1. Paul Sava: WE seismic imaging
Velocity
Sava & Biondi
Wave-equation MVA by inversion of differential image perturbations
Wave-equation MVA: Born, Rytov and beyond
SEP 113
SEG 2003
EAGE2003
SEP114
Multiples
Sava & Guitton
Multiple attenuation in the image space
Migration
Sava & Fomel
Seismic imaging using Riemannian wavefield extrapolation
SEP 114
I am Paul Sava and I am interested in seismic imaging using wavefield extrapolation techniques. This table summarizes the topics I worked on over the last year, and includes the various co-authors on each subject.
My main research topic is velocity estimation using WE techniques. This is also the subject of my PhD thesis. In the last two reports, we have addressed the limitations of WEMVA related to the Born approximation by using what we call ‘differential image perturbations’. We have also shown how our technique can be employed for Rytov WEMVA, and we have explored the relationships between the different flavors of WEMVA. This year I had two presentations on this subject, one at this SEG meeting and another at the EAGE convention in summer.
Another topic I worked on is multiple attenuation in the image space. We used the best tools at our disposal, including WE migration, angle-domain CIGs and hi-resolution Radon transforms, and we obtained very encouraging results. This topic was part of the previous report and also the subject of an SEG presentation this morning.
Finally, an interesting topic I worked on recently is wavefield extrapolation in Riemannian coordinates. This is joint work with my former colleague Sergey Fomel who is currently with the BEG at UT Austin.

2. Sava & Fomel: Riemannian wavefield extrapolation
Cartesian coordinates
Riemannian coordinates
Here is an illustration of this idea using the Marmousi model. On your left, you can see the velocity model in Cartesian coordinates; on your right, you can see the same velocity model in RC defined for a particular location on the surface. In both panels, red lines identify rays and blue lines identify wavefronts.
We can extrapolate downward in depth in Cartesian coordinates, or we can extrapolate forward in time in Riemannian coordinates. Here is an example where we used a 15 deg extrapolation kernel in both spaces. The data is represented by equally spaced impulses. Extrapolation in CC is only accurate up to 15 deg from the extrapolation direction, which is down in depth. Likewise, extrapolation in RC is only accurate in the vicinity of the extrapolation direction which is changing in space according to the velocity model.
Extrapolate
Extrapolate
Cartesian coordinates
Riemannian coordinates

3. Sava & Fomel: Riemannian wavefield extrapolation
Extrapolate
Interpolate
Cartesian coordinates
Riemannian coordinates
Here are, for comparison, the results of extrapolation in CC and RC.
At the top, we have the results of extrapolation in CC, followed by interpolation in RC.
At the bottom, we have the results of extrapolation in RC, followed by interpolation in CC.
The left and right panels are comparable one-to-one.
A direct comparison shows, as expected, that downward continuation is only accurate up to 15 deg. This is visible in both CC and RC. In contrast, Riemannan extrapolation is much more accurate at large angles, which can in principle be overturning.
The applications of our technique include imaging of steeply dipping or overturning reflections.
There are plenty of other examples in the report and I would be glad to hear your comments or suggestions on this or the other two subjects.
Thank you.
Extrapolate
Interpolate
Cartesian coordinates
Riemannian coordinates