1. By Thang Ha & Yuji Kim University of Oklahoma, 2016
Seismic Reprocessing: Constrained Conjugate Gradient Least-Squares Migration and Migration-Driven 5D Interpolation: Application to Jeju Basin Marine Data
By Thang Ha & Yuji Kim
University of Oklahoma, 2016

2. Motivation
Nowadays, technology evolution has enabled us to acquire much denser, higher fold, full-azimuth data, thus producing high quality seismic images. Yet, it does come with a catch: our demand on seismic imaging quality keeps increasing. This makes images processed 10 years ago inadequate for modern interpretation.

3. What do we do to get high quality images?
Acquire and process new data
Reprocess old data with new techniques
Expensive

4. With the not-so-promising present…
The first option is very costly and time consuming. Given the not-so-promising present, most of the oil industry would prefer the 2nd way: to reprocess the data.

5. Seismic Reprocessing
Consist of many steps, including velocity refinement, advanced static correction, noise suppression, and migration
The last step, migration, is the actual “engine” to convert the acquired data to seismic images. Some migration algorithm requires regularized input data
Two methods are shown in this project to address migration and regularization issues:
Constrained Conjugate Gradient Least-Squares Migration (LSM) and
Migration-Driven 5D Interpolation

6. Outline
Theory behind Constrained Conjugate Gradient Least-Squares Migration
Theory behind Migration-Driven 5D interpolation
Application to Jeju Basin Data (South Korea)
Conclusions
Acknowledgement

7. Constrained Conjugate Gradient Least-Squares Migration
4 elements:
Migration
Least-Squares
Conjugate Gradient
Constraint

8. Migration Work by “swiping” trace data along ellipsoidal surfaces
“swiped” images constructively interfered at reflection events
Focus diffraction
Move reflectors to their correct location
Shape of ellipsoids depend on velocity model
image from xsgeo.com

9. Least-Squares
Migration can be understood as a filter – an operator – applied on acquired data, to produce images.
Similarly, a reverse filter – an operator to convert seismic reflectivity images to acquired data is commonly known as “demigration” or forward modeling operator L
d=Lm, where
+ d: acquired data
+ L: forward modeling (demigration) operator
+ m: seismic reflectivity images

10. Least-Squares
We want to get seismic reflectivity image m, so we have to calculate the inverse of L: L-1
However, in practice, it’s impossible to invert L
Yet, we can approximate L-1 by LT, the transpose of L, which is basically migration operator
m=LTd

11. Least-Squares
In short, we can never have the exact solution to the equation d=Lm
The next best thing: find m so that the magnitude of the difference (d-Lm), or the squares of the difference, (d-Lm)2, is the least
Thus “Least-Squares”

12. Conjugate Gradient Method
Developed by Hestenes and Stiefel (1952)
Among the first-order iterative methods to solve Least-Squares problem, Conjugate Gradient method is the fastest (i.e. has the highest rate of convergence)
Detail of math-to-geophysics translation of the Conjugate Gradient method is provided in a 10-page single-spaced appendix.

13. Let’s keep things simple, otherwise…

14. Constraint
Beware that the acquired data contains both signal AND noise
If we try to solve for the reflectivity model m too exactly, then we also try to make m represent the noise in our data!
Constraint is used to enhance signal and reduce noise
We use Structure-Oriented Filter (SOF) as the constraint for Least-Squares Migration. SOF works by smoothing data where we have strong coherent reflectors while keeping faults sharp

15. Too complicated to be represented by a flow chart
m0=SOF(m0)=0
Original Data (d0=r0)
Migrated Data
Migrate
SOF
Update residual:
r1=r0-α1*Lh0
α1=<g0.g0>/<Lh0.Lh0>
Lh0
(g0=h0)
Demigrate
Update model:
SOF(m1)=α1*h1
Update directional vector:
v1=SOF(m1)/α1 r1 α1
Update conjugate gradient:
h1=g1+β1v1
β1=<g1.g1>/<g0.g0> g1
Migrate v1 h1

16. Better be represented by a step-by-step workflow
We made it easier for you by creating the least-squares migration workflow GUI. It’s all about keeping track with which step you are at.
The top part of the GUI shows you what step you clicked at which iteration you are in.
Each button will specify the program to be run in LSM workflow, sometimes with a required change of parameter (such as migration with or without antialias).

17. LSM workflow is in AASPI Prestack Utility

18. Outline
Theory behind Constrained Conjugate Gradient Least-Squares Migration
Theory behind Migration-Driven 5D interpolation
Application to Jeju Basin Data (South Korea)
Conclusions
Acknowledgement

19. What are 5 Dimensions and what is interpolation for?
Migration-Driven
Inline, Xline, Offset, Azimuth, Time
Source-X, Source-Y, Rec-X, Rec-Y, Time
Inline, Xline, Offset Tile X, Offset Tile Y, Time
Interpolation helps balance amplitude across seismic survey
Some advanced migration algorithm, such as wave- equation migration, required regularized input, which can only be archived through interpolation
Conventional

20. Conventional 5D Interpolation
Acquisition before interpolation
Acquisition after interpolation
(Trad, 2005)
Demonstration of 5D interpolation with double number of receiver line. Note: this is done on prestack raw gathers, without involving any migration or demigration.

