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PhD Defense Local Reverse Time Migration with VSP Green’s Functions Xiang Xiao UTAM, Univ. of Utah May 1, 2008 99 pages Outline • • • • • Introduction and overview SSP VSP SWP interferometric transform Local reverse time migration: horizontal reflector imaging Local reverse time migration: salt flank imaging with transmitted P-to-S waves Summary 2 Overview SSPVSP Local RTM Local RTM PS Summary Outline • • • • • Introduction and overview SSP VSP SWP interferometric transform Local reverse time migration: horizontal reflector imaging Local reverse time migration: salt flank imaging with transmitted P-to-S waves Summary 3 Overview SSPVSP Local RTM Local RTM PS Summary Data Time Depth Model Offset r(x) Offset Forward modelling D(g|s) Migration Image Inverse Migration m(x) Low subsalt resolution, Defocusing! Overview SSPVSP Local RTM Local RTM PS 4 Summary Subsalt Imaging Modelbased m(x) ~ ~ Modelbased G(x|s) s * G(x|g)* D(g|s)dg g ds s D(g|s) g G(x|s) G(x|g) x 5 Overview SSPVSP Local RTM Local RTM PS Summary Subsalt Imaging Forward direct m(x) ~ ~ G(x|s) s Backward reflection * G(x|g)* D(g|s)dg g s Errors in the overburden and salt body velocity model D(g|s) g G(x|s) G(x|g) ds x Defocusing 6 Overview SSPVSP Local RTM Local RTM PS Summary Interferometric Imaging Databased m(x) ~ ~ Modelbased G(x|s) s * G(x|g)* D(g|s)dg g g ds s G(x|s) G(x|g) x 7 Overview SSPVSP Local RTM Local RTM PS Summary Local Reverse Time Migration Backward Direct wave G(x|s)= G(x|g’)* D(g’|s)dg’ g’ Local VSP Green’s function g s G(x|s) G(x|g) x g’ 8 Overview SSPVSP Local RTM Local RTM PS Summary Local Reverse Time Migration Backward approx m(x) ~ ~ G(x|s) s Backward reflection * G(x|g)* D(g|s)dg g g ds s G(x|s) G(x|g) x g’ 9 Overview SSPVSP Local RTM Local RTM PS Summary Outline • • • • • Introduction and overview SSP VSP SWP interferometric transform Local reverse time migration: horizontal reflector imaging Local reverse time migration: salt flank imaging by transmitted P-to-S waves Summary 10 Overview SSPVSP Local RTM Local RTM PS Summary Outline • SSP VSP SWP interferometric transform – – – Motivation Theory Numerical Tests • • – SEG/EAGE salt model Double datuming Conclusions 11 Overview SSPVSP Local RTM Local RTM PS Summary I. Why we need more VSP? SSP Seabed Salt Target VSP Surface related statics •Twice Once Overburden velocity error •Twice Raypath Once •Longer Attenuation •More Frequency Shorter •Lower Less Higher Resolution •Lower Higher 12 SSPVSP Motivation Theory Numerical Tests Conclusions How to get more VSP? SSP VSP x B RVSP x B S2 x B S2 A S2 A S1 A S1 RVSP S1 VSP G(B|A) ~~ SSP G(A|x)* G(B|x) dx S2 13 SSPVSP Motivation Theory Numerical Tests Conclusions 3D Application 3D SSP 3D VSP Low fold Naturally datuming ! High fold ! SSP + VSP RVSP ! 3D RVSP SSPVSP Motivation Theory 14 Numerical Tests Conclusions Receiver coverage Shot coverage S Seabed Salt SSP/RVSP aperture Target VSP aperture X g 15 SSPVSP Motivation Theory Numerical Tests Conclusions Use it, or lost it… High folds ! SSP + VSP RVSP ! 3D RVSP Well log SSP, VSP Better Geologic interpretation ! Salt Better image under the salt ! 