At this time I am testing this formulation on synthetic data. I created a ten trace angle gather (Figure 1) using the basic form of Bortfeld's equations. Figure 1 also contains the stacked trace of this angle gather. There are five events with different reflectivities.
The results of the inversion are in Figure 2 and are fairly accurate. The answers are:
|Event||Correct RO||Est. RO||Correct Rsh||Est. Rsh||Correct RP||Est. RP|
The solutions for RO have been found correctly. There is some error in the solution for RP and this in turn has produced some error in the calculated values for Rsh. However, the errors are small so it seems that this form can be successfully inverted. The fact that it is not dependent on interval velocities makes it preferable to other forms of the Bortfeld approximation.