Kirchhoff vs Crosscorrelation Migration Kirchhoff Mig. Crosscorr. Mig. X (m) 1000 0.5 km 2.5 km 0.5 km 2.5 km 950 Depth (m) 1950 0.5 km 2.5 km 0.5 km 2.5 km

Kirchhoff vs Crosscorrelation Migration Kirchhoff Mig. Crosscorr. Mig. X (m) 1000 0.5 km 2.5 km 0.5 km 2.5 km 950 Depth (m) 1950 0.5 km 2.5 km 0.5 km 2.5 km

VSP Images with Static Errors Kirchhoff Mig. Crosscorr. Mig. X (m) 1000 0.5 km 2.5 km 0.5 km 2.5 km 950 Depth (m) 1950 0.5 km 2.5 km 0.5 km 2.5 km

VSP Images with Static Errors Kirchhoff Mig. Crosscorr. Mig. X (m) 1000 0.5 km 2.5 km 0.5 km 2.5 km 950 Depth (m) 1950 0.5 km 2.5 km 0.5 km 2.5 km

Field RVSP Images with Static Errors Kirchhoff Mig. Crosscorr. Mig. 1000 0.0 km .9 km 950 Depth (m) 1950 0.0 km .12 km 0.0 km .12 km

Enhancing Illumination Coverage of VSP by Crosscorrelation Migration Interferometric Imaging Jianhua Yu Gerard T. Schuster In this talk, we would like to give our investigation on enhancing illumination coverage of VSP by xcorrmig. University of Utah

Outline Motivation Crosscorrelation Migration SEG/EAGE Model 2-D RVSP Field Data The talk includes five parts. First is motivation, In the second part, I give a brief introduction to xcorrmig method; then I shown some examples including SEG mode, and field data example. Finally it is conclusion. Conclusions

Outline Motivation Crosscorrelation Migration SEG/EAGE Model 2-D RVSP Field Data motivation Conclusions

Problems with VSP Imaging Quality? Limited recording aperture Narrow illumination coverage Static errors at VSP well caused by location errors First we will see what factors affect VSP image quality

Solution: Xcorr Migration of Ghost Reflections Widens illumination coverage VSP CDP Another question may ask: Why use crosscorrelation migration method? (1) It increases the illumination coverage. Look this cartton. Ghost xcorrmig provides wider illimunation

Solution: Xcorr Migration of Ghost Reflections Widens illumination coverage VSP CDP Eliminates Rec. Statics: No Need to Know Rec. Location Eliminates ~ ½ of the Raypath Another question may ask: Why use crosscorrelation migration method? (1) It increases the illumination coverage. Look this cartton. Ghost xcorrmig provides wider illimunation

Outline Motivation Crosscorrelation Migration SEG/EAGE Model 2-D RVSP Field Data Conclusions

Crosscorrelation Migration Kirchhoff Migration of Crosscorelograms m(x) = (g, s, t + t ) gx sx s g s g s Another question may ask: Why use crosscorrelation migration method? (1) It increases the illumination coverage. Look this cartton. Ghost xcorrmig provides wider illimunation g

How do you remove kinematic effects of propagating through unintersting parts of medium? Uninteresting Part of Medium

Pick Direct Arrival Time T and shift all Uninteresting Part of Medium { M T Pick Direct Arrival Time T and shift all Traces by T M Uninteresting Part of Medium

Pick Direct Arrival Time T and shift all Traces by T M M M Uninteresting Part of Medium

Shifting Traces Removes Kinematic Effects Of Propagating through Uninteresting Parts of Medium M Uninteresting Part of Medium

Shifting Traces Removes Kinematic Effects Of Propagating through Uninteresting Parts of Medium M Uninteresting Part of Medium

m(x) = (g, t + t ) Kirchhoff Migrate psuedo-shot gathers Shifting Traces Removes Kinematic Effects Of Propagating through Uninteresting Parts of Medium. . Source Moved to Surface g M M m(x) = (g, t + t ) gx g Mx Kirchhoff Migrate psuedo-shot gathers Can replace time-shifted traces by crosscorrelograms

Interferometric Summary Wider, taller coverage. Eliminates well statics and uninteresting parts of the medium.  VSP Above Source Imaging { Wider Coverage ?

