Limitations in resolving velocity-depth ambiguity by tomography

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Seismic Data Analysis
Seismic-data-analysis.jpg
Series Investigations in Geophysics
Author Öz Yilmaz
DOI http://dx.doi.org/10.1190/1.9781560801580
ISBN ISBN 978-1-56080-094-1
Store SEG Online Store


Reflection traveltime tomography can be surprisingly successful in updating an initial model with significant errors. Consider, for instance, the velocity-depth model in Figure 9.5-25 with constant layer velocities. This model is indeed practically consistent with the input seismic data as verified by the depth image in Figure 9.5-25b and the modeled zero-offset traveltimes overlayed on the unmigrated stacked section in Figure 9.5-25c.

Perform prestack depth migration using the initial model to derive the image section in Figure 9.5-26a and compute the residual moveout semblance spectra of the selected image gathers in Figure 9.5-27. Note the significant moveout errors manifested by the semblance peaks which are off the zero moveout centerline on the spectra. Now, compute the horizon-consistent residual moveout semblance spectra along the depth horizons shown in Figure 9.5-26b and note the significant departures from the zero moveout line (Figure 9.5-28). Pick the residual moveout profiles from these spectra and perform a tomographic update to obtain a new set of interval velocity profiles and depth horizons as shown in Figure 9.5-29.

Combine the updated interval velocities and reflector geometries to create the updated velocity-depth model shown in Figure 9.5-30a. Note that this model is fairly close to the updated models derived from the applications of time-to-depth conversion (Figure 9.5-16a) and layer-by-layer inversion (Figure 9.5-23a) strategies. Model verification tests (Figures 9.5-30b,c) and residual moveout semblance spectra (Figures 9.5-31 and 9.5-32) demonstrate the feasibility and accuracy of the updated model in Figure 9.5-30a.

As demonstrated by the extreme case of an erroneous initial model (Figure 9.5-25), a tomographic update can steer the model toward an acceptable final model. How far, though, can we go with tomography to obtain a finely accurate model? In the following model experiments, we shall examine this fundamentally important question regarding tomography.

Figure 9.5-33 shows horizon-consistent residual moveout semblance spectra derived from image gathers that were created by prestack depth migration of the synthetic data as in Figure 9.1-2a using the initial velocity-depth model shown in Figure 9.1-5b. Shown in Figure 9.5-34 are the results of tomographic updating — the interval velocity profiles before (thin curves) and after (thick curves) the tomographic update, and the updated velocity-depth model itself. Compare with the initial velocity-depth model shown in Figure 9.1-5b and the true velocity-depth model shown in Figure 9.1-1b. Compare with the true model (Figure 9.1-1) and the initial model (Figure 9.1-5) and note that tomographic update has produced a result fairly close to the true model. A close-up of the center portions of the initial model, the final model, and the true model after the tomographic update is shown in Figure 9.5-35.

Iterate the updating process until the residual moveout for all the layers is minimized. Specifically, perform prestack depth migration using the tomographically updated velocity-depth model in Figure 9.5-34 and generate a new set of image gathers. Compute a new set of residual moveout semblance spectra from the image gathers as shown in Figure 9.5-36. Compare with the residual moveout spectra in Figure 9.5-33 before the tomographic update and note that the residual moveout after the update has been reduced significantly.

We now test the tomographic update in the presence of large errors in the initial velocity-depth model. Consider the velocity-depth model shown in Figure 9.1-1 based on the parameters listed in Table 9-2. We shall deliberately introduce errors to this model by setting the velocities for layer H3 to a constant value of 2550 m/s and for layer H4 to a constant value of 3250 m/s. The erronenous velocity-depth model is shown in Figure 9.5-37.

