1. Mapping 2D multiples to image space
Gabriel Alvarez
Mapping 2D multiples to image space
Good evening:
My name is Gabriel Alvarez. My main research interest is the attenuation of multiples in the image space. This summer I was working on understanding the mapping of 2D specularly-reflected and diffracted multiples. I gave a presentation about that yesterday afternoon.

2. Specularly-reflected multiple
Half-subsurface offset (m)
-200
-400
400
200
1000
1200
1400
Depth (m)
Half-aperture angle (degrees) 20 10 40 30
Depth (m)
1200
1400
1600
SODCIG
Let me show you here a subsurface-offset-domain common image gather and the corresponding angle domain common image gather for a specularly-reflected multiple from a flat water-bottom. The red lines represent the analytical solutions that I computed and that you read on my paper in the current report.
Two things to take away from these figure are that the specularly-reflected multiples migrate as primaries and that, when migrated with velocity faster than water velocity they map to the negative subsurface offsets.
ADCIG
Flat water-bottom

3. Diffracted Multiple RaypathhD mD hD V1
Zdiff V2
Xdiff
Finally, here is the case of the diffractor sitting on top of the dipping reflector. Again, the image space coordinates can be computed from the data space coordinates and the position of the diffractor. φ

4. SODCIGs Diffracted multiple. Dipping water-bottom
Half-subsurface offset (m)
-800
800
Depth (m)
1000
1600
1400
1200
1800
Half-subsurface offset (m)
-800
800
Depth (m)
1000
1600
1400
1200
1800
Half-subsurface offset (m)
-800
800
Depth (m)
1000
1800
1400
1200
1600
Here again are three common image gathers again showing that the diffracted multiple can map to positive or negative subsurface offsets depending on the relative position of the gather location with respect to the diffractor.
Diffracted multiple. Dipping water-bottom

5. ADCIGs Diffracted multiple. Dipping water-bottom
Half-aperture angle (degrees)
-40 40
Depth (m)
1400
2000
1600
Half-aperture angle (degrees)
-40 40
Depth (m)
1400
2000
1600
-40 40
Depth (m)
1400
2000
1600
Half-aperture angle (degrees)
Finally, here are three angle gathers at different locations with respect to the diffractor.
Diffracted multiple. Dipping water-bottom