# Residual moveout analysis

Series Investigations in Geophysics Öz Yilmaz http://dx.doi.org/10.1190/1.9781560801580 ISBN 978-1-56080-094-1 SEG Online Store

We begin with building an initial velocity-depth model from the data as in Figure 9.4-15 using the time-to-depth conversion strategy described in model building. Figure 9.5-1a shows the time-migrated stacked section with a set of interpreted horizons that correspond to layer boundaries with significant velocity contrast. Perform Dix conversion of the horizon-consistent rms velocity profiles (Figure 9.5-1b) to derive the interval velocity profiles as shown in Figure 9.5-1c. Clearly, you often are compelled to apply some smoothing to the rms velocity profiles before Dix conversion and even apply additional smoothing to the interval velocity profiles afterwards. Then, perform image-ray depth conversion of the time horizons interpreted from the time-migrated section (Figure 9.5-1a) to generate the depth horizons. Finally, combine the interval velocity profiles with the depth horizons to create the velocity-depth model shown in Figure 9.5-2a.

Figure 9.4-15  An unmigrated CMP-stacked section with seven time horizons that correspond to layer boundaries with significant velocity contrast.

Complete the analysis by checking for consistency of this estimated initial velocity-depth model with the depth image derived from poststack depth migration and the stacked section. Note that the reflector geometries inferred by the depth image shown in Figure 9.5-2b are in agreement with the depth horizons. Additionally, observe that the actual reflection traveltimes on the stacked section are in good agreement with the modeled zero-offset traveltimes as shown in Figure 9.5-2c.

We now check for consistency of the initial velocity-depth model in Figure 9.5-2a with prestack data and update it by correcting for the residual moveout observed on image gathers derived from prestack depth migration. Image gathers are like moveout-corrected CMP gathers with vertical axis in depth. Unlike in CMP gathers, however, events in image gathers are in their migrated positions. Shown in Figure 9.5-3a is an image section derived from prestack depth migration of the data associated with the stacked section in Figure 9.5-2c using the initial velocity-depth model in Figure 9.5-2a. Superimpose the depth horizons from the velocity-depth model onto the image section and make some minor adjustments where necessary by re-interpreting the depth horizons (Figure 9.5-3b). Selected image gathers associated with the depth image from prestack depth migration are shown in Figure 9.5-4.

How do we make use of the image gathers to update the initial velocity-depth model? First, consider applying to a CMP gather conventional stacking velocity analysis. Compute the velocity spectrum (velocity analysis) and pick a velocity function. Following the normal-moveout correction of the CMP gather using this velocity function, events should look flat if the velocity function had been picked correctly. If the picking was done incorrectly, then you would observe events with residual moveout. In principle, this residual moveout can be computed and used to update the initially picked velocity function.

Analogous to the conventional stacking velocity analysis, if the initial velocity-depth model has been estimated with sufficient accuracy, then the image gathers derived from prestack depth migration using this model should exhibit flat events associated with the layer boundaries included in the model. Any errors in layer velocities and/or reflector geometries, on the other hand, should give rise to residual moveout along those events on the image gathers. Again, in principle, this residual moveout can be determined and used for model updating as illustrated in Figure 9.5-5. The image gather in Figure 9.5-5a exhibits events with residual moveout represented by the purple trajectories. Assume that the residual moveout is parabolic and compute the semblance spectrum as shown in Figure 9.5-5b. The horizontal axis of the semblance plane represents the depth error and the vertical axis represents the depth of the event. The semblance spectrum has two quadrants that correspond to positive and negative residual moveouts, or equivalently, to positive and negative depth errors. A flat event would yield a semblance peak that coincides with the vertical axis with zero depth error, whereas an event with residual moveout would yield a semblance peak situated either in the left or right quadrant depending on the sign of the depth error.

