GEOMETRY-BASED DECON

In chapter deconvolution was considered

to be a one-dimensional problem. We ignored spatial issues. The one-dimensional approach seems valid for waves from a source and to a receiver in the same location, but an obvious correction is required for shot-to-receiver spatial offset. A first approach is to apply normal-moveout correction to the data before deconvolution. Previous figures have applied a t² amplitude correction to the deconvolution input. (Simple theory suggests that the amplitude correction should be t, not t², but experimental work, summarized along with more complicated theory in IEI, suggests t².) Looking back to Figure , we see that the quality of the deconvolution deteriorated with offset. To test the idea that deconvolution would work better after normal moveout, I prepared Figure 6.

 

wz27nmo
Figure 6 Data from Yilmaz and Cumro dataset 27 after t² gain illustrates deconvolution working better after NMO.

Looking in the region of Figure 6 outlined by a rectangle, we can conclude that NMO should be done before deconvolution. The trouble with this conclusion is that data comes in many flavors. On the wider offsets of any data (such as Figure ), it can be seen that NMO destroys the wavelet. A source of confusion is that the convolutional model can occur in two different forms from two separate physical causes, as we will see next.