PSDM STRUCTURAL MODEL CONSTRAINTS: CASE STUDIES Authors: Jorge Sánchez Littau and Marcelo Koremblit CGGVeritas Argentina Summary The purpose of Pre-Stack Depth Migration (PSDM) is to produce an accurate image of the earth’s interior. To get this picture we need an interval velocity model whose accuracy depends on our subsurface knowledge. The process begins with a model that includes prior information and is optimized through PSDM-Tomography iterations until the process converges to a stable model-solution. The model can be very simple, for example parallel flat layers used for Pre-Stack Time Migration (PSTM), or it can be complex, according to our knowledge of the geology of the area. This knowledge can allow us to keep invariant certain model parameters in successive iterations. In this paper, we discuss some cases of constraints imposed on the initial model that allow us to produce reasonable images consistent with known geology. Introduction Pre-Stack Depth Migration (PSDM) is a proven seismic imaging tool. It has generated images consistent with geological structure, and has defined faults and estimated depths with acceptable accuracy, etc. However, a permanent topic of discussion is the relationship between the results of the PSDM and velocity model used for its generation. That is, how and how much the model influences the resulting PSDM: how often are the migration algorithms and velocity field adjustments, such as tomography, able to achieve a reasonable convergence to "reality"? One of the central problems of the suitable model generation for the PSDM lies in the non uniqueness of the solution; because different models lead to different acceptable results. So it is necessary to constrain them using geological, seismic and well information. At the same time, the model optimization, usually by reflection tomography, is limited by the seismic quality, structure complexity, lateral velocity changes, etc. The simplest model is built with flat, parallel layers of constant velocity. Although this model seems naive, it is commonly used, generating a simple Pre-Stack Time Migration (PSTM). The similarity of images produced by different processors, even with different layered velocity models lies in the fact that it is structurally unchanged (parallel flat layers) and it is shown in time. Generally, more realistic models are derived by using two methods: from stacking/PSTM velocities, and from geologic models built in time. In the first method, stacking or PSTM velocities become interval velocity models which are then converted to depth. It may happen that the resulting model has little relation to the geological structure, because velocities are picked to improve the stacked section or the PSTM. The second method builds the model from time horizon interpretation, and with a velocity field retrieved either from well information or from stacking velocities converted to interval velocities. The problem with this method is that all interpretation is in time; therefore the method cannot recognize velocity anomalies, which generate structural deformations, instead assigning them to the structural model. For this reason, we need to constrain PSDM velocity models based on geologic knowledge and using seismic data. Generally we use three possible model constraints (Robein, 2010):

(1) Smoothing the entire velocity field to reduce non-geological oscillations (Bishop, 1985). Of course, this is in conflict with achieving structural detail; but more detail should appear on the image than in the velocity model.

(2) It is very important to have an accurate picture of the shallow horizons, because errors there distort deeper horizons as statics errors (Landa, 1998).

(3) Velocities are approximately constant within the layers ("dip-steered" constraint).

In this paper we present some examples where imposing these constrains before updating the velocity field contributes to a geologically consistent PSDM that improves on PSTM.

(1) Faults Faults produce major lateral velocity changes, resulting in "pull-up" or "sag” in the seismic displayed in time (Fagin, 1997; Trinchero, 2000;Gochuioco, 2002). For PSDM, the problem of converting to depth arises from the inability of velocity model updating techniques to recognize anomalies generated by a (highly localized) fault. This is mainly due to the narrowness of the anomaly, the lack of vertical resolution and non hyperbolic residual normal move out (Kosloff, 2002). Some methods propose the application of highly detailed tomography, with mixed results (Birdus, 2010). Whatever detail tomography provides, there is still the need to smooth the overall velocity model to avoid oscillations in the depth conversion. Figures 1 and 2 show a line from a 3D project where the fault anomaly about 500 m wide. To solve this problem, updated tomographic velocities were constrained only in the shallow reflectors, successfully removing the pull-up effect. Figure 1a shows the PSTM image, with pull-up in the central area. Figure 1b shows the PSDM image, produced with a velocity model that constrains the tomography in order to remove the anomaly in the shallow reflectors. The constraint has also resulted in improvement on the deeper horizons. This section is shown with velocity overlay in Figure 2b, to be compared with the PSTM. Figure 2a, shows the PSDM image that used the same depth velocities as the PSTM on the same line. The distortion generated by the pull-up is combined with deformation due to an insufficient smoothing of the velocity model. The PSDM with a smoothed velocity field with a longer filter and corrected anomaly of the fault is shown on figure 2b.

