Hask Data Set

 

hdata
Figure 7 Hask Data Set

The "Hask" data set refers to Haskell-Thompson synthetic modeling. The dataset was modeled to resemble a North Sea data set donated by Mobil. We successfully apply LSJIMP to the Hask data set given in Figure for imaging and suppressing the multiple energy. In Figure , we compare the raw data to the data generated by applying a forward modeling operator to our image, notice that much of the multiple energy is removed. Next, we compare our present result with results presented by Brown (2002) in Figure . It can be observed that now we are doing a better job of multiple suppression in shallow parts. The primary reason being inclusion of crosstalk modeling operator in LSJIMP. The method used by Brown (2002) is equivalent to current method , with $\bold \epsilon$ for crosstalk in equation (8) set equal to zero. To improve our performance on the Hask data set, we then took advantage of the fact that hask is also a shallow water-bottom data set and used the improved crosstalk-modeling strategy discussed in the previous section. Unfortunately, the results as given in Figure do not seem to improve a lot.

We also tried a non-linear scheme Brown (2004) for updating reflection coefficients between two runs of LSJIMP. The presence of correlated events in the data residual ($\bold r_d$) hints at the likelihood for further improvements in estimates of the reflection coefficients. The main idea of the updating scheme is to compute a scalar update to the reflection coefficient of the $m^{\rm th}$ multiple generator, $\Delta \alpha_m$, such that  

$$\Vert \bold r_d - \Delta \alpha_m \; \bold d_{i,k,m} \Vert^2$$ (14)

is minimized. We could not see any noticable difference with non-linear updates, as demonstrated in Figure .

 

hask1
Figure 8 Comparison of (a) raw data and (b) results from first run of LSJIMP.

 

hask-comp
Figure 9 Comparison of (a) raw data, (b) results presented in SEP-111 and (c) present results. Notice that a lot of multiple energy in the shallow parts is eliminated in our present results.

 

hask2
Figure 10 Comparison of results from (a) LSJIMP, (b) LSJIMP(modified) and (c) LSJIMP after non-linear update.