16 SSPVSP Motivation Theory Numerical Tests Conclusions What is the benefit ? SSP + VSP RVSP – Sources are closer to the target; – Higher fold virtual RVSP data are obtained; – No velocity model is needed; – Multi-arrival are considered; Salt 17 SSPVSP Motivation Theory Numerical Tests Conclusions How to skip overburden? VSP VSP s Virtual Source Gather s g’ s g’ g g’ g g No velocity model is needed ! SWP VSP G(g|g’) ~~ VSP G(g’|s)* G(g|s) dx S 18 SSPVSP Motivation Theory Numerical Tests Conclusions Application Application of VSPSWP transform: Virtual Source Gather Salt flank imaging s P and S wave checkshot Sediment imaging g’ Multiple/teleseismic imaging g 4D Reservoir monitoring Shear wave splitting and crack orientation Seismic while drilling …… 19 SSPVSP Motivation Theory Numerical Tests Conclusions Outline • SSP VSP SWP interferometric transform – – – Motivation Theory Numerical Tests • • – SEG/EAGE model Double datuming Conclusions 20 Overview SSPVSP Local RTM Local RTM PS Summary SEG/EAGE Salt Model P-wave velocity model Depth (m) 0 Velocity (m/s) 4500 3600 1500 -7850 SSPVSP Offset (m) Motivation Theory Numerical Tests 7850 Conclusions 21 SSP Data Geometry… SSP P-wave velocity model Depth (m) 0 Velocity (m/s) 4500 3600 1500 -7850 SSPVSP Offset (m) Motivation Theory Numerical Tests 7850 Conclusions 22 Data Synthetic SSP CSG Time (s) 0 6 -2000 Offset (m) 2000 23 SSPVSP Motivation Theory Numerical Tests Conclusions VSP Geometry… P-wave velocity model Depth (m) 0 Velocity (m/s) 4500 3600 1500 -7850 Offset (m) 7850 24 SSPVSP Motivation Theory Numerical Tests Conclusions Data 0 0 Time (s) Synthetic VSP CRG Time (s) Synthetic SSP CSG 6 6 -7850 Offset (m) 7850 -7850 Offset (m) 7850 25 SSPVSP Motivation Theory Numerical Tests Conclusions Synthetic RVSP CSG 0 Time (s) 1.4 km Comparison 6 Redatumed RVSP 0 Traces comparisons 2 Time (s) Time (s) Amplitude Zoom area 6 6 -7850 26 Offset (m) 7850 Zoom View of Traces Normalized Amplitude Direct waves are cut Redatumed RVSP trace 3 poor data folds Time (s) 5.5 27 SSPVSP Motivation Theory Numerical Tests Conclusions Another Datuming Results P-wave velocity model Depth (m) 0 Velocity (m/s) 4500 3600 1500 -7850 Offset (m) 7850 28 SSPVSP Motivation Theory Numerical Tests Conclusions Synthetic RVSP CSG 0 Time (s) 2.4 km Comparison 6 Redatumed RVSP 0 Time (s) Amplitude Traces comparisons 2 6 -2000 Time (s) 6 29 Offset (m) 2000 Zoom view Normalized Amplitude Direct waves are cut Redatumed RVSP trace 2.5 poor data folds 6 Time (s) 30 SSPVSP Motivation Theory Numerical Tests Conclusions SEG/EAGE Salt Model P-wave velocity model Depth (m) 0 Velocity (m/s) 4500 3600 1500 -7850 SSPVSP Offset (m) Motivation Theory Numerical Tests 7850 Conclusions 31 Shot 320 SSP primary WEM 20 Hz Depth (km) 1.5 3.5 Shot 320 RVSP WEM 20 Hz Depth (km) 1.5 32 3.5 -4 Offset (km) 4 SEG/EAGE salt model 33 shots SSP WEM 20 Hz 33shots VSP WEM 20 Hz 33 RVSP+VSP WEM 20 Hz Depth (km) 0 3.6 Depth (km) 0 33 3.6 -4 Offset (km) 4 -4 Offset (km) 4 SSPVSPSWP Transform s g s s’ s’ s’ g g s’ g g’ g’ s’ g’ 34 SSPVSP Motivation Theory Numerical Tests Conclusions 645 shots SSP WEM 1% error in migration model 2% error in migration model 3% error in migration model Depth (km) 0 3.6 Depth (km) 0 35 3.6 -8 Offset (km) 8 -8 Offset (km) 