Local Migration with Extrapolated VSP Green’s Functions Xiang Xiao and Gerard Schuster Univ. of Utah

Outline Motivation

Outline Motivation Local VSP Migration Theory

Outline Motivation Numerical Tests Sigsbee VSP Data Set GOM VSP Data Set

Outline Motivation Local VSP Migration Theory Numerical Tests Sigsbee VSP Data Set GOM VSP Data Set Conclusions

Motivation Problem: VSP Migration image distorted by overburden+statics Solution: Local VSP Migration

Outline Motivation Local VSP Migration Theory Numerical Tests Sigsbee VSP Data Set GOM VSP Data Set Conclusions

Theory: Standard VSP Migration direct reflection Reflections: R(g) reflection g G(x|g)*R(g)  g x G(x|s)W(  ) x Backproject Forwardproject Standard VSP migration image: m(x) = G(x|g)*R(g)  g /G(x|s)W(  ) Backprojected refl.Forwardproject. direct Src. Wavelet: W(  ) s ~ ~ G(x|g)*R(g)  g G(x|s)*W(  )*

Theory: Local VSP Migration direct reflection Reflections: R(g) reflection g G(x|g)*R(g)  g x Backproject direct

Theory: Local VSP Migration direct reflection Backproject Direct waves: D(g) Reflections: R(g) reflection g G(x|g)*R(g)  g x Backproject direct D(g) G(x|g)*D(g)  g Backprojected refl.Backproject. direct Local VSP migration image: m(x) = G(x|g)*D(g)  g G(x|g)*R(g)  g ~ ~  g G(x|g)D(g)*  g Static killer FAST 3D RTM

Local vs Standard VSP Migration Reflection Illumination Zones ~ ~ Local VSP migration image: m(x) G(x|g)*R(g)[  g G(x|g)*D(g)]*  g Standard VSP migration image: m(x) ~ ~ G(x|g)*R(g)  g [G(x|s)W(  Backprojected refl. Forwardprojected direct. Backproject. direct Standard VSP Reflection Illum. Zone Local VSP Reflection Illum. Zone

Benefits of Local VSP Migration Target oriented!Target oriented! –Only a local velocity model near the well is needed. –Salt and overburden are avoided. –Fast 3D RTM Source statics are automatically accounted for.Source statics are automatically accounted for. Liabilities of Local VSP Migration Limited illumination ZoneLimited illumination Zone Standard VSP Reflection Illum. Zone Local VSP Reflection Illum. Zone

Outline Motivation Local VSP Migration Theory Numerical Tests Sigsbee & Schlumberger VSP Data GOM VSP Data Set Conclusions

Sigsbee P-wave Velocity Model 0 Depth (km) m/s Offset (km) 279 shots 150 receivers

15 Local Reverse Time Migration Results Depth (km) -33Offset (km) True modelMigration image f = fault f d d (1) (2) (3) d = diffractor Virtual well

Outline Motivation Local VSP Migration Theory Numerical Tests Sigsbee & Schlumberger VSP Data GOM VSP Data Set Conclusions

17 Depth (km) Offset (km) Schlumberger 2D Isotropic Elastic Model shots 287 receivers

Direct P PPS PSS Depth (km) Time (s) VSP CSG X-component VSP CSG Z-component 4 Depth (km) 8 4 Two-component VSP Synthetic Data Set (Acknowledge VSFusion)

km/s (a) P-wave submodel Depth (km) Depth (km) Offset (km) (b) P-wave background 1D model km/s Offset (km) 0 1.8

Depth (km) Offset (km) Local RTM Image

Outline Motivation Local VSP Migration Theory Numerical Tests Sigsbee & Schlumberger VSP Data GOM VSP Data Set Conclusions

Depth (m) Offset (m) GOM VSP Well and Source Location m offset 2800 m 3200 m Salt 82 m m offset

Z-Component VSP Data Depth (m) Traveltime (s) Salt Salt Direct P Reflected P Reverberations

m offset (1) (2) (3) (1) specular zone, (2) diffraction zone, (3) unreliable zone 3.3 Depth (km) Offset (m) 39 receivers reflectivity

Local VSP Migration Images 600m and 1500 m offsets Depth (km) Offset (m) m Image 1500 m Image

Conclusions Synthetic tests show accurate imaging around well by Local VSP. Field data results?Synthetic tests show accurate imaging around well by Local VSP. Field data results? Advantages:Advantages: Only local velocity model needed Only local velocity model needed Inexpensive target oriented RTM Inexpensive target oriented RTM Statics removed Statics removed Disadvantages:Disadvantages: Smaller illumination zone: Smaller illumination zone: Less resolution Less resolution vs G(g|x)*G(x|s)* vs G(g|x)*G(x|s)

Acknowledgment We thank the sponsors of the 2007 UTAM consortium for their support.We thank the sponsors of the 2007 UTAM consortium for their support. We thank VSFusion for Schlumberger modelWe thank VSFusion for Schlumberger model We thank BP for VSP DataWe thank BP for VSP Data Prev. WorkPrev. Work Yonghe Sun (UTAM report 2004) Yonghe Sun (UTAM report 2004) Jianhua Yu (UTAM report 2005) Xiao Xiang (Geophysics 2006)

28 Subsalt Imaging s x G(x|g) g G(x|s) m(x) ~ ~ G(x|s) Forward direct s ds * D(g|s) G(x|g)* Backward reflection g D(g|s)dg Errors in the overburden and salt body velocity model Defocusing Overview SSP  VSP Local RTMLocal RTM PSSummary

29 Local Reverse Time Migration s x G(x|g) g G(x|s) g’ G(x|s)= G(x|g’)* D(g’|s)dg’ Backward Direct wave g’ Local VSP Green’s function Overview SSP  VSP Local RTMLocal RTM PSSummary

30 m(x) ~ s ~ ds g’ G(x|g’)* D(g’|s) dg’ Backward D(g’|s) G(x|g)* D(g|s)dg Backward D(g|s) g * x1x1 (1) (2) x2x2 x3x3 (3) s g g’ Illumination Zones (1) specular zone, (2)diffraction zone, (3) unreliable zone, Theory Motivation Numerical Tests Conclusions

31 Depth (km) 10 0 Offset (km) (a) Ray tracing direct P (c) PPS events (d) Pp events (b) PSS events Depth (km) 10 0 Offset (km) Aperture by Ray Tracing Introduction Numerical Tests Conclusions Theory

Theory: Local VSP Migration direct reflection Direct waves: D(g) Reflections: R(g) reflection g G(x|g)*R(g)  g x Backproject Backproject Migration image: m(x) = G(x|g)*R(g)  g G(x|g)W(  ) Backprojected refl.Forwardproject. direct G(x|g)W(  ) direct D(g)

Sigsbee P-wave Velocity Model 0 Depth (km) m/s 12.5 Offset (km) 279 shots 150 receivers287 recs 291 recs

34 P-to-S ratio = 2.7 Velocity Profile S Wave P Wave Depth (m) m 3200 m Salt Incorrect velocity model P-to-S ratio = 1.6 Introduction Numerical Tests Conclusions Velocity (m/s) Theory

35 X-Component VSP Data Depth (m) Traveltime (s) Salt Direct P Reflected P ReverberationsDirect S Introduction Numerical Tests Conclusions Theory

m offset Depth (km) Offset (m) 0100 Offset (m) Without deconvolution With deconvolution Introduction Numerical Tests Conclusions Theory

Depth (km) 13 0 VSP CSG VSP CSG 013 Time (s)