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Zero offset image resolution

To compare the result of the different imaging conditions, we build a constant velocity model of five dipping layers pinching-out to the right of the model. The deepest reflector has the steepest dip angle $(\approx 63^{\circ})$ and the shallowest has zero dip. Figure [*] shows a comparison of three different imaging conditions. Figure [*]a uses the crosscorrelation imaging condition, Figure [*]b the 1-D deconvolution imaging condition along the time dimension ($\lambda=0.05$) and Figure [*]c the 2-D deconvolution imaging condition in the (xs,t) plane ($\lambda=0.05$). Notice the better resolution of the 2-D deconvolution image.

The better stability of the 2-D deconvolution image is demonstrated by comparing Figure [*] and Figure [*]. They display the result of the 1-D deconvolution and the 2-D deconvolution for different $\lambda$ values at a fixed x position (1.96 km in Figure [*]).

Notice that when $\lambda$ decreases, the 1-D deconvolution result presents low frequency noise. The stacking across the shot position [equation (3)] reduces the high frequency noise but might increase some low spatial frequency noise that is periodic with the shot positions. In the case of 2-D deconvolution, when $\lambda$ decreases, the noise contaminates the image in all the spatial frequency bandwidth. However, the signal to noise ratio for this imaging condition is much higher than for the 1-D deconvolution imaging condition.

 
Comp_1d_epsst
Figure 5
Effect of lambda on 1-D deconvolution. From bottom to top: crosscorrelation, $\lambda=0.05$, $\lambda=0.005$ and $\lambda=0.0005$
Comp_1d_epsst
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From this results, we can conclude that the 2-D deconvolution imaging condition in the (xs,t) plane gives a better resolution than the other imaging conditions. The 2-D deconvolution final image is less sensitive to the choice of $\lambda$ and is less affected by the low frequency noise visible in the 1-D deconvolution result. The less sensitivity to $\lambda$ choice is important, since deconvolution major handicap is the selection of the regularization parameter.

 
Comp_epsst
Figure 6
Effect of lambda on 2-D deconvolution. From bottom to top: crosscorrelation, $\lambda=0.05$, $\lambda=0.005$ and $\lambda=0.0005$
Comp_epsst
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next up previous print clean
Next: CIGs and velocity analysis Up: Results with synthetic data Previous: Results with synthetic data
Stanford Exploration Project
7/8/2003