Reduced-Time Migration of Converted Waves David Sheley University of Utah

Outline MotivationMotivation Migration TheoryMigration Theory Error AnalysisError Analysis Synthetic Data ResultsSynthetic Data Results Field Data ResultField Data Result Conclusions & Future WorkConclusions & Future Work

PP vs PS Transmission Migration Depth Offset 0 Z Receiver Well Source Well X 0

PP Reflection Migration X Source Well Receiver WellP P = ? P =? 0 Depth Z 0 Offset

Receiver Well Converted Wave Migration Source Well X P PPS PS V p,V s = ? =? 0 Depth Z 0 Offset

Outline MotivationMotivation Migration TheoryMigration Theory Error AnalysisError Analysis Synthetic Data ResultsSynthetic Data