Much like picking a velocity function from a conventional stacking velocity semblance spectrum, a vertical function that represents the depth-dependent residual moveout can be picked from the semblance spectrum in Figure 9.5-5b. This function can then be used to correct for the residual moveout as shown in Figure 9.5-5c. The actual steps to make the residual moveout correction are as follows:

1. Extract the interval velocity function from the velocity-depth model at the image-gather location where the residual moveout analysis is to be done.
2. Convert the image gather from depth to time using the interval velocity function.
3. Assume that the residual moveout of events on the image gather in time is parabolic and compute the semblance spectrum for a range of negative and positive moveouts.
4. Apply the residual moveout correction to the image gather.
5. Compute a new rms velocity function from the results of the residual moveout analysis.
6. Compute a new interval velocity function (equation 1) from the updated rms velocity function at the image-gather location.
7. Convert the image gathers back to depth using the new interval velocity functions.
8. Finally, update the velocity-depth model using the new interval velocity functions.

 ${\displaystyle v_{n}={\sqrt {\frac {V_{n}^{2}\tau _{n}-V_{n-1}^{2}\tau _{n-1}}{\tau _{n}-\tau _{n-1}}}},}$ (1)

In principle, residual moveout analysis can be carried out for image gathers at some spatial interval. The residual moveout spectra computed from the image gathers displayed in Figure 9.5-4 indicate varying degrees of errors in the initial velocity-depth model shown in Figure 9.5-2a. An alternative way to measure the residual moveout is by computing it along the depth horizons themselves. Shown in Figure 9.5-6 are the horizon-consistent residual moveout semblance spectra. The vertical axis of the semblance plane represents the depth error which corresponds to either positive or negative residual moveout.

Pick the residual moveout profiles from the semblance spectra as shown in Figure 9.5-6 and combine them with the depth horizons to create the residual moveout section shown in Figure 9.5-5d. This section gives an impression of how much residual moveout, thus the range of errors in the initial velocity-depth model, is present on image gathers as a function of depth and distance along the line.

Figure 9.5-7a shows the interval velocity profiles before (as in Figure 9.5-1c) and after the residual moveout update, and Figure 9.5-7b shows the updated depth horizons displayed on top of the initial velocity-depth model as in Figure 9.5-2a. When combined, the updated interval velocity profiles and depth horizons yield the updated velocity-depth model shown in Figure 9.5-8a.

Following the update, the new model needs to be checked for consistency with the input seismic data. Figure 9.5-8b shows the image section derived from prestack depth migration using the updated model in Figure 9.5-8a. Note that the depth horizons associated with the updated model, when superimposed on the image section, coincide with the reflectors that correspond to the layer boundaries. The modeled zero-offset reflection traveltimes using the updated model also are in good agreement with the observed traveltimes of the events on the unmigrated stacked section that are associated with the layer boundaries included in the velocity-depth model of Figure 9.5-8a.

To further verify the accuracy of the updated model, compare the residual moveout semblance spectra computed from the image gathers at selected locations along the line after the model update (Figure 9.5-9) with those before the update (Figure 9.5-4). Note that most of the semblance peaks are now positioned along the vertical axis of the semblance spectra that corresponds to zero residual moveout. The horizon-consistent residual moveout spectra after the model update are shown in Figure 9.5-10. Superimposed on these spectra are the residual moveout profiles that were picked from the spectra before the update (Figure 9.5-6). Note that the residual moveout errors have been reduced significantly after the model update.

The residual moveout analysis of image gathers and the update of velocity-depth model should be performed iteratively until the velocity-depth model and the depth image are consistent [1]. Consistency may be achieved with only a few iterations for cases where residual moveouts are small. Sometimes, consistency is never achieved even after several iterations. This often occurs when the initial residual moveouts are caused largely by significant errors in the initial velocity-depth model. An erroneous initial estimate most likely is a result of rapid lateral velocity variations less than a spread length (models with horizontal layers). In general, updating velocity-depth models based on residual moveout analysis of image gathers yields acceptable results for moderately complex structures associated with compressional and extensional tectonics. However, it may not be suitable for complex overburden structures associated with overthrust or salt tectonics.

## References

1. Deregowski, 1990, Deregowski, 1990, Common-offset migrations and velocity analysis: First Break, 8, 225–234.