8 33 shots VSP WEM 1% error in migration model 2% error in migration model 3% error in migration model Depth (km) 0 3.6 Depth (km) 0 36 3.6 -8 Offset (km) 8 -8 Offset (km) 8 645 shots SSP primary WEM 20 Hz Depth (km) 0 3.5 Shot 320 BSSP WEM 20 Hz Depth (km) 1.5 37 3.5 -8 Offset (km) 8 645 shots SSP primary WEM 20 Hz Depth (km) 0 3.5 Shot 320 BSSP WEM 20 Hz Depth (km) 1.5 38 3.5 -8 Offset (km) 8 39 Conclusions • Natural datuming, no velocity model is needed ! • Higher fold virtual VSP data are obtained ! • Source are closer to the target, less approximation. • Better resolution. 40 SSPVSP Motivation Theory Numerical Tests Conclusions Outline • • • • • Introduction and overview SSP VSP SWP interferometric transform Local reverse time migration: horizontal reflector imaging Local reverse time migration: salt flank imaging with transmitted P-to-S waves Summary 41 Overview SSPVSP Local RTM Local RTM PS Summary Outline • Local reverse time migration: horizontal reflector imaging – – – Motivation Theory Numerical Tests • • – Sigsbee VSP Data Set GOM VSP Data Set Conclusions 42 Local RTM Motivation Theory Numerical Tests Conclusions VSP Forward Modeling s VSP data g D(g|s) x 43 Local RTM Motivation Theory Numerical Tests Conclusions Reverse Time Migration s VSP data g D(g|s) x 44 Local RTM Motivation Theory Numerical Tests Conclusions Reverse Time Migration Forward direct m(x) ~ ~ G(x|s) Backward data * s G(x|g)* D(g|s)dg g G(x|g) ds s G(x|s) g Backward D(g|s) Forward direct x 45 Local RTM Motivation Theory Numerical Tests Conclusions Reverse Time Migration (RTM) Forward direct: 1) Salt velocity model is required, but hard to build. 2) Errors due to imperfect velocity models. 3) Need to estimate statics, anisotropy, etc. G(x|g) s G(x|s) g Backward D(g,s) Forward direct x 46 Local RTM Motivation Theory Numerical Tests Conclusions VSPSWP Interferometry s g x Migrate virtual source gather D(g|g’) g’ Limitations 1) s and x are at different sides of the well 2) Image near vertical structures 47 Local RTM Motivation Theory Numerical Tests Conclusions Outline • Local reverse time migration: horizontal reflector imaging – – – Motivation Theory Numerical Tests • • – Sigsbee VSP Data Set GOM VSP Data Set Conclusions 48 Local RTM Motivation Theory Numerical Tests Conclusions Key Idea of Local RTM (a) VSP data: P(g|s)=T(g|s)+R(g|s) s g Reflection R(g|s) x Transmission T(g|s) 49 Local RTM Motivation Theory Numerical Tests Conclusions Key Idea of Local RTM (a) VSP data: P(g|s)=T(g|s)+R(g|s) s g (b) Backward reflection R(x|s)= s R(g|s) (c) Backward transmission x T(g|s) T(x|s)= G(x|g)*R(g|s) g g s g R(g|s) G(x|g)*T(g|s) Local VSP Green’s function g x x T(g|s) (d) Crosscorrelation g m(x)= R(x|s)*T(x|s) s R(g|s) x 50 Local RTM Motivation Theory Numerical Tests Conclusions Deconvolution Imaging Condition (d1) Crosscorrelation imaging condition m(x)= R(x|s)*T(x|s) s (d2) Deconvolution imaging condition m(x)= R(x|s)*T(x|s) T(x|s)*T(x|s) s s g R(g|s) x 51 Local RTM Motivation Theory Numerical Tests Conclusions Benefits • Target oriented! – Only a local velocity model near the well is needed. – Salt and overburden is avoided. – Fast and easy to perform. • Source statics are automatically accounted for. • Immune to salt-related interbed crosstalk. 