Table 9-2. Parameters of the model with horizontal layers and constant-velocity near-surface layer.
Layer Velocity (m/s) Depth (m)
H1 1500 100
H2 2000 1000
H3 2400 – 2700 1500
H4 3000 – 3500 1800
H5 4500 2250
H6 3000 2700

By adopting the distorted model in Figure 9.5-37 as the initial velocity-depth model, perform prestack depth migration, generate image gathers and compute residual moveout semblance spectra as shown in Figure 9.5-38. Note the large moveouts caused by the velocity errors associated with layers H3 and H4. The tomographic update shown in Figure 9.5-39a has modified the velocities for layers H3 and H4, and for the underlying layers. Specifically, the constant-velocities assigned to layers H3 and H4 have been replaced with laterally varying velocity profiles that are consistent with the actual velocity profiles shown in Figure 9.1-1. Nevertheless, compare the profiles in Figures 9.1-1a and 9.5-39a and note that the velocity estimate for the underlying layer H5 has been adversely influenced by the tomographic update applied to the layers above.

A close-up of the central portions of true velocity-depth model (Figure 9.1-1b), the initial velocity-depth model (Figure 9.5-37b), and the updated velocity-depth model (Figure 9.5-39b) is shown in Figure 9.5-40. Although the errors in the initial velocity-depth model for the shallow layers have been reduced, note that, in general, starting with an initial velocity-depth model with large errors, tomographic updating does not always produce satisfactory results.

The fact that the tomographic update for one layer is influenced by the errors in the parameters for the layers above is best illustrated by the model in Figure 9.1-18. This is the model with horizontal layers (Table 9-2) but with a near-surface layer H1 with laterally varying velocities between 800 m/s and 1500 m/s. Results of earth model estimation using Dix conversion are shown in Figure 9.1-21c. Consider this model as the initial velocity-depth model and perform prestack depth migration of the data associated with the stacked section in Figure 9.1-19a, generate image gathers, and compute the residual moveout semblance spectra shown in Figure 9.5-41. Pick the spectra to obtain the residual moveout profiles by tracking the semblance peaks, then use these profiles in a tomographic update to get the new model shown in Figure 9.5-42. Use the resulting model as input to a second iteration for model updating. Compare the resulting residual moveout spectra shown in Figure 9.5-43 with those from the first iteration shown in Figure 9.5-41 and note that the second iteration has reduced the residual moveout, significantly. The updated model from the second iteration is shown in Figure 9.5-44. A close-up of the central portions of the intermediate velocity-depth model (Figure 9.5-42b), the velocity-depth model updated for the second time (Figure 9.5-44b), and the true velocity-depth model (Figure 9.1-18b) is shown in Figure 9.5-45. Compare these estimates with the close-up view (Figure 9.1-22b) of the initial velocity-depth model shown in Figure 9.1-21c. The lesson to learn from this experiment is not to start with an initial model (Figure 9.1-21c) with large errors and expect a tomographic update to correct for these errors.

Finally, we shall update the model shown in Figure 9.1-24 which was estimated by coherency inversion. Consider this model as the initial velocity-depth model and perform prestack depth migration, generate image gathers, and compute the residual moveout spectra shown in Figure 9.5-46. Pick the spectra, again, by tracking the semblance peaks to obtain the residual moveout profiles. Then use these profiles in a tomographic update to get the new model shown in Figure 9.5-47. A close-up of the central portions of the initial velocity-depth model (Figure 9.1-24b), the updated velocity-depth model (Figure 9.5-47b), and the true velocity-depth model (Figure 9.1-18b) is shown in Figure 9.5-48.

Based on the results of the experiments using Dix conversion and coherency inversion applied to the model with a near-surface layer that has lateral velocity variations (Figure 9.1-18), again, the lesson to learn is that, whatever the strategy used in the model building, if you start with an initial model with large errors, do not expect tomographic updating to correct for these errors.

We now examine reflection traveltime tomography for its ability to update an initial model in the presence of a complex overburden. Figure 9.5-49a shows the rms velocity profiles along the time horizons in Figure 9.4-28a. Dix conversion yields the interval velocity profiles shown in Figure 9.5-49b. Admittedly, some editing and smoothing before and after Dix conversion were done to tame the interval velocities to behave in a structurally sensible manner.