Interferometric Summary Wider, taller coverage. Eliminates well statics and uninteresting parts of the medium.  VSP Above Source Imaging { Wider Coverage M m(x) = (g, t + t ) gx g Mx Kirchhoff Migrate psuedo-shot gathers

Outline Motivation Crosscorrelation Migration SEG/EAGE Model 2-D RVSP Field Data Let me show one example. Conclusions

SEG/EAGE Model V = 1.5 - 3.0 km/s Well 256 Sources Depth (km) 2 X (km) V = 1.5 - 3.0 km/s Depth (km) This is SEG geology model. And its velocity model. Velocity ranges from 1.5 km.s to 3.0 km.s SEG/EAGE Model 2 X (km) 3

Acquisition Parameters: Well location: (1.5 km, 0 km) Source interval: 10 m Source number: 256 Acquisition Parameters: Well 1 km Depth (km) Receiver interval: 10 m Receiver depth range: 0.1 -1 km Receiver number: 91 Here I show the main parameters. Sample interval: 1 ms Recording length: 3 s 2 X (km) 3

Depth (km) 0.2 0.9 CSG 160 Time (s) This is one common source gather (#160) 3

Depth (km) 0.2 0.9 Ghosts (CSG 160) Time (s) 3 Ghosts (CSG 160) Time (s) Same shot gather but after separating primaries from ghosts 3

CRG 60 Xcross 60 X (km) 1.4 2.4 X (km) 2.4 Time (s) 3 2.4 Time (s) Left panel is common receiver gather (#60). Green line indicates the master trace. And the right shows the crosscorrelograms. CRG 60 3

Kirchh Mig (45) Xcorr Mig (45) Xcorr. Mig(15’) 0.5 Depth (km) 2.0 0.5 The comparison of standard migration and xcorr migration results. 2.0 0.5 2.5 0.5 2.5 0.5 2.5 X (km)

Static Errors at Well Well Depth (m) 900 50 Raw Data Well Depth (m) 900 50 Raw Data Static errors (ms) To investigate the robust of xcorr migration, I add static errors at the receiver location in the well. -50 Static Errors at Well

Kirchhoff Migration Static Error: 0 X (km) Static Error: 25 ms 2.5 0.5 Depth (km) Here are the standard migration result with different static erorrs 2.0 0.5 2.5 0.5 2.5 0.5

Crosscorrelation Migration Static Error: 0 X (km) Static Error: 25ms 2.5 Static Error: 50 ms 0.5 Depth (km) Here the xcorr migration with different static variance level. It is clear that static erorr has little influence to the new migratioon method. 2.0 0.5 2.5 0.5 2.5 0.5

Primary vs Multiple Image Velocity Model Primary vs Multiple Image Depth (km) 11 16 16 X (km) X (km)

Contents Motivation Crosscorrelation Imaging Condition SEG/EAGE Model 2-D RVSP Field Data Another exanple is from 2-D field RVSP data Conclusions

Depth (ft) 30 900 Raw Data(CRG15) Time (s) 0.3 Raw Data(CRG15) Time (s) Common receiver gather before separation 0.3

Depth (ft) 30 900 Ghosts Time (s) Ghost reflections 0.3

Field Data (CSG 25) Trace No. 5 24 Trace No. Time (s) 1.2 0.2 5 24 0.5 xcorr data (muted) 5 24 0.5 Master trace Raw data (muted) Time (s) Common source gather and its crosscorrelograms. Master trace is at the left trace. 1.4

X (ft) X (ft) 400 400 200 Standard mig Xcorr. mig Depth (ft) 1300 400 400 200 Standard mig Xcorr. mig Depth (ft) Comparison of standard (left) and xcorr migration (right). Note the difference in the deeper part. 1300

Exxon Data Standard Well data Xcorr. Depth (ft) 1100 Depth (ft) The comparison of well log data (center), stabndard migration (left 4 traces) and xcorr migration result (right 4 traces) 1100

Outline Motivation Crosscorrelation Migration SEG/EAGE Model 2-D RVSP Field Data conclusions Conclusions

Crosscorrelogram Migration Conclusions Increased illumination coverage in the VSP image. VSP ->CDP Eliminate the static errors in the well No need to know source (RVSP) or receiver location (VSP) Half sensitivity to velocity migration errors than mult. migration by “mirrors”.