52 Local RTM Motivation Theory Numerical Tests Summary Outline • Local reverse time migration: horizontal reflector imaging – – – Motivation Theory Numerical Tests • • – Sigsbee VSP Data Set GOM VSP Data Set Conclusions 53 Local RTM Motivation Theory Numerical Tests Conclusions Sigsbee P-wave Velocity Model m/s 0 4500 Depth (km) 279 shots 150 receivers 1500 9.2 Offset (km) -12.5 12.5 54 Local RTM Motivation Theory Numerical Tests Conclusions Local Reverse Time Migration Results Migration image True model 4.6 (2) Depth (km) d (1) f (1) specular zone (2) diffraction zone (3) unreliable zone d (3) f = fault 9.2 -3 Local RTM Motivation Offset (km) Theory Numerical Tests 3 d = diffractor 55 Conclusions Outline • Local reverse time migration: horizontal reflector imaging – – – Motivation Theory Numerical Tests • • – Sigsbee VSP Data Set GOM VSP Data Set Conclusions 56 Local RTM Motivation Theory Numerical Tests Conclusions GOM VSP Well and Source Location Source @150 m offset @600 m offset @1500 m offset Depth (m) 0 2800 m Salt 82 receivers 4878 3200 m Offset (m) 0 1829 57 Local RTM Motivation Theory Numerical Tests Conclusions Velocity Profile S Wave P Wave 0 Depth (m) Incorrect velocity model P-to-S ratio = 2.7 2800 m Salt P-to-S ratio = 1.6 3200 m 4500 0 Velocity (m/s) 5000 0 Velocity (m/s) 5000 58 Local RTM Motivation Theory Numerical Tests Conclusions Z-Component VSP Data 2652 Reflected P Depth (m) Salt Reverberations Direct P 3887 1.2 3.0 Traveltime (s) 59 Local RTM Motivation Theory Numerical Tests Conclusions 2652 X-Component VSP Data Reflected P Depth (m) Salt Direct S Reverberations Direct P 3887 1.2 3.0 Traveltime (s) 60 Local RTM Motivation Theory Numerical Tests Conclusions Local Reverse Time Migration Result 3.3 39 receivers Depth (km) (2) (1) (3) 3.9 reflectivity 0 Offset (m) 100 (1) specular zone, (2) diffraction zone, (3) unreliable zone 61 Local RTM Motivation Theory Numerical Tests Conclusions 150 m offset Without deconvolution With deconvolution Depth (km) 3.3 3.9 0 Offset (m) 100 0 Offset (m) 100 62 Local RTM Motivation Theory Numerical Tests Conclusions 600 m offset Without deconvolution With deconvolution Depth (km) 3.3 4.4 0 Offset (m) 600 0 Offset (m) 600 63 Local RTM Motivation Theory Numerical Tests Conclusions 1500 m offset Without deconvolution With deconvolution Depth (km) 3.3 4.4 0 Offset (m) 600 0 Offset (m) 600 64 Local RTM Motivation Theory Numerical Tests Conclusions Conclusions • Subsalt reflectors are accurately imaged near the well with subsalt velocity model only. • Diffractors are also imaged. • Illuminates horizontal subsalt reflectors around a vertical well. • GOM local RTM image agrees with the well reflectivity. • Deconvolution imaging condition helps. 