Primary-Only Imaging Condition And Interferometric Migration

Primary-Only Imaging Condition And Interferometric Migration
M. Zhou Geology and Geophysics Department University of Utah

Outline POIC POIC-Radon Filter RTD+POIC Interferometric Migration (IM)
Summary

Outline POIC Why POIC What is POIC Examples Conclusions

Courtesy of Dr. Hongchuan Sun
3-Layer Model Depth (km) 5 Distance (km) 3 A Shot Gather Primary Time (s) Multiple 4 Trace Number 80 Courtesy of Dr. Hongchuan Sun

Courtesy of Dr. Hongchuan Sun
KM Image 3-Layer Model Depth (km) Depth (km) Multiple 5 5 Distance (km) 3 Distance (km) 3 Courtesy of Dr. Hongchuan Sun

Objective of POIC Data ( primary + multiple )
Primary-only imaging condition Image ( primary + multiple ) POIC Motivation Theory Examples Conclusions

obs Smear Event at along Ellipse Standard Migration Image Condition
Primary Multiple S R X S R Next few slides were shown last year, and I will briefly review them. Suppose we have a shot at position “s” and receiver at “r” which receiver the signals associated with a model. The standard Kirchhoff migration imaging condition use only the traveltime information to smear the data along an ellipse where the calculated traveltime matches the observed traveltime. The left panel is for the primaries, the primary energy is smeared to the correct positions. The right panel is for the multiple events, however, the energy is smeared to the wrong places which causes the migration artifacts. Depth Multiple artifacts X

obs pred. obs pred. obs pred. pred. pred.
Smear Event at along Ellipse if obs pred. = Migration + POIC Imaging Cond obs pred. = obs pred. = Primary Multiple S R X S R pred. In POIC, the angle information is used to separate the primaries with multiples. Only the primary events can satisfy both conditions, most of the non-zero offset multiples can not so that they are not migrated. It’s obvious that the POIC does not work well with the near-offset data because the angle differences between the primary and multiple events are very small. Depth pred. X

Outline POIC Why POIC What is POIC Examples Conclusions
SMARRT JV. Data Unocal Marine Data Conclusions

SMARRT JV. Pluto 1.5 Vp model
Depth (Km) 9 30 Distance (km)

Zero-offset Data 1 Time (Sec) 5 5 25 Distance (km)

POIC Image KM Image 1 Depth (km) 6 7 Distance (km) 30

KM Image POIC Image 1.0 Depth (km) 2.5 1.0 Depth (km) 2.5 5
Distance (km) 30

KM Image 4 Depth (km) 6 POIC Image 4 Depth (km) 6 7 Distance (km) 23

KM Image 5 Depth (km) 6 POIC Image 5 Depth (km) 6 9 Distance (km) 22

KM Image POIC Image 3 Depth (km) 5 25 30 25 30 Distance (km)

KM Image POIC Image 4 Depth (km) 6 10 20 10 20 3 Depth (km) 5 25 30 25
Distance (km) Distance (km)

Outline POIC Why POIC What is POIC Examples Conclusions SMARRT JV.
Unocal Marine Conclusions

Unocal Data 240 geophones per shot 236 shots in two lines
Common-shot gather 240 geophones per shot 236 shots in two lines 2-way time (s) Good afternoon, my name is Min Zhou. My topic today is “POIC+Radon filtering of the near-offset multiples”. Maximum data fold 60 3 Trace Number 240

Parabolic Radon Demultiple
Unocal Data Process Flow Chart Velocity CMP NMO Interval Velocity Radon CMP NMO Correction Parabolic Radon Demultiple Inverse NMO KM Migration POIC CSG Incidence Angle CRG Take-off Angle POIC Migration Good afternoon, my name is Min Zhou. My topic today is “POIC+Radon filtering of the near-offset multiples”.

Unocal Data Offset (Km) Offset (Km) 2 2 0.5 Time (s) Time (s) 2.0
2 2 0.5 Time (s) Time (s) Good afternoon, my name is Min Zhou. My topic today is “POIC+Radon filtering of the near-offset multiples”. 2.0 CMP after NMO CMP after Radon

Stack image after Radon
Unocal Data Stack image Stack image after Radon 0.5 2-way time (s) Good afternoon, my name is Min Zhou. My topic today is “POIC+Radon filtering of the near-offset multiples”. 3 400 1400 400 1400 CDP Number CDP Number

Unocal Data KM image Distance (Km) 8 KM image after Radon Depth (Km) 4
KM image after Radon Depth (Km) Good afternoon, my name is Min Zhou. My topic today is “POIC+Radon filtering of the near-offset multiples”. 4 Distance (Km) 8

Unocal Data KM image POIC image Depth (Km) 4 Distance (Km) 8
Depth (Km) Good afternoon, my name is Min Zhou. My topic today is “POIC+Radon filtering of the near-offset multiples”. 4 Distance (Km) 8 Distance (Km) 8

