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 values at a fixed x position (1.96 km in Figure ).
Notice that when 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 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.
Figure 5 Effect of lambda on 1-D deconvolution. From bottom to top: crosscorrelation, , and
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 and is less affected by the low frequency noise visible in the 1-D deconvolution result. The less sensitivity to choice is important, since deconvolution major handicap is the selection of the regularization parameter.
Figure 6 Effect of lambda on 2-D deconvolution. From bottom to top: crosscorrelation, , and