Regularization operator accuracy

It is clear that the geological inversion is strongly dependent on the regularization operator. Since this operator may be constructed from picked reflectors, it is important to know what happens if the reflector is not picked well. To examine this, I created a regularization operator from the ``reflectors'' picked in Figure . In this figure, note that the picked reflectors cross the correct dips at the depths between 3 and 3.4 kilometers and 3.7 and 4.1 kilometers. They cross themselves at depth 4.5 kilometers. The picked reflector beginning at depth 3.75 km follows the correct dip for the most part, but ignores the slight change in dip at the fault at CMP position 7.2 km. The water bottom has been correctly picked. The picked reflector beginning at depth 4.2 km follows the correct dip, but continues well into the shadow zone where it may or may not be correct. Also within the shadow zone is a completely absurd picked reflector put there to see if any event can be created there. Finally, note that the top and bottom of the salt have not been picked at all. This will leave the preconditioning operator in the salt area to be interpolated from the picked reflectors. In this section, I will refer to the dips and reflectors from the migration result as ``real'' or ``correct'' and the dips and reflectors used for the inversion as ``picked.''

 

reftest
Figure 15 Migration result with the picked ``reflectors'' overlaid. These reflectors do not match the correct reflectors and should produce a bad result.

The result of using this regularization operator for geological RIP is seen in Figure . As expected, the result isn't good. In the areas where the picked dips were considerably wrong, such as at the left side between 3 and 3.4 kilometers and 3.7 and 4.1 kilometers, there are almost no events at all in the result. This is also true for the ``M'' shaped picked reflector in the shadow zone area. In these areas, the data fitting goal from equation () has rejected the attempted regularization, essentially canceling out all of the image. However, elsewhere in the shadow zone, where the picked dips are reasonable, there is good continuation of the real events underneath the salt. In the area where the picked reflectors cross, there is a similar canceling of energy, but it is reassuring to see that the inversion has handled the crossing dips without becoming unstable. Finally, it is clear that not picking the salt boundaries has caused major problems. Since no picked dips were provided in the area of the salt, the steering filter interpolated the dip of the water bottom down through this region. The result shows strong events where the dip of the water bottom is similar to that of the salt boundaries, but very low energy elsewhere, once again due to the rejection of the regularization by the data fitting goal.

 

2dfilttest
Figure 16 Result of 3 iterations of the geologically regularized result with badly picked reflectors.

This experiment showed that the inversion will reject dips that are incorrectly picked where data exists. The data fitting goal () assures that picked dips that generate an event which interferes with the data are rejected. Picked dips that generate an event that doesn't interfere with existing data are allowed. Picked dips that cross, or meet at a point can be accommodated by the inversion. It is necessary to pick reflectors wherever the dominant dip changes.