Zoom View KM image POIC image Distance (Km) 8 6 KM image after Radon
1.1 Depth (Km) Good afternoon, my name is Min Zhou. My topic today is “POIC+Radon filtering of the near-offset multiples”. 1.6 6 8 Distance (Km)

Zoom View KM image KM image after Radon Distance (Km) 5.5 8.0
POIC image 2.0 Depth (Km) Good afternoon, my name is Min Zhou. My topic today is “POIC+Radon filtering of the near-offset multiples”. 2.5 5.5 8.0 Distance (Km)

Zoom View KM image POIC image Distance (Km) KM image after Radon 3.5
4.5 1.2 Depth (Km) Good afternoon, my name is Min Zhou. My topic today is “POIC+Radon filtering of the near-offset multiples”. 1.6 3.5 4.5 Distance (Km)

Conclusions POIC effectively remove some surface related multiples
POIC is as fast as Kirchhoff POIC performs better than the traditional Radon methods POIC Motivation Theory Examples Conclusions

Conclusions POIC might miss weak events POIC uses simple kinematic
(pick more events) POIC uses simple kinematic ray- tracing (Wave-equation datuming) POIC performs better when near-offset data are not used (POIC-Radon Filter) POIC Motivation Theory Examples Conclusions

Summary

Outline POIC-Radon Filter Motivation Methodology Example Conclusions

POIC Review near-offset data are not used Problem:
POIC performs better when near-offset data are not used POIC-Radon Motivation Methodology Example Conclusions

Zoom views KM Image POIC Image 1 Depth (km) 3 7 Distance (km) 30 7

Original Data: CMP 8703 1 Time (s) 7 -2.0 0.0 2.0 Offset (km)
POIC-Radon Motivation Methodology Example Conclusions

Multiples by POIC: CMP 8703 1 Time (s) 7 -2.0 0.0 2.0 Offset (km)
POIC-Radon Motivation Methodology Example Conclusions

How to Fill the Near-offset Gaps?
Picking Prediction Interpolation Radon transform POIC-Radon Motivation Methodology Example Conclusions

Radon + POIC: Simple Test
Data Primaries Offset (km) -2 2 Multiples + Offset (km) -2 2 Predicted Multiples Time (s) 0.3 Offset (km) -2 2 POIC-Radon Motivation Methodology Examples Conclusions

- t -p Domain Fitted Primaries Data Predicted Multiples
Fitted Primaries Data Predicted Multiples Fitted Multiples Fitted Multiples Predicted Multiples - Time (s) 0.3 p (us/m2) -0.05 0.15 p (us/m2) -0.05 0.15 POIC-Radon Motivation Methodology Examples Conclusions

Radon + POIC: Simple Test
Errors Fitted Primaries Time (s) 0.3 Offset (km) -2 2 Offset (km) -2 2 POIC-Radon Motivation Methodology Examples Conclusions

Outline POIC-Radon Filter Motivation Methodology Example: SMARRT Data
Conclusions

Predicted Multiples by POIC
SMAART Data: CMP8703 Data Predicted Multiples by POIC 1 1st 2nd water bottom 1st subsalt sediments 1st – 3rd salt top Time (s) 8 -2.5 2.5 -2.5 2.5 Offset (km) Offset (km)

Predicted Multiples by POIC
SMAART Data: CMP8703 Predicted Multiples by POIC Time (s) 9 Offset (km) -2.5 2.5 Primaries Fitted Multiples by Radon -2.5 2.5 Offset (km)

Depth Images with Near-offset Data
KM Image POIC Image Distance (km) 7 25 POIC+Radon Image 1 Depth (km) 8 7 25 Distance (km)

KM Image POIC Image POIC+Radon Image 1 Depth (km) 2.8 10 23 10 23 Distance (km) Distance (km)

KM Image POIC+Radon Image POIC Image 3.5 Depth (km) 6.5 10 24 10 24 Distance (km) Distance (km)

Depth Images with All Data
POIC Far-offset Data + POIC+Radon near offsets Distance (km) 7 25 POIC+Radon All Data Depth (km) Compare the images for all the data (near-offset + far-offset data). KM, POIC, and POIC+Radon. 8 7 25 Distance (km)

Conclusions POIC-Radon filter can separate multiples and primaries in near offsets Near-offset multiples should be predictable by far-offset ones in t - p domain POIC-Radon Motivation Methodology Example Conclusions

Conclusions

Outline RTD + POIC Motivation Methodology Example Conclusions

POIC Review POIC uses simple kinematic ray- tracing Problem:
RTD + POIC Motivation Methodology Example Conclusions

