Previous: The optimization problem
Up: Multi-component Source Equalization
Next: CONCLUSION
Previous Page: The optimization problem
Next Page: CONCLUSION

Results

The optimization problems described by and are solved using a conjugate-gradient method. I chose to constrain the first filter in each of the series of filters to unity. Thus the first shot gather was my reference gather. I applied the equalization process using about 50 shot gathers in a two second time window, knowing that this time window averages over a fair amount of energy that is radiated from the source with different emergence angles. I chose to use a medium length filter of about 40 points (160 msec). Results of those equalizations are shown in two groups. First a minimization described by for the components , and (capital letters denote source components, lower-case letters denote receiver components). I am only showing one component of the 9c dataset due to space limitations in this abstract. The prediction error filters obtained are shown in Figures . The filter obtained after about 40 iterations is minimum phase.

There seem to be hardly any time shifts between different source points. The amplitude in the main peak and lower energy wavelet characterize all the filters consistently. Figure shows a comparison between the raw prestack time slice and the filtered version. The differences in that time slice are small but noticeable. The continuity in character of the time slice is increased. Figure is obtained from maximizing symmetry in the prestack data using the objective function , where all components are equalized simultaneously. The offdiagonal elements in the three-by-three filter set show identical behavior. Again the filters are consistent along the line and exhibit the similar properties as the filters in Figures . The short 1-D filters equalize by averaging over an angular distribution of radiation pattern. The amount of averaging is determined by the time window and number of different arrivals within the time window.