ADDITIONAL CONCERNS

The methodology raises several additional questions:

• How well does the method recover the correct interval velocity?

  We constructed a synthetic interval velocity model, and then modeled a CMP gather using a finite difference code, Figure . We then picked RMS velocities and attempted to estimate our interval velocity. As Figure  shows, we did a very good job of recovering the correct interval velocity.

   

  synthetic-data Figure 6 Modeled synthetic data.

   

  synthetic Figure 7 Initial interval velocity, picked RMS curve, and inverted interval velocity curve.

  

• How well does the method handle bad data?

  Using the same dataset (Figure ) we introduced some low-energy noise to our velocity scan and then attempted to invert back to our interval velocities. As Figure shows, even with the grossly inaccurate RMS picks at approximately 1.5 seconds we were still able to recover a reasonable interval velocity curve.

   

  gap Figure 8 Left panel, RMS picks overlaying semblance scan with noise introduced at approximately 1.5 seconds. Right panel, the resulting interval velocity curve, the curve without the bad data, and our bad-data RMS curve.

  

• Is our preconditioned variable zero mean and approximately white? To obtain maximum benefit from preconditioning we want our preconditioning variable ($\bold p$) to be white Nash and Sofer (1996). Not surprisingly the preconditioned variable for this problem is not quite zero-mean. Velocity generally increases with depth, which means the slope of velocity will on average be greater than one. Considering the limited resolution of the seismic method, it is not surprising that our preconditioned variable does not meet the second whiteness criteria either.
   

  xvals Figure 9 Our preconditioned variable for the continuous case.