By using the interval velocity profiles shown in Figure 9.5-49b, the time horizons interpreted from the time-migrated section shown in Figure 9.4-28a were converted to depth by way of image rays. Then, these depth horizons were combined with the interval velocity profiles (Figure 9.5-49b) to create an initial velocity-depth model. This was followed by depth migration of the stacked section in Figure 9.4-28b using the initial velocity-depth model, which in turn, was revised based on the interpretation of the depth-migrated section. A second iteration of poststack depth migration (Figure 9.5-50a) produced a velocity-depth model (Figure 9.5-49c) that is consistent with the reflection times observed on the unmigrated stacked section (Figure 9.5-50b).

Actually, the now consistent velocity-depth model in Figure 9.5-49c is what we shall update by way of reflection tomography. To begin with, perform prestack depth migration and generate image gathers as in Figure 9.5-51. Compute the residual moveout semblance spectra and observe that there are semblance peaks that are off the center line, indicating the presence of residual moveout. Stacking of the image gathers yields the image section from prestack depth migration shown in Figure 9.5-52. The significant improvement in imaging the diapiric structure and the base-salt reflector (horizon H8 as in Figure 9.5-50a) becomes obvious when this section is compared with the poststack depth-migrated section in Figure 9.5-50a. Nevertheless, the fact that the semblance spectra (Figure 9.5-51) exhibit residual moveout along the events associated with the layer boundaries included in the velocity-depth model suggests that the image from prestack depth migration may be improved by updating the initial velocity-depth model.

Now here is a dilemma that we have to live with when updating velocity-depth models. As a result of the inevitable muting of the image gathers (Figure 9.5-51), there is often insufficient offset range to accurately measure residual moveouts for shallow horizons. Because of the very poor residual moveout spectra, shallow horizons can be unreliable in model updating. Errors in the model parameters for the shallow layers will of course adversely affect the estimation and updating of the model parameters for the deeper layers. At greater depths, although there is sufficient cable length, faster velocities prevent recognition of velocity or depth errors with adequate resolution.

There is of course some mid-range of depths and velocities for which residual moveout semblance spectra can be used for model updating. In the present example, residual moveout semblance spectra associated with horizons H5 to H8 (as denoted in Figure 9.5-50a) were computed and picked as input to the reflection traveltime tomography solver (Section J.6). When picking the residual moveout profiles from the semblance spectra in Figure 9.5-52, keep in mind not to track all the rapid fluctuations that are much less than a cable length. These are the manifestations of the lateral velocity variations in the layers above as was demonstrated by the experiments conducted using synthetic data in models with horizontal layers.

The workflow for tomographic updating — prestack depth migration to generate image gathers, computing residual moveout along events associated with the layer boundaries, picking residual moveout profiles and using them as input to the tomography to derive the updates for layer velocities (Figure 9.5-53a) and reflector geometries (Figure 9.5-53b), were repeated twice to produce the final model and image shown Figure 9.5-54. In each iteration, the first four layers were kept unchanged because of poor estimates for residual moveout along the horizons that correspond to the base of these layers (H1 through H4). Compare the images from prestack depth migrations shown in Figures 9.5-52a and 9.5-54a obtained from the initial and final velocity-depth models of Figures 9.5-52b and 9.5-54b, respectively, and note that the differences are marginal.

Iterative tomographic updating, as demonstrated by the model experiments in this section, does not necessarily result in convergence of an initial model to a final model with zero residual moveout. Instead, the solution may just wobble and never converge. This scenario is especially likely for cases of complex overburden structures as in the present example. In such cases, additional information; such as well control, check-shot velocities, and geologic constraints, is required to derive an acceptable final model.

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Limitations in resolving velocity-depth ambiguity by tomography
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