Why RTD KM Image POIC Image 1 Depth (km) 3 7 Distance (km) 30 7
Another zoom view, the multiple artifacts associated with the water bottom are also removed. But the image resolution from POIC is not so good as the one from KM due to lack of the near-offset data. 3 7 Distance (km) 30 7 Distance (km) 30

Why RTD KM image POIC image 6 Depth (km) 9 5 25 5 25 Distance (km)
Compare the images for all the data (near-offset + far-offset data). KM, POIC, and POIC+Radon. 9 5 25 5 25 Distance (km) Distance (km) RTD + POIC Motivation Methodology Example Conclusions

Large velocity variation
Why RTD Offset (km) Complex Rough topography Large velocity variation Accurate Expensive RTM RTD + Depth (km) Phase-shift Kirchhoff POIC Efficient Approx. Less Complex

Outline RTD + POIC Motivation Methodology Example Conclusions

d(x’|x’’)=g*(s|x’) d(s|x”)
Implement RTD d(s|x’’) d(s|r) d(x’|x’’) d(s|x’’) S R d(s|x’’)= g*(r|x’’) d(s|r) Depth d(x’|x’’)=g*(s|x’) d(s|x”) x’’ x’ Distance

Outline RTD + POIC Motivation Methodology Example: SMARRT Data
Conclusions

SMAART JV. Pluto 1.5 Vp model
RTD + POIC SMAART JV. Pluto 1.5 Vp model Depth (Km) 9 30 Distance (km)

Zero-offset Data After Datuming Reflectivity Model Below Datum
SMAART JV Data Time (Sec) Zero-offset Data After Datuming 1 Reflectivity Model Below Datum Depth (Km) 7 Distance (km) 10 20 5

Zero-offset Data from surface
1 Time (Sec) 5 5 25 Distance (km)

KM Depth Images Before Datuming After Datuming 6 Depth (km) 9 5 25 5

POIC Depth Images Before Datuming After Datuming 6 Depth (km) 9 5 25 5

Depth Images after Redatuming
KM image POIC image Reflectivity Model 6 Depth (km) Compare the images for all the data (near-offset + far-offset data). KM, POIC, and POIC+Radon. 9 5 25 5 25 Distance (km) Distance (km) Motivation Theory Examples Conclusions

Depth Images after Redatuming
KM image POIC image Depth (km) Distance (km) Distance (km) Distance (km) Depth (km) Compare the images for all the data (near-offset + far-offset data). KM, POIC, and POIC+Radon. RTD + POIC Motivation Methodology Example Conclusions

Conclusions RTD helps reveal deeper structure
RTD + KM provides good depth image RTD + POIC helps to suppress multiples and preserve the primaries RTD + POIC Motivation Methodology Example Conclusions

Summary

Outline Interferometric Migration Motivation Theory Examples
Synthetic Data Chevron Field Data Conclusions

Motivation Migrate the CDP data, we need to correct:
Shot / geophone statics Overburden velocity errors RTM Motivation Theory Examples Conclusions

Theory: Reduced Time Migration
obs oil Standard Mig: = m(x) d(g,s) e t - i cal oil w t obs ref Surface t cal oil obs - = tstatics tmodel + mig t cal ref obs - = tstatics tmodel + mig Reference = tstatics tmodel ~ Oil RTM Motivation Theory Examples Conclusions

obs oil Standard Mig: = m(x) d(g,s) e t - i cal oil w t obs ref t mig oil ref ~ = Surface RTM Mig: = m(x) d(g,s) e -i w t cal oil mig ( ) + d(g,s) ~ = t cal oil e -i w ) + mig ref ( _ t obs ref ) cal oil e -i w + ( _ ) t cal oil ( ref d(g,s) = e -i w obs Reference f(g,s) Oil d(g,s) f(g,s) = e -i w t obs ref RTM Motivation Theory Examples Conclusions

Three steps for RTM: 1. Pick the reference reflection times t obs ref d(g,s) f(g,s) = e -i w t obs ref 2. Shift the data with picked times 3. Migrate the shifted data by RTM formula: m(x) _ = ) t cal oil ( ref e -i w f(g,s) RTM Motivation Theory Examples Conclusions

Theory: Interferometric Migration
d(s|g) For fixed s, g and x, how to find s’ and g’? s g Surface g” Fermat’s Principle specular t (x|g’|g) < (x|g”|g) diffraction g’ s’ Reference picked = t (x|g’|g) (g’|g) (x|g’) + calculated Oil x RTM Motivation Theory Examples Conclusions

Three steps for IM: 1. Pick the reference reflection times t obs ref 2. Find specular points s’ and g’ at reference layer 3. Migrate the data by IM formula: m(x) + = ) t obs ss’ e -i w f(g,s) cal ( s’x gg’ g’x RTM Motivation Theory Examples Conclusions