Conclusions Loss of some lateral resolution? Xcorr Narrow Angle Kirchhoff Wide Angle vs Be careful about virtual multiple Ghost is weaker than primary Extra summation compared to KM

Acknowledgments UTAM sponsors Exxon for 2-D field data J. Claerbout + J. Rickett II evolved from daylight imaging

X (ft) X (ft) 400 400 200 Standard mig Xcorr. mig Depth (ft) 1300 400 400 200 Standard mig Xcorr. mig Depth (ft) Comparison of standard (left) and xcorr migration (right). Note the difference in the deeper part. 1300

Geological Model (2001) X(km) 0 4 Depth(km) 3 0 4 Depth(km) In 2001, we proposed a crosscorrelation migration method and tested using a flat-layered model to test 3 (2001)

Too simple? Widen illumination? If there are static errors in well? Migration Result Using Crosscorrelation Imaging X (km) 1.6 2.1 Too simple? Widen illumination? Time (s) If there are static errors in well? Here is the crosscorrelation migration result using ghost reflections. It matches well with true geologic model. But there are severasl questions that may arise? This model is too simple? How does crosscorrelation migration result work for realistic model? VSP imaging has narrow limited coverage. Does this method help to address this problem? Is this method sensitive to the statics errors in the drilling hole? 2.2

Why Use Crosscorrelation Migration? Widen the illumination coverage in the VSP image VSP geometry Equivalent surface geometry Xcorr The second benefit we can get is by using xcorr. Imaging condition, the VSP geometry is transformed into CDP geometry. That will has contribution to increase the illumination coverage.

Find R(x,z) but not know source location Seismic Ghost Reflection Ghost Direct Find R(x,z) but not know source location ?

t } m(x) = (g, t + t ) Seismic Interferogram: Correlate Traces Seismic Ghost Reflection Master Ghost Direct has kinematics of primary reflection x Ghost Direct x Direct x Direct t } 1 2 M m(x) = (g, t + t ) gx g Mx M Kirchhoff Migrate psuedo-shot gathers M

RVSP Well Receiver Source Ghost Direct Wave Primary This is RVSP geometry. There are three knids of waves: Primary, ghost reflection, and direct waves. Source RVSP

Ghost Reflection Imaging Condition: There are two geophones. At the geophone G, the ghost reflection travel time is ???, and we also observe the direct waves s x

After Crosscorrelation of Two Traces at Locations g & g’ After crosscorrelation of two traces at g’ and g, director traveltime at g is become like this; the ghost reflection traveltime is becoming s x

After Crosscorrelation of Two Traces at Locations g & g’ The new ghost imaging equation imply that after crosscorrelation of two traces, the imaging condition is equivalent to a reflection imaging conditon where source is at g’ position and geophone at g. s x

After Crosscorrelation of Two Traces at Locations g & g’ This equation is our xcorrmigration imaging condition. s x

Recall Green’s Theorem Every Surface Point = Source Point

Why is there insensitivity to static errors in the well? g’ g x Static errors Another question we mak ask? Why is this new crosscorrelation migration insensitive to static errors in the well ? First equation is ghost reflection travetime. There is static error at the well delta tao s. substitute equation 2 into 1, we get the equation 3. after some slightly arrangement, the crosscorrelation imaging condition is the bottom equation. It is free of sttic errors.

Crosscorrelogram Migration Migrated Image Crosscorrelograms Crosscorrelation Imaging Condition This is the basic crosscorrelation migration equation. Input data are the crosscorrelograms.. Using new imaging condition, we can got the final result.

Field Data Well data Xcorr. Migration Depth (ft) 1100

Exxon Data Well data Standard Migration Depth (ft) 1100