65 Local RTM Motivation Theory Numerical Tests Conclusions Outline • • • • • Introduction and overview SSP VSP SWP interferometric transform Local reverse time migration: horizontal reflector imaging Local reverse time migration: salt flank imaging with transmitted P-to-S waves Summary 66 Overview SSPVSP Local RTM Local RTM PS Summary Outline • Local reverse time migration: salt flank imaging by transmitted P-to-S waves – – – Motivation Theory Numerical Tests • • – Schlumberger VSP Data Set GOM VSP Data Set Conclusions 67 Local RTM PS Motivation Theory Numerical Tests Summary Standard P-to-S Migration Forward source P m(x) ~ ~ G(x|s) Backward data S * s G(x|g’)*D(g’|s)dg’ ds g’ s P Converted wave VSP D(g|s) x S Salt and overburden velocity model is needed g’ 68 Local RTM PS Motivation Theory Numerical Tests Summary Interferometric P-to-S Migration Virtual source gather D(g|s) * D(g’|s) ds D(g|g’) ~~ s G(x|g) * G(x|g’) * D(g|g’) dg’dg m(x) ~ ~ g’ g s P P g x S g’ 69 Local RTM PS Motivation Theory Numerical Tests Summary Kirchhoff P-to-S Migration m(x) ~ ~ e-iwtsx e-iwtxg’ D(g’|s)dg’ ds s g’ s P Converted wave VSP D(g|s) P x g S g’ 70 Local RTM PS Motivation Theory Numerical Tests Summary Reduce Time Migration m(x) ~ ~ e-iw(tsx+terror) s pick e-iwtxg’ D(g’|s)dg’ ds g’ pick t error =( t sx+ t xg’ )- ( tsx + pick pick ~( t sx+ t xg )- ( tsx + txg’ ) txg ) s P Converted wave VSP D(g|s) P x g S g 71 Local RTM PS Motivation Theory Numerical Tests Summary Outline • Local reverse time migration: salt flank imaging by transmitted P-to-S waves – – – Motivation Theory Numerical Tests • • – Schlumberger VSP Data Set GOM VSP Data Set Conclusions 72 Local RTM PS Motivation Theory Numerical Tests Summary Local Reverse Time Migration Theory Backward P Backward S * m(x) ~ ~ G(x|g’)* D(g’,s) dg’ s g’ G(x|g)* D(g,s)dg ds g s P P g x S g’ 73 Local RTM PS Motivation Theory Numerical Tests Summary Outline • Local reverse time migration: salt flank imaging by transmitted P-to-S waves – – – Motivation Theory Numerical Tests • • – Schlumberger VSP Data Set GOM VSP Data Set Conclusions 74 Local RTM PS Motivation Theory Numerical Tests Summary Schlumberger 2D Isotropic Elastic Model 0 Depth (km) 291 shots 287 receivers 10 -12 0 Offset (km) 12 75 Local RTM PS Motivation Theory Numerical Tests Summary Aperture by Ray Tracing (a) Ray tracing direct P (b) PSS events Depth (km) 0 10 (d) Pp events (c) PPS events Depth (km) 0 10 -12 Local RTM PS 0 Offset (km) Motivation 12 Theory -12 Numerical Tests 0 Offset (km) Summary 12 76 Two-component VSP Synthetic Data Set VSP CSG X-component Depth (km) 4 8 VSP CSG Z-component Depth (km) 4 PSS Direct P PPS 8 0 Time (s) 8 77 Local RTM PS Motivation Theory Numerical Tests Summary (a) P-wave submodel km/s km/s 4.5 2.5 2.0 1.0 Depth (km) 6.0 (b) S-wave submodel 8.7 (c) P background model (d) S background model km/s 4.5 2.5 2.0 78 Depth (km) 6.0 km/s 8.7 0 Offset (km) 1.8 1.0 0 Offset (km) 1.8 Comparison with Migration Methods (a) Standard Kirchhoff (b) Reduced-time migration (RM) Depth (km) 6 8.7 (c) Interferometric migration (IM) (d) Local RTM Depth (km) 6 8.7 0 1.8 Offset (km) 0 1.8 Offset (km) 79 Local RTM PS Motivation Theory Numerical Tests Summary Local RTM without wavefield separation Depth (km) 6 8.7 0 Offset (km) 1.8 80 Local RTM with wavefield separation Depth (km) 6 8.7 0 Offset (km) 1.8 81 Local RTM using Z component only Depth (km) 6 8.7 0 Offset (km) 1.8 82 Outline Motivation Theory Numerical Tests Schlumberger VSP Data Set GOM VSP Data Set Conclusions 83 Local RTM PS Motivation Theory Numerical Tests Summary GOM VSP Well and Source Location Source @150 m offset @600 m offset @1500 m