21. Conventional 5D Interpolation: Coherence Map
2 km
Although acquisition footprint is suppressed after 5D interpolation, the result is actually SMEARED. This is because the DIFFRACTIONs coming from the edges of those channels are incorrectly interpolated in the pretack raw gather.
Migrated image without 5D interpolation
High
Low
Coherence
Migrated image with 5D interpolation
(Chopra and Marfurt, 2013)

22. 2D simple fault model Distance (km) 10 Sedimentary rock: v=2500m/s
Distance (km) 10
Sedimentary rock:
v=2500m/s
d=2200kg/m3
Depth
(m)
To demonstrate the smearing of conventional FFT interpolation, I made a simple 2D fault model with one fault in the middle of the survey, and two layers: sedimentary rock and basement rock.
Basement rock:
v=5000m/s
d=2750kg/m3
1000

23. Shot gather before NMO Amplitude Distance (m) 10000 0.5 Time (s) 1.0
Distance (m)
10000
Amplitude
Positive
Negative
0.5
Time (s)
1.0
This is a shot gather close to the middle of the survey. The diffraction can be seen as hyperbolic events emerging from symmetric reflection signal. These hyperbola are much weaker than the reflectors.
1.5

24. Shot gather after NMO Amplitude Distance (m) 10000 0.5 Time (s) 1.0
Distance (m)
10000
Amplitude
Positive
Negative
0.5
Time (s)
1.0
After NMO has been applied. Note how the hyperbolic diffraction is deformed. One thing for sure: it is NOT FLATTEN!!!
1.5

25. Shot gather after NMO, decimated
Distance (m)
10000
Amplitude
Positive
Negative
0.5
Time (s)
1.0
I decide to decimate the data where diffraction occurs.
1.5

26. Shot gather after NMO, decimated, FFT interpolated
Distance (m)
10000
Amplitude
Positive
Negative
0.5
Time (s)
1.0
This is the result of 2D FFT interpolation. Note how bad diffraction was interpolated. FFT interpolate flattened event really good, but when it comes to diffraction, horizontal interpolation generate “kiosk pyramid” artifact, which smear the hyperbola.
1.5

27. Migration-Driven 5D Interpolation
Use Demigration (the reverse of migration, i.e. forward modeling) as the “engine” for interpolation
Defocus diffraction events into hyperboloids
With appropriate parameters, ONE iteration may already be enough

28. Original CDP gathers Amplitude 0.2 0.4 Time (s) 0.6 0.8 1.0 Positive
0.2
Negative
0.4
Time (s)
0.6
0.8
1.0

29. Demigrated CDP gathers
Amplitude
Positive
0.2
Negative
0.4
Time (s)
0.6
Reflectors are enhanced. Noise is reduced.
0.8
1.0

30. Migrated original data
Amplitude
Positive
0.2
Negative
0.4
Time (s)
0.6
0.8
1.0

31. Migrated result of demigrated data
Amplitude
Positive
0.2
Negative
0.4
Time (s)
0.6
See the low frequency in the 1st migration result? It’s reduced thanks to the band-pass filter in demigration.
0.8
1.0

32. Stacked image of migrated original data
0.2
Amplitude
Positive
Negative
0.4
Time (s)
0.6
0.8
1.0

33. Stacked image of migrated result of demigrated data
0.2
Amplitude
Positive
Negative
0.4
Time (s)
0.6
Similarly, low-frequency caused by reverberation is reduced in the final stacked image. The main point is that the migrated result of demigration data CLOSELY RESEMBLE the migrated result of original data. This ensures demigration is working properly and can be used as the “engine” for interpolation.
0.8
1.0

34. The Math Behind The Scene…
Inspired by Projection Onto Convex Sets (POCS)
Abma and Kabir (2006) followed POCS approach for 2D interpolation using Fourier Transform
2D FFT
Threshold remove low amplitude
2D inverse FFT
Reinsert original traces
X1: Original data
C: Desired migrated Result
D: Desired interpolated result
Projection toward C: migration (plus SOF filtering)
Projection toward D: demigration (plus limiting bandpass filter)

