Real data

Two field data CMP's are also analyzed with the BP algorithm. With an order of magnitude increase in size, as well as much energy in the data that leads to a more full model space, convergence does not seem as well behaved for real data. For the CMP with bad traces in Figure , we needed only 10 minutes of CPU time. Normally, this computation requires user intervention to stop the process as it looked to become unstable. The multiple ridden data of Figure , however, required about 40 minutes to compute. The model space used in both examples was only approximately 2.5-fold overcomplete, and this fact may contribute to the problems experienced. Interestingly, with the regularization parameter $\delta=1$, the algorithm has a drastic denoising effect as well.

Figure compares the predicted data from CG least squares inversion, the Huber norm inversion, and the BP inversion. The noise reduction of the near traces is remarkable and deserves further research. A very powerful linear noise train bounds the data to the right, which we hypothesize is the result of the near offset noise in the raw data. Figure contains four powerful noisy traces between 2200 - 2700 m/s. Also noticeable is the tendency for the forward model to bifurcate real events into a correct and a fast event such as at 1.25 seconds. Replacing the high amplitude ringing trace with zeros did not fix the problem.

 

badtr
Figure 4 Modeled data after inversion compared to original a CMP that suffers from bad traces and substantial near offset noise.

 

vel-badtr
Figure 5 Velocity panel comparison. The different output of the different programs makes direct comparison impossible. The left panels scan to much higher velocity than was necessary.

 

vbadsolo Figure 6 Presentation of the envelope of the velocity scan provides a better look at the location of the focus of energy. The several vertical noise traces probably lead to the poor quality of the predicted data (right panel, Figure ). Disappointingly, some events have bifurcated.

Figure compares the predicted data from CG least squares inversion, the Huber norm inversion, and the BP inversion. The BP solver had great difficulty with the multiples infested CMP. The garbage in the low velocity range above 1.4 seconds is troublesome. This may contribute to the problems analyzing this data, as I may not have made the model space large enough to achieve the necessary overcompleteness, or the linear events are not well described by the hyperbolic dictionary. This type of data is a good candidate to try the amalgamated linear/hyperbolic radon transform of Trad et al. (2001).

 

mult
Figure 7 Modeled data after inversion compared to original a CMP that suffers from internal multiples and strong ground roll.

 

vmultsolo Figure 8 Presentation of the envelope of the velocity scan provides a better look at the location of the focus of energy.