as the same velocity model is used for the migration and the de-migration. 2

3 Non-linear depth tomography One can kinematically re-migrate all of the local kinematic invariants with any depth velocity model for: - Predicting the RMO corresponding to the current velocity model, and in particular the final velocity model, without having to re-run a presdm, as shown in figure 7 where the RMO in initial and final velocity models is compared. Un-migrated time Common Offset CMP/CIP gather slope m h m slope h Migration velocity model Kinematic de-migration - Performing a linearized velocity update from the Frechet derivatives computed in the vicinity of the modeled ray-paths. he RMO prediction step that involves a non linear remodeling of the wave path as well as the velocity update step can be repeated within a unique tomographic inversion run, hence the non-linear nature of this invariants-based depth tomography. m presdm or presm X m h dip δrmo Figure 6: Observed data in migrated domain (in blue) and Velracer M time and time slope kinematic invariants (in red) Figure 7: QC of RMO before and after invariants-based tomography yellow color indicates no data area 3

4 If the volumetric event picking is redundant and accurate enough, a final depth velocity model, as accurate as it can be in the illuminated area, is obtained directly from a single picking step in the pre-stack migrated domain. Starting from presm gathers When a completed time imaging project is available, an invariants-based velocity update can decrease significantly the depth imaging turnaround time, mainly because the user no longer has to: - Build carefully an initial depth velocity model by some Dix compliant stretch of the time velocity model. A simplistic initial depth velocity model is rather considered as it is only used by the tomography. - Run a presdm, then pick the RMO from image points gathers and pick the structural dip from adequate sub-stack images. he dip and RMO picking is rather performed in the migrated time domain that provides the most cost effective stack power enhancer. he underlying idea is that event picking requires mainly a good signal to noise ratio and not a precise positioning. Positioning will be dealt with by the non-linear nature of the depth tomography. hus, when starting with presm data, no compromise is made on the quality of the kinematic invariants that are obtained via prestack time de-migration. Compared to the conventional depth imaging workflow, only the de-migration step is different. It has to be tuned to the travel-time computation used by the presm algorithm (shifted hyperbolas (Castle, 1994), rays in a 1D model ). he cost-effectiveness of the 3s- presm method is due to the simplicity of the travel-time curves used in the presm. Application to field data We apply the slope depth tomography to a marine presm dataset from deep-water Senegal margin. he area of interest shows plenty of turbidite features located in particular below a thin carbonate layer (2.5 seconds below surface) inside a deformed cretaceous layer down to 3.5 seconds below seabed. he presm common image point gathers show some misfocusing, in particular in the shallow subsurface below the seabed (1.5s below surface), as shown in top of figure 8. wo parameter volumetric RMO picking of the presm was performed in a m offset range. Figure 9 shows a quite detailed and structured picture of the misfocusing after minimal co-filtering of the C 2 and C 4 coefficients. he filtered RMO and structural dip information is then tomographically inverted, as shown in figure 10. As a result, the velocities just below the seabed are slightly decreased and the velocities in the upper cretaceous are quite consistently increased. he presdm computed with the updated depth velocity model can be compared to the presm image that served as a starting point. he gathers are much flatter, as illustrated in bottom part of figure 8, especially in the vicinity of the seabed and in the lower part of the section. he effect on the stack image is mild. However, the structures below the thin carbonate layer (at 2.5sec.) are better delineated as shown in the zoomed images in figure 11 (zoom corresponds to red rectangle in figure 10). presdm 2s- 2s- 3s- Figure 8: initial presm gathers and final presdm gathers converted to time 4

5 Conclusion We have shown the latest state of the art invariants-based tomography. New development makes use of an additional slope invariant defined in the un-migrated CMP domain. As a result, the velocity model building toolbox is more versatile because it can invert data picked in any of the three following domains, migrated depth, migrated time and un-migrated time. We have illustrated the effectiveness Raw C 2 of the method on an offshore Senegal dataset for which time imaging data were available. Acknowledgment We thank Edison for the authorization to show field data. We also thank CGGVeritas for the authorization to present this work. Raw C 4 Filtered C 2 Filtered C 4 Figure 9: raw and filtered C 2 and C 4 RMO attributes from presm 0 before update after tomography 5km V = after-before -70m Initial RMO histogram Final RMO histogram V: blue=vel. decrease, red=vel. increase RMO dots: blue=vel. too slow, red=vel. too fast Figure 10: Depth tomography: initial and final velocity models with superimposed RMO 5

6 presm presdm converted to time 2.2s Figure 11: presm and presdm converted to time 2.8s References Billette, F., G. Lambaré, Velocity macro-model estimation by stereotomography: Geophysical Journal International, 135: Chauris, H., M. Noble, G. Lambaré, and P. Podvin, Migration velocity analysis from locally coherent events in 2-D laterally heterogeneous media, Part I : heoretical aspects. Geophysics, 67(4): Guillaume, P., F. Audebert, P. Berthet,, B. David, A. Herrenschmidt, and X. hang, D Finite-offset tomographic inversion of CRP-scan data, with or without anisotropy, 71 st annual SEG meeting, Expanded Abstracts, , INV2.2. Guillaume, P., N. Chazalnoël, A. alaalout, X. hang, D. Epili and V. Dirks, D finite-offset tomography model building: Green Canyon, Gulf of Mexico, 73 rd annual SEG meeting, Expanded abstracts, Le Meur, D., R. Siliqi, and F. Adler, Reliable parameter fields for Non-Hyperbolic Normal Move Out, EAGE extended abstracts, L-25. Lambaré, G., Stereotomography, Geophysics, in press. Lambaré, G., P. Herrmann, J.P. ouré, L. Capar, P. Guillaume, N. Bousquié, D. Grenié, and S. imine, From time to depth imaging a fast and accurate workflow. EAGE extended abstracts, C006. Siliqi, R., P. Herrmann, A. Prescott and L. Capar, Automatic Dense High Order RMO Picking, EAGE extended abstracts, P037. Woodward, M., P. Farmer, D. Nichols and S. Charles, Automated 3D tomographic velocity analysis of residual move-out in pre-stack migrated common image point gathers, 68 th annual SEG meeting, Expanded Abstracts,