Infill of 3-D seismic data from a quarry blast

Finding missing data (filling empty bins) requires use of a filter. In this subsection we will assume that the filter is known. In the next we will see how to find the filter. Except for using a 2-D convolution operator instead of a 1-D one, the theory is all the same in 2-D as it was in 1-D in Chapter , equations () to (), and there is no reason to repeat it because the helix converts 2-D to 1-D. An open question is how many conjugate-direction iterations are needed in missing-data programs. When estimating filters, I set the iteration count niter at the number of free filter parameters. Theoretically, this gives me the exact solution. The number of free parameters in the missing-data estimation, however, could be very large. This fact implies impractical compute times for the exact solution (and thus calls for preconditioning). I find that where gaps are small, they fill in quickly. Where the gaps are large, they don't, and more iterations are required.

Figure 4 shows an example of replacing missing data by values predicted from a 3-D PEF. The data was recorded at Stanford University with a $13\times 13$ array of independent recorders. The figure shows 12 of the 13 lines each of length 13. Our main goal was to measure the ambient night-time noise. By morning about half the recorders had dead batteries but the other half recorded a wave from a quarry blast. The raw data was distracting to look at because of the many missing traces so I interpolated it using parameters for the small filter mentioned with subroutine print3() .

 

passfill90
Figure 4 The left 12 panels are the inputs. The right 12 panels are outputs.