offset Depth (m) 0 2800 m Salt 82 receivers 4878 3200 m Offset (m) 0 1829 84 Local RTM PS Motivation Theory Numerical Tests Summary Velocity Profile S Wave P Wave 0 Depth (m) Incorrect velocity model P-to-S ratio = 2.7 2800 m Salt P-to-S ratio = 1.6 3200 m 4500 0 Velocity (m/s) 5000 0 Velocity (m/s) 5000 85 Local RTM PS Motivation Theory Numerical Tests Summary Z-Component VSP Data 2652 Reflected P Depth (m) Salt Reverberations Direct P 3887 1.2 3.0 Traveltime (s) 86 Local RTM PS Motivation Theory Numerical Tests Summary 2652 X-Component VSP Data Reflected P Depth (m) Salt Direct S Reverberations Direct P 3887 1.2 3.0 Traveltime (s) 87 Local RTM PS Motivation Theory Numerical Tests Summary Processing Workflow Original Data Rotate components Pick desired events Median filtering Migration (KM, RM, IM, RTM) 88 Local RTM PS Motivation Theory Numerical Tests Summary Migration of PPS Raypath Coverage Depth (m) 2000 Salt 39 receivers 4200 0 Local RTM PS Motivation Offset (m) Theory 200 Numerical Tests 89 Summary Migration of PPS KM RM IM Depth (m) 2000 Salt 4200 0 Offset (m) Local RTM PS 200 Motivation 0 Offset (m) Theory 200 Numerical Tests 0 Offset (m) Summary 90 200 Migration of PPS RM IM, sediment flood Local RTM Depth (m) 2000 Salt 4200 0 Offset (m) Local RTM PS 200 Motivation 0 Offset (m) Theory 200 Numerical Tests 0 Offset (m) Summary 91 200 150 m Offset LRM Image (a) Without deconvolution (b) With deconvolution Depth (km) 2.9 3.9 92 0 Offset (m) 100 0 Offset (m) 100 600 m Offset LRM Image (a) Without deconvolution (b) With deconvolution Depth (km) 2.9 4.4 93 0 Offset (m) 600 0 Offset (m) 600 1500 m Offset LRM Image (a) Without deconvolution (b) With deconvolution Depth (km) 2.9 4.4 94 0 Offset (m) 600 0 Offset (m) 600 Reduce Time Migration Image a) Synthetic 2.4 c) 600 m offset b) 150 m offset Reduce time migration Reduce time migration Depth (km) 2800 m 4.5 Salt 3200 m 95 Summary • Target oriented! – Only a local velocity model near the well is needed. – Salt and overburden is avoided. – Fast and easy to perform. • Source statics are automatically accounted for. • Immune to salt-related interbed crosstalk. 96 Local RTM PS Motivation Theory Numerical Tests Summary Summary • • • • • Introduction and overview SSP VSP SWP interferometric transform Local reverse time migration: horizontal reflector imaging Local reverse time migration: salt flank imaging with transmitted P-to-S waves Summary 97 Overview SSPVSP Local RTM Local RTM PS Summary Acknowledgements • Dr. Gerard Schuster and my committee members: Dr. Michael Zhdanov, Dr. Robert smith, Dr. Cari Johnson, Dr. Jianming Sheng for their advice and constructive criticism; • Scott Leaney and Hornby Brian for their help on modeling; 98 Acknowledgements • UTAM friends: – Jianhua Yu and Yonghe Sun on the research; – Jianming Sheng and Min Zhou for their experiences on interferometric imaging; – Zhiyong Jiang and Ruiqing He for their help on classes; – Travis Crosby and all UTAM students for their cheerful attitude; All UTAM sponsors for their support; • Family – My parents, brother and sister; • Friends – Liyun Ma, Min Zhou, Jun Wang, Shuqian Dong, Chaoxiong Ma, who encouraged me to continue on with my research. 99 Questions? 100