Synthetic Test: Model 10m X 10m grid 300 shots/geophones
3 Offset (km) 1 2 Depth (km) km/s 4.5 10m X 10m grid 3.5 300 shots/geophones 20 Hz Ricker wavelet 2.5 The first synthetic model is discretized onto a mesh of 51 by 81 gridpoints with a grid spacing of 1 meter. There are 41 shots and 41 geophones located at the shot/geophone wells with an interval of 2 m. The synthetic shot gathers are calculated by the FD wave equation solver with a 200 hz Ricker wavelet. 1.5 True Model RTM Motivation Theory Examples Conclusions

Migration Velocity Model
Synthetic Test: Model 3 Offset (km) 1 2 Depth (km) 3 Offset (km) 3.5 4.5 1.5 2.5 km/s 1 2 The first synthetic model is discretized onto a mesh of 51 by 81 gridpoints with a grid spacing of 1 meter. There are 41 shots and 41 geophones located at the shot/geophone wells with an interval of 2 m. The synthetic shot gathers are calculated by the FD wave equation solver with a 200 hz Ricker wavelet. True Model Migration Velocity Model RTM Motivation Theory Examples Conclusions

Synthetic Test: Migration
3 Offset (km) 3 Offset (km) 0.8 2 0.8 2 IM Image with Wrong Model Depth (km) The first synthetic model is discretized onto a mesh of 51 by 81 gridpoints with a grid spacing of 1 meter. There are 41 shots and 41 geophones located at the shot/geophone wells with an interval of 2 m. The synthetic shot gathers are calculated by the FD wave equation solver with a 200 hz Ricker wavelet. KM Image with Wrong Model RTM Image with Wrong Model RTM Motivation Theory Examples Conclusions

Incorrect Reference Depth
3 Offset (km) 3 Offset (km) 0.8 2 0.8 2 RTM Image (undulating reference) RTM Image (reference at 0.9 km) Depth (km) The first synthetic model is discretized onto a mesh of 51 by 81 gridpoints with a grid spacing of 1 meter. There are 41 shots and 41 geophones located at the shot/geophone wells with an interval of 2 m. The synthetic shot gathers are calculated by the FD wave equation solver with a 200 hz Ricker wavelet. KM Image with Wrong Model RTM Image (reference at 0.8 km) RTM Motivation Theory Examples Conclusions

Stack section (courtesy of Jianming Sheng)
Field Data: stack Offset (km) 12 0.5 990 shots 180 geophones Interval 25 m Two-way Time (s) trace length s Synthetic fault model which is discretized one to a 61 by 141 grid with a grid interval of 1.5 m. 18 sources and 36 geophones are located at the left and right sides of the model, respectively. sample interval 4 ms 4.0 Stack section (courtesy of Jianming Sheng) RTM Motivation Theory Examples Conclusions

Field Data: Time migration Time Migration with NMO Velocity
Offset (km) 12 One-way Time (s) Synthetic fault model which is discretized one to a 61 by 141 grid with a grid interval of 1.5 m. 18 sources and 36 geophones are located at the left and right sides of the model, respectively. 1.5 Time Migration with NMO Velocity RTM Motivation Theory Examples Conclusions

Field Data: Time migration Standard Time Migration with NMO Velocity
6 Offset (km) 12 0.4 One-way Time (s) Synthetic fault model which is discretized one to a 61 by 141 grid with a grid interval of 1.5 m. 18 sources and 36 geophones are located at the left and right sides of the model, respectively. 1.4 Standard Time Migration with NMO Velocity RTM Motivation Theory Examples Conclusions

Field Data: Time migration Standard Time Migration
Offset (km) 8 11 0.5 RTM Time Migration One-way Time (s) Synthetic fault model which is discretized one to a 61 by 141 grid with a grid interval of 1.5 m. 18 sources and 36 geophones are located at the left and right sides of the model, respectively. 0.8 Standard Time Migration RTM Motivation Theory Examples Conclusions

Field Data: Time migration Standard Time Migration
Offset (km) 7 11 0.9 RTM Time Migration One-way Time (s) Synthetic fault model which is discretized one to a 61 by 141 grid with a grid interval of 1.5 m. 18 sources and 36 geophones are located at the left and right sides of the model, respectively. 1.2 Standard Time Migration RTM Motivation Theory Examples Conclusions

Conclusions RTM/IM is effective in suppressing:
statics; RTM/IM is effective in suppressing: timing error by overburden velocity. RTM/IM is as cheap as standard migration RTM focuses structures with incorrect reference geometry RTM Motivation Theory Examples Conclusions

Summary

Summary Apply POIC to SMARRT & Unocal data Develop POIC-Radon filter
Combine POIC with RTD Apply IM and RTD to CDP data

Acknowledgements I thank Jerry for his guidance, support and encouragement I thank my committee members for their comments and support

Primary-Only Imaging Condition And Interferometric Migration

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