The data

Given the operators I have chosen to use in this experiment, selecting data to test is straightforward. I need data that will result in a model that requires interpolation and will make differences in frequency content of various results obvious. Since the regularization operator is a steering operator, the data can have varying dips. To meet these simple requirements, I chose to take a 2-D slice from the familiar ``qdome'' model Claerbout (1995). The masking operator ${\bf W}$ contains enough zeros to defeat the inversion operator, making the regularization operator necessary. Figure  shows the data multiplied by the masking operator (${\bf Wd}$) I used for this experiment. I am displaying it this way to make comparison with the inversion results simpler. Figure  also shows the ``ideal'' model that would be obtained if ${\bf W}$ was simply an identity operator.

 

datmod
Figure 1 Left panel is the data weighted by the masking operator used for the inversion problems, right panel is the ideal model we get when the masking operator is replaced with an identity operator.