Synthetic example

At this early stage we decided to show how the method works on a simple synthetic. Figure 1 shows a sea floor with a series of water-bottom multiples. The amplitude of the reflector increases as a function of angle, something that frequency methods have had difficult time handling. The multiple model was constructed by downward continuing Bevc (1995) the sea floor reflection, Figure 2. As a result the amplitude information is incorrect, but the kinematics is correct.

 

bee-cmp Figure 1 A simple CMP gather with multiples.

 

bee-mult Figure 2 CMP gather in Figure 1 datumed to the surface and back to the seafloor. Note how the amplitude information is wrong but the general kinematics is correct.

Once we have our data and noise model we estimated a space varying filter for each by applying fitting goal (4). To conserve memory we put a new filter every 15th point in time and third point in offset (Figure 4). These two filters were then used, and fitting goal (3) were applied. Figure 3 shows the result of the separation. We can see some residuals of the filter patches but generally we have done a good job in removing the multiple while preserving the signal.

 

signoi
Figure 3 The estimated primaries and mulitpes from Figure 1.

 

pef
Figure 4 Space varying filter composition. A different filter is placed inside each patch. The filter estimation problem is done globally, with the filter coefficient smoothed in a radial direction.