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

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

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

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

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

2. Downward continuation with joint NMO analysis 1 Reflector A 2 Reflector B

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

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

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

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

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

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.

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

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

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

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

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！