1. Making Marchenko imaging work with field data and the bumpy road to 3D
Alex Jia*, Antoine Guitton, and Roel Snieder
Center for Wave Phenomena, Colorado School of Mines

3. RTM
Marchenko Imaging
pros
whole model
easy implementation
target orientated
remove artifacts by internal multiples
cons
artifacts by internal multiples
require wavelet
learning curve (e.g. acquisition geometry)

4. outline Complications: Marchenko imaging: how and why?
missing near offsets
data calibration
Why is 3D Marchenko necessary and challenging?

5. surface response to virtual source
Marchenko equations
background
velocity model
surface data
surface response to virtual source
(reverse VSP data)
first arrival

6. up-going and down-going Green’s function
Marchenko equations
background
velocity model
surface data
up-going and down-going Green’s function
first arrival

7. up-going and down-going Green’s function
Marchenko equations
background
velocity model
surface data
up-going and down-going Green’s function
Marchenko image
first arrival

8. 1 G+ 2 3

9. a b G-

10. missing near offsets: 7 traces, 214 m

11. retrieved Green’s function
full offset
missing near offsets
difference

12. missing near offset stronger for shallow events and near offset events
maximum missing near offset
D: depth of reflector
T: dominant wave period
assumption: hyperbolic assumption for flat multi-layered earth (details in CWP report)

14. full offset
missing near offsets
RTM

15. data calibration input 1: surface reflection response
input 2 : first arrival
amplitude should match

16. retrieved Green’s function
scale=0.5
scale=1
scale=1.5

18. data calibration
scale=0.5
scale=1
scale=1.5

19. * synthetic first arrival field 0.001 0.001
The question you may ask is how we calibrate the field data? Because we have a background velocity model and we use this model to construct our first arrival. We can also use this model to simulate surface data with amplitudes that can match the first arrival. Thus, we now have the simulated surface data that has the required amplitude, and we have the field data we need to calibrated. Hence, we can obtain a scaling factor by comparing the amplitude the field data and modelled data, and use this scaling factor to calibrate the field data.

20. 0.001
synthetic
first arrival
0.001 *
field (scaled)

21. 2D can be deceptive

22. Green’s function in 3D structure
x=0.5, y=1, z=0.5
x=0.5, y=1, z=0
Goal: retrieve the Green’s function from a VS at (x=0.5, y=1, z=0.5) to a surface receiver at (x=0.5, y=1,z=0)

23. retrieved
x=0.5, y=1, z=0.5
x=0.5, y=1, z=0

24. retrieved
x=0.5, y=1, z=0.5
x=0.5, y=1, z=0

25. retrieved
modelled
x=0.5, y=1, z=0.5
x=0.5, y=1, z=0

26. (dense in-line, sparse x-line)
3D Marchenko
ocean bottom data
streamer data
(dense in-line, sparse x-line) (
(Wang et al. 2009)