PSTM PSDM scaled to time

Fig. 1 a) PSTM. Notice the pull up effect under the fault. b) PSDM with velocities updated with tomography constraints and scaled to time for comparison

(courtesy Cepcolsa, Colombia)

Fig. 2 a) PSDM converted to time using PSTM velocities.

b) PSDM velocities updated with constrained tomography (courtesy Cepcolsa, Colombia)

500 m

500 m

1a 1b

2a 2b

(2) Submarine canyons

In marine surveys, differences in water column thickness produce a distortion in the time image. This happens because the water velocity is usually significantly lower than sediment velocities. The effect can be seen in faults, and especially in submarine canyons. This case is a 2D seismic example in deep water. The offset-depth ratio is low for reflectors under the canyons, causing a great difficulty for velocity estimation of the shallow sediments. Interval velocities obtained from PSTM were also inadequate, as exemplified on figure 3a, which shows a detail of a PSDM with PSTM velocities converted to interval. The complete 2D PSTM is shown in figure 4a. Optimization PSDM velocities standard methods have difficulties in completely removing the effect of the Canyon, and then some methods have been developed in such sense (Birdus, 2009). In this case the velocity model was constrained to update in a way to give geologic-structural consistency. Comparison of velocity models derived from the PSTM and the constrained one, overlapping to the resulting PSDM, are shown on the left and right side of Figure 3, respectively. The result of the constrained velocity update is a model where shallow sediments preserve the velocity profile regardless of the depth, as it is expected for deep water. PSDM with PSTM derived velocities PSDM with constrained velocities

Fig. 3 a) PSDM with interval velocities converted from those used for PSTM

b) PSDM with constrained velocity field. (Courtesy CGGV, ANCAP) Images of the whole line are shown in figure 4. Figure 4a shows the PSTM, and figure 4b shows the PSDM performed with constrained velocities, scaled to time with a smoothed velocity field for comparison. The constrained model has improved the continuity of shallow and deep sediments.

1000 m

3a 3b

Fig. 4a: PSTM

Fig. 4b: PSDM in time

Fig. 4 a) PSTM

b) PSDM with constrained velocities on the model and scaled to time with smoothed velocities (courtesy CGGV, ANCAP)

3000 m

3) Fold Thrust Fault Thrust fault seismic results are characterized by poor imaging and a low sensitivity to velocity field adjustment, resulting from sparse sampling, abrupt topography, and high structural dip. We typically observe poor imaged signal in the lack of definition and continuity in the PSDM stack, and even more in the depth gathers. The low signal level can cause poor sensitivity to velocity changes: even at major horizons, large velocity changes produce small or uninterpretible changes in the residual NMO curvature of the gathers and the stack. Therefore, sometimes it is necessary to establish a complete a priori velocity model, and then perform small changes iteratively to improve the final PSDM stack. Figure 5 shows a 2D seismic line, containing areas of different quality. Figure 5a shows a PSDM with velocities obtained from the PSTM. Figure 5b shows the PSDM, performed by constraining the velocity model by extrapolating well velocities through the horizons of a geological-seismic model (“dip-steered” constraint model). There is an improvement in seismic quality resulting from the use of the geological-seismic model, as shown in the circled areas.

Fig. 5a: PSDM with optimized PSTM velocities

Fig. 5b: PSDM “dip-steered” constraint model

Fig. 5 a) PSDM with interval velocities from PSTM

b) PSDM from “dip-steered” constraint model (Courtesy Pacific Rubiales, Colombia)

CONCLUSIONS We have shown several examples of constraints on PSDM velocity model building, from details such as fault pull-up corrections and submarine canyon imaging, to complete models where the seismic quality is poor. Applying appropriate constraints improves the image quality in a region around where the constraints have been applied. In all cases we have shown, converting PSTM velocities to interval velocities for the initial model has failed to produce adequate PSDM velocities. This has happened because the flat-layered models used by the PSTM (either flat-layered or structured, using depth-corrected PSTM velocities), in spite of their convenience and repeatability, are not consistent with actual geology. When the models make use of geologic-seismic consistency, the imaging results are improved. BIBLIOGRAPHY Birdus, S., 2009, Geomechanical modeling to resolve velocity anomalies and image distortions

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