35. Projection Onto Convex Sets
Decimated synthetic example
Abma and Kabir (2006)

36. Projection Onto Convex Sets
After 1 iteration
Abma and Kabir (2006)

37. Projection Onto Convex Sets
After 8 iterations
Abma and Kabir (2006)

38. New Migration-Driven 5D Interpolation Workflow
Original Data
Structural Oriented Filtering
Looking good? No
Migrate
Yes
Merge
Demigrate into interpolated locations
5D interpolated migrated result
Looking good?
New method: not involves constrained conjugate gradient least-squares migration.
Demigration: can change band-pass filter at each iteration toward desirable result
Merge: can normalize interpolated data to make it has approximately the same RMS amplitude with original data
Migration: only need to migrate interpolated traces and then merge with the migrated result of the original data by a simple sum. Can have anti-alias turned on or off.
We can also have interpolated result to be used in some advanced migration algorithm that requires the input to be regularized (like wave-equation migration)
5D interpolated result

39. Outline
Theory behind Constrained Conjugate Gradient Least-Squares Migration
Theory behind Migration-Driven 5D interpolation
Application to Jeju Basin Data (South Korea)
Conclusions
Acknowledgement

40. Application to Jeju Basin Data (South Korea)
Introduction
Project
3D Marine seismic processing of KIGAM survey acquired over a fluvial system, Jeju Basin, South Korea
Acquired by
Korean Institute of Geoscience and Mineral Resources (KIGAM)
Location
Jeju Basin , South Korea
Acquisition in three campaigns
1st phase : 2012
2nd phase : 2013
3rd phase : 2014
Data processing
1st phase : Hawkins(2013)
2nd phase : Larry Aboaba (2014)
3rd phase : Yuji Kim (2014 ~)
Data type
SEG-D format
Navigation data in UKOOA p1/90 format
Well log
Dragon-1 well (1993)
New method: not involves constrained conjugate gradient least-squares migration.
Demigration: have different bandpass filters, broaden after each iteration to “carry” more data.
Merge: can normalize interpolated data to make it has approximately the same RMS amplitude with original data
Migration: only need to migrate interpolated traces and then merge with the migrated result of the original data by a simple sum.
We can also have interpolated result to be used in some advanced migration algorithm that requires the input to be regularized (like wave-equation migration)
Regional map of the East China Sea.

41. Application to Jeju Basin Data
Acquisition parmeters
Streamer/Source on figuration
2/2
Streamer length
2.4 km (1st, 3rd phase)
2.1 km (2nd phase)
Streamer depth
7 m
Source depth
5 m
Record length
5 s
Sample rate
2 ms
Group interval
12.5m
No of Groups
192 per streamer
Shot interval
25 m
Bin size
6.25 x 25 m
Sail direction
135 / 315 degree (1st, 2nd phase)
45 /225 degree (3rd phase)
3rd phase
1st, 2nd phase
New method: not involves constrained conjugate gradient least-squares migration.
Demigration: have different bandpass filters, broaden after each iteration to “carry” more data.
Merge: can normalize interpolated data to make it has approximately the same RMS amplitude with original data
Migration: only need to migrate interpolated traces and then merge with the migrated result of the original data by a simple sum.
We can also have interpolated result to be used in some advanced migration algorithm that requires the input to be regularized (like wave-equation migration)
Phase 1-3 seismic survey areas.

42. Application to Jeju Basin Data
Total Energy
Phase 1-2 fold map
High
Low
3rd phase
1st, 2nd phase
5 km
Feathering
Phase 3 fold map
New method: not involves constrained conjugate gradient least-squares migration.
Demigration: have different bandpass filters, broaden after each iteration to “carry” more data.
Merge: can normalize interpolated data to make it has approximately the same RMS amplitude with original data
Migration: only need to migrate interpolated traces and then merge with the migrated result of the original data by a simple sum.
We can also have interpolated result to be used in some advanced migration algorithm that requires the input to be regularized (like wave-equation migration)
Phase 1-3 seismic survey areas.

43. Application to Jeju Basin Data
Total Energy
Feathering, sparse sampling in cross-line direction
High
Amplitude
Total energy
Low
New method: not involves constrained conjugate gradient least-squares migration.
Demigration: have different bandpass filters, broaden after each iteration to “carry” more data.
Merge: can normalize interpolated data to make it has approximately the same RMS amplitude with original data
Migration: only need to migrate interpolated traces and then merge with the migrated result of the original data by a simple sum.
We can also have interpolated result to be used in some advanced migration algorithm that requires the input to be regularized (like wave-equation migration)

44. Application to Jeju Basin Data
Preconditioning workflow
Import
Individual SEG-D
Add Navigation data & Merge SEGD’s
Geometry Applied Data
Resampling & Bandpass filtering
Velocity Analysis
(1km x1km)
Surface Related Multiple Elimination
Are Surface Related Multiple Present?
Brute Stack
Deconvolution
PSTM Migration and Stacking
PSTM Seismic Volume
Least-squares migration
Attribute
Volume
Generate
Attribute Volume
Detailed NO
YES
New method: not involves constrained conjugate gradient least-squares migration.
Demigration: have different bandpass filters, broaden after each iteration to “carry” more data.
Merge: can normalize interpolated data to make it has approximately the same RMS amplitude with original data
Migration: only need to migrate interpolated traces and then merge with the migrated result of the original data by a simple sum.
We can also have interpolated result to be used in some advanced migration algorithm that requires the input to be regularized (like wave-equation migration)

