1. Yue Du Mark Willis, Robert Stewart AGL Research Day
Three VSP Algorithms: Surface Seismic Transform, NMO and Migration Velocity Analyses
Yue Du
Mark Willis, Robert Stewart
AGL Research Day
April 2nd, 2014
Houston, TX

2. Talk outline Motivation & introduction
VSP has higher resolution, target oriented, small data volume
Three algorithms
1. Transforming VSP to surface seismic data;
2. Downward continuation of surface shots with joint NMO velocity analysis;
3. Residual moveout migration velocity analysis
Future work
-Hess VSP survey

3. 1. Transforming VSP to surface seismic records
(Schuster , 2009)
Convolving the left and middle VSP traces produces the right-side trace
characterized by a SSP event with a longer traveltime and raypath. The virtual
receiver for the SSP reflection is at the location B and the star symbol ∗ denotes
convolution.
Part 1
Part 2

4. Two-layer model simulation results
Surface seismic shots
Simulating shot from VSP
1.2D acoustic finite difference modeling
2.Seprate waveform convolution— without first arrivals
3.Artifacts—taper
4.Borehole receiver coverage
Simulating shot from VSP with taper
Reduced receiver coverage

5. 2D & 3D simulation results
Left – Actual surface shot
Middle – simulated surface shot from the Part 1
Right – simulated shot from Part 2

6. 2. Downward continuation with joint NMO analysis1
Reflector A 2
Reflector B

7. Downward continuation
Raw data
Downward continued data
Reflection A
Reflection A
Reflection B
Reflection B
Reflection B
Reflection B 7

8. NMO correction and semblance spectra analysis
Before NMO correction
After NMO correction
Reflection A
Reflection A
Reflection B
Reflection B
Reflection B
Reflection B
Receiver 2
Receiver 1
Receiver 2
Receiver 1 8

9. 3. Migration velocity analysis
migration depth, m V
XOZ coordinates
source s X O δ g O’
receiver
Tilted ellipse coordinates UO’V’ U
Reflector
To investigate the residual moveout curvature, we analytically simulate the Kirchhoff migration algorithm in a single CIG.
This figure shows the Kirchhoff ellipse with foci which are located at the example source and receiver pair (shot offset, s, is -3550m, and the receiver depth, g, is 1000m). The intersection (red star) of the tilted ellipse and CIG position shows the depth that this trace will be migrated into the CIG.
We solve for the migration intersection(MI) of a CIG and a single migration ellipse, with changing the coordinate system from X (horizontal) and Z (depth), to one that follows the tilt of the ellipse.
CIP Z
XOZ coordinates x
X, m

10. The intersections of tilted migration ellipses
Correct velocity
depth, m
source1
source2
source3
migration depth, m
Receiver
Slow velocity
X, m
Slow velocity
source1
source2
source3
Each ellipse cuts the CIG at a different depth (z1, z2, z3), and that only Shot 2 (red curve) has its contribution at the actual reflector depth. If, however, we use a migration velocity which is too slow, Figure 2b shows that the ellipses will become smaller and the intersections will be shallower at depths ( , , ).
Correct velocity
depth, m
Receiver
Source X, m
X, m

11. Residual moveout after migration
Unstacked CIG
RMO for a CIG
Slow velocity
depth, m
Depth, m
Correct velocity
After we collect the extreme point depth for each receiver, we can put them together to get the residual moveout curve. Figure 4 uses a 21 receiver array covering depths from 1000 to 2000m. Figure 4a shows the residual moveout alignments in the source offset domain M(s,z). The groups of red lines show the unstacked, migrated depths with different migration velocities (A-slow, B-correct and C-fast). The black points on the red lines are the extreme points for each receiver. Figure 4b displays the extreme points in the receiver offset domain M(g,z), revealing clear trends of the residual moveout curvature. The B curve is flat when the migration velocity is equal to the true velocity, and the depth falls onto the true reflector depth.
Fast velocity
source x
receiver depth, m
Source X, m

12. Shot gather for source x=0
VSP multi-layer model
Modeling data with reflection events only
time, ms
Receiver gather R1
Source offset
1000
2000
3000
4000
Shot gather for source x=0
Receiver depth
time, ms
1000
2000
3000
Then we extend this concept to more complex models using an iterative RMS velocity scheme. This figure shows the example layered model. We did synthetic modeling with reflection events only. This figure shows the first receiver gather. And this one shows the shot gather for source x=0.

13. Downward continuation with joint NMO analysis
Pick RMS velocity
Interval velocity model
True velocity model
Estimated velocity model 13

14. Migration velocity analysis
RMO After Migration
Vmig = 0.9 Vtrue
Velocity Model
Tilted Ellipse RMOs
A (Vlayer4=0.9Vtrue)
A’ (Vlayer4=0.95Vtrue)
B (Vlayer4=Vtrue)
C (Vlayer4=1.05Vtrue)
C’ (Vlayer4=1.1Vtrue)
2600
Depth, m
Depth, m
2700
If the velocities were known for all layers, using Equation 11 we could create a Vrms for each layer and receiver pair. If we were to use the corresponding Vrms to migrate each event separately, they each would be very close to being flat and aligned. So we next devise a layer stripping strategy to iteratively derive the velocity for each layer. . Using the true velocity produces a nearly flat event (Figure 9a(B)), which is at a slightly deeper depth than the actual reflector. This is due to the Vrms approximation, which is only for zero offset. The exact shapes of the residual moveout differ between Figures 4b and 9a due to the use of different Vrms values for each receiver in the layered case.
2800
Receiver Depth, m
Receiver Depth
Velocity, m/s

15. Migration velocity analysis
RMO After Migration
Vmig = Vtrue
Velocity Model
Tilted Ellipse RMOs
A (Vlayer4=0.9Vtrue)
A’ (Vlayer4=0.95Vtrue)
B (Vlayer4=Vtrue)
C (Vlayer4=1.05Vtrue)
C’ (Vlayer4=1.1Vtrue)
2600
Depth, m
Depth, m
2700
If the velocities were known for all layers, using Equation 11 we could create a Vrms for each layer and receiver pair. If we were to use the corresponding Vrms to migrate each event separately, they each would be very close to being flat and aligned. So we next devise a layer stripping strategy to iteratively derive the velocity for each layer. . Using the true velocity produces a nearly flat event (Figure 9a(B)), which is at a slightly deeper depth than the actual reflector. This is due to the Vrms approximation, which is only for zero offset. The exact shapes of the residual moveout differ between Figures 4b and 9a due to the use of different Vrms values for each receiver in the layered case.
2800
Receiver Depth, m
Receiver Depth
Velocity, m/s

16. Summary
VSP geometry is asymmetric, thus it is hard to apply velocity analysis tools from surface seismic
The three algorithms can be used separately or together to help VSP analyses
Transforming to surface seismic records from VSP data has limitations

17. Thank you！ Acknowledgements Allied Geophysical Lab and its supporters
Halliburton
Thank you kindly Michele Simon and colleagues at Hess for contributing the 3D time-lapse Bakken data for our future research. We also express our appreciation to Richard Van Dok at Sigma3 for data preparation.
Thank you！