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# 2-D SYNTHETIC EXAMPLE

Figure  shows a 2-D synthetic example. A dataset containing a single dipping plane wave (apparent velocity 3 km/sec) has had applied to it the statics solution shown in Figure . The trace spacing is 20 meters and the time sampling interval is four milliseconds. A single dip estimation was performed at the middle receiver, using all ten neighboring traces. The statics estimated by the algorithm are shown in Figure . While the relative shifts are correct, there is a time shift that reflects the presence of a DC bias in the random statics values that I chose to apply. This bias has been removed from the solution.

The crosscorrelation functions for each receiver for the first two iterations are displayed in Figure . Figure  shows the improvement in the stack over the course of the first two iterations. Actually a single iteration was sufficient in this simple case.

In Figure , random noise has been added to the synthetic. The statics solution in Figure  is similar to the previous one, but there is a clear linear trend in the solution that represents poorly estimated long wavelength statics. These become even more problematic on a larger 3-D example in the following section.

Figure  shows the result of applying the statics to the noisy data. After statics application, the data have been interpolated onto the original recording geometry by a local slant stack at the correct dip. A median filter has been used in place of the straight stack, and the output has been weighted by the semblance. This nonlinear weighting enhances the coherent signal. Because a single time window was used in this example, some alignment of noise along the same dip can be seen.

syn2d
Figure 1
A 2-D synthetic example. The statics shown in Figure  have been applied to a dataset containing a single dipping plane wave.

 statin2d Figure 2 Random statics applied to create the data in Figure .

 statout2d Figure 3 Statics solution estimated by the algorithm.

stak2d
Figure 4
Iterative improvement of the local slant stack. The bottom trace is the initial stack. Each additional trace represents the result of updating the static solution for a single receiver. The first ten traces correspond to the first iteration of the algorithm, the second ten to the second iteration.

xcor2d
Figure 5
Display of crosscorrelations for the first two iterations. From bottom to top, the first ten traces are the crosscorrelations for the ten different receivers for iteration one, the next ten for iteration two.

noise2d
Figure 6
Synthetic with random noise added.

noiseout2d
Figure 7
Noisy synthetic after application of statics, followed by interpolation onto the original grid, using a median filter and semblance weighting. A single semblance computation window was used for the entire trace, and some alignment of the noise can be seen.

 noisestat2d Figure 8 Statics solution for noisy data. Compared with Figure , here there is a trend from lower left to upper right, indicating that the long wavelength statics have not been determined well.

Next: 3-D SYNTHETIC EXAMPLE Up: Cole: Statics estimation by Previous: Interpolation
Stanford Exploration Project
11/16/1997