45. Application to Jeju Basin Data (Least-squares migration)
Migration and demigration
New method: not involves constrained conjugate gradient least-squares migration.
Demigration: have different bandpass filters, broaden after each iteration to “carry” more data.
Merge: can normalize interpolated data to make it has approximately the same RMS amplitude with original data
Migration: only need to migrate interpolated traces and then merge with the migrated result of the original data by a simple sum.
We can also have interpolated result to be used in some advanced migration algorithm that requires the input to be regularized (like wave-equation migration)

46. Application to Jeju Basin Data (Least-squares migration)
Migration and demigration
New method: not involves constrained conjugate gradient least-squares migration.
Demigration: have different bandpass filters, broaden after each iteration to “carry” more data.
Merge: can normalize interpolated data to make it has approximately the same RMS amplitude with original data
Migration: only need to migrate interpolated traces and then merge with the migrated result of the original data by a simple sum.
We can also have interpolated result to be used in some advanced migration algorithm that requires the input to be regularized (like wave-equation migration)

47. Application to Jeju Basin Data (Least-squares migration)
LSM workflow
Residuals from each iteration
# iteration
Residual r0
r1 (1st iteration)
r2 (2nd iteration)
r3 (3rd iteration)
Acquisition footprint
3rd iteration
Sobel-filter
similarity
1st iteration
2nd iteration
High
New method: not involves constrained conjugate gradient least-squares migration.
Demigration: have different bandpass filters, broaden after each iteration to “carry” more data.
Merge: can normalize interpolated data to make it has approximately the same RMS amplitude with original data
Migration: only need to migrate interpolated traces and then merge with the migrated result of the original data by a simple sum.
We can also have interpolated result to be used in some advanced migration algorithm that requires the input to be regularized (like wave-equation migration)
Low

48. Application to Jeju Basin Data (Least-squares migration)
Kirchhoff migration
Least-squares migration
Amp
Pos
(a) Amplitude
Neg
New method: not involves constrained conjugate gradient least-squares migration.
Demigration: have different bandpass filters, broaden after each iteration to “carry” more data.
Merge: can normalize interpolated data to make it has approximately the same RMS amplitude with original data
Migration: only need to migrate interpolated traces and then merge with the migrated result of the original data by a simple sum.
We can also have interpolated result to be used in some advanced migration algorithm that requires the input to be regularized (like wave-equation migration)

49. Application to Jeju Basin Data (Least-squares migration)
Kirchhoff migration
Least-squares migration
Sobel-filter
similarity
(b) Coherence
High
Direction of acquisition (45 degree)
Low
New method: not involves constrained conjugate gradient least-squares migration.
Demigration: have different bandpass filters, broaden after each iteration to “carry” more data.
Merge: can normalize interpolated data to make it has approximately the same RMS amplitude with original data
Migration: only need to migrate interpolated traces and then merge with the migrated result of the original data by a simple sum.
We can also have interpolated result to be used in some advanced migration algorithm that requires the input to be regularized (like wave-equation migration)

50. Application to Jeju Basin Data (Least-squares migration)
Conclusion
Least squares migration reduces artifacts resulted from incomplete data (e.g. poor sampling).
Constrain factor reduces the number of iterations to converge.
The LSM on marine data effectively alleviates acquisition footprint, which is shown in slices through coherence and curvature attributes.
New method: not involves constrained conjugate gradient least-squares migration.
Demigration: have different bandpass filters, broaden after each iteration to “carry” more data.
Merge: can normalize interpolated data to make it has approximately the same RMS amplitude with original data
Migration: only need to migrate interpolated traces and then merge with the migrated result of the original data by a simple sum.
We can also have interpolated result to be used in some advanced migration algorithm that requires the input to be regularized (like wave-equation migration)

51. Acknowledgement
We want to thank all of our AASPI sponsors for the generous support
Thank KIGAM for providing access to Jeju basin dataset
Thank CIMAREX for providing access to Panhandle dataset
New method: not involves constrained conjugate gradient least-squares migration.
Demigration: have different bandpass filters, broaden after each iteration to “carry” more data.
Merge: can normalize interpolated data to make it has approximately the same RMS amplitude with original data
Migration: only need to migrate interpolated traces and then merge with the migrated result of the original data by a simple sum.
We can also have interpolated result to be used in some advanced migration algorithm that requires the input to be regularized (like wave-equation migration)

52. Thank you for your participation!