Real data example

I tested the methodology on a real 3-D marine dataset from the North Sea. Previous uses of AMO and common azimuth migration have resulted in noticeable acquisition footprint in the first 1300 meters Biondi (1999); Vaillant and Sava (1999). I regularized, and then migrated, the volume using three different approaches. In the first approach I ignored the azimuth information to form my 4-D volume, I will refer to this methodology as the `stack' approach. In the second approach I approximated the Hessian matrix by a diagonal based on a reference model, the `reference' approach. And finally applied up to 120 conjugate iterations, `inverse' approach. Figure  shows all three result. The top panel is the `stack' approach, the center is the `reference' approach, and the bottom panel is the `inverse' approach. All the remaining figures will be of the same form.

 

cube Figure 1 The top panel is the `stack' approach, the center is the `reference' approach, and the bottom panel is the `inverse' approach.

Figure   compares a depth slice at 900 m. Note at `A' what looks like noise on the `stack' and `reference' result, turns into a fault on the `inverse' result At `B' we see a steeply dipping reflector come into focus when we apply the `reference' approach. The acquisition footprint visible at `C' diminishes with the `reference' approach, and is almost completely absent in the `inverse' result. At a depth of 1360 m (Figure ) we can see similar improvements. At `A' we see fault reflection that is not visible on the `stack' result, barely visible on the 'reference' result become very evident on the `inverse' result. At `B' we see significant acquisition footprint in the `stack' result, it is reduced significant in the `reference' result, and in the `inverse' result we begin to see additional fine featured geology appear. At `C' we a portion of fault in the `stack' result, continuous segment in the `reference' result, and the entire fault reflection in the `inverse' result.

 

depth1 Figure 2 The top panel is the `stack' approach, the center is the `reference' approach, and the bottom panel is the `inverse' approach. Note at `A' what looks like noise on the `stack' and `reference' result, turns into a fault on the `inverse' result At `B' we see a steeply dipping reflector come into focus when we apply the `reference' approach. The acquisition footprint visible at `C' diminishes with the `reference' approach, and is almost completely absent in the `inverse' result.

 

depth2 Figure 3 The top panel is the `stack' approach, the center is the `reference' approach, and the bottom panel is the `inverse' approach. At `A' we see fault reflection that is not visible on the `stack' result, barely visible on the 'reference' result become very evident on the `inverse' result. At `B' we see significant acquisition footprint in the `stack' result, it is reduced significant in the `reference' result, and in the `inverse' result we begin to see additional fine featured geology appear. At `C' we a portion of fault in the `stack' result, continuous segment in the `reference' result, and the entire fault reflection in the `inverse' result.

Figure  shows a cross-line located at 7200m. Note the fault reflection at `A' that is barely visible in the `stack' result appear in the 'reference' result, and become coherent in the `inverse' result. Note the small faults at `B' that are not visible in the `stack' or `reference' result become evident in the `inverse' result. Figure  shows a cross-line at 8200m. Note the small faults become much more evident as we progress from the `stack' to the `inverse' result. At `B' we see the migration artifacts dramatically decrease as we move from the `reference' to the `inverse' result.

 

xline1 Figure 4 The top panel is the `stack' approach, the center is the `reference' approach, and the bottom panel is the `inverse' approach. All three figures show a cross-line located at 7200m. Note the fault reflection at `A' that is barely visible in the `stack' result appear in the 'reference' result, and become coherent in the `inverse' result. Note the small faults at `B' that are not visible in the `stack' or `reference' result become evident in the `inverse' result.

 

xline2 Figure 5 The top panel is the `stack' approach, the center is the `reference' approach, and the bottom panel is the `inverse' approach. All three figures show a cross-line located at 7200m. Note the small faults become much more evident as we progress from the `stack' to the `inverse' result. At `B' we see the migration artifacts dramatically decrease as we move from the `reference' to the `inverse' result.

Figure  shows an inline section at 3100m. Note the steeply dipping reflectors that are not visible at `A' in the `stack' result come into focus in the inverse result. At `B' we see a peak that isn't visible in either the `stack' or `reference' result appear in the inverse result. At `C' we see a package of reflectors that are incoherent in the `stack' result become clearer as we move to the `reference' and `inverse' result. Figure  shows an inline section location at 3960m. At `A' the complex folding above the salt intrusion come into focus in the `inversion' result. The set of reflectors above the salt come into focus as we advance to more sophisticated techniques at `B'. At `C' we see the salt reflection come into focus as we move to the `reference' and `inverse' approach.

 

iline1 Figure 6 The top panel is the `stack' approach, the center is the `reference' approach, and the bottom panel is the `inverse' approach. All three figures show a in-line located at 3100m. Note the steeply dipping reflectors that aren't visible at `A' in the `stack' result come into focus in the inverse result. At `B' we see a peak that isn't visible in either the `stack' or `reference' result appear in the inverse result. At `C' we see a package of reflectors that are incoherent in the `stack' result become clearer as we move to the `reference' and `inverse' result.

 

iline2 Figure 7 The top panel is the `stack' approach, the center is the `reference' approach, and the bottom panel is the `inverse' approach. All three figures show a in-line located at 3960. . At `A' the complex folding above the salt intrusion come into focus in the `inversion' result. The set of reflectors above the salt come into focus as we advance to more sophisticated techniques at `B'. At `C' we see the salt reflection come into focus as we move to the `reference' and `inverse' approach.