Real Data Example

Real data from the Gulf on Mexico will now be examined. Figure shows the RMS velocity.

 

vrms
Figure 9 RMS velocity for Gulf of Mexico data.

Figures and show the previous inversion results done by Valenciano et al. (2003) and Witten and Grant (2006), respectively. Notice that Figure is smoother than Figure . This is because Figure uses an approximate $\ell_1$ norm.

 

vintOld
Figure 10 Inversion result from Valenciano et al. (2003).

 

vintOldcvx
Figure 11 Inversion result from Witten and Grant (2006).

The results from both previous inversion schemes have limitations. Valenciano et al. (2003) uses an approximate $\ell_1$ norm and has no stopping criterion. Thus it requires as many iterations as the user is willing to execute. For the result shown here, 800 conjugate gradient steps were taken. Witten and Grant (2006) is hampered by the use of the MATLAB based icvx software Grant et al. (2006), limiting its use to small problems.

 

vint
Figure 12 Inversion result from scheme presented in this paper. The inversion appears to be working properly as all of the main features seen in the Figures and . The smoothing along the midpoint axis does not work.

Although Figure is not perfect, the inversion result for the method presented in this paper is close to the previous results. The result in Figure took only 108 iterations. All of the major features are present in all three inversion results. The main difference is in the smoothness of the result.