Tomographic velocity estimation

In order to perform the tomographic velocity estimation, the first step is to pick reflectors in the image domain after migration with a velocity model that is first guess. Figure  shows the initial velocity model that was used. The initial velocity model was determined by setting 1500 (m/s) for the water velocity and linearly increased with respect to depth from the ocean bottom. Figure  shows the image obtained by stacking thirty-one images of the surface-oriented plane-wave synthesis imaging with -30 through +30 degrees for the incidence angle range. Figure  shows some of the CSL gathers selected from the image cube before stack and reveals velocity error by showing curvatures of the reflector images from horizontal aligning with respect to the incidence angles. I manually picked eight reflectors to be used for velocity analysis; these are displayed in Figure .

The next step in the tomographic velocity estimation process is the measurement of traveltime errors along the reflector picked. In the algorithm proposed in this thesis (chapter 4), the traveltime errors are inferred from the residual moveout (RMO) velocity measured. The RMO velocity analysis is performed along the reflector picked and the results of it are shown in Figure .

Finally the traveltime errors are back projected to obtain the slowness field error of the reference model. This requires the calculation of the back projection operator by means of ray tracing. A modified reflector location using the RMO velocity is used to trace rays instead of using the reflector picked as the starting location of the ray tracing, The modified reflector locations are shown in Figure . Figure  shows the updated velocity model that is obtained by inversion of the traveltime errors.

The prestack data set is again imaged with the updated velocity model by means of plane wave synthesis imaging; the new image is shown in Figure . The CSL gathers shown in Figure  confirm the accuracy of the velocity updated by showing horizontal alignment of the images with respect to the incidence angle.

 

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Figure 3 CMP gathers section of Mobil AVO dataset after interpolation.

 

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Figure 4 Velocity model of initial guess.

 

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Figure 5 Image obtained by thirty-one plane wave syntheses.

 

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Figure 6 Selected CSL gathers after zero-iterations.

 

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Figure 7 Reflector locations picked for tomographic inversion.

 

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Figure 8 Reflector locations positioned according to RMO velocity.

 

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Figure 9 Reflector locations positioned according to RMO velocity.

 

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Figure 10 Velocity model after one iteration of tomographic velocity estimation.

 

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Figure 11 Image obtained by thirty-one plane wave syntheses.

 

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Figure 12 Selected CSL gathers after one-iteration.