CONCLUSION

The results from these two simulation examples must be considered in a very limited sense. Without a test on real data and/or more sophisticated synthetic cases, which may include more geological reflector models, noise, statics etc, the Tieman method cannot be satisfactorily tested. I tested the case in which there are many events of apparently different character in dip and in depth, creating a multitude of confused hyperbolas on a common shot gather. These two applications confirm the following:

• 1) that the Tieman method does work, which is apparent when the the striking similarity of the two transforms in the 80 point sample case are considered
  
• 2) that it handles stacking of sparsely sampled offsets better than the slant stack direcly applied to shot point data.

The other extreme would be to test Tieman`s method and a direct shot gather slant stack on a model with a few reflectors of gradually changing dip. Also I did not deal with sparse sampling along midpoints which could be the source of inaccuracy for the Tieman method. Finally tests on real data are necessary to fully examine the applicability of this method. These preliminary results are promising and indicate that a better method of evaluating dips in shot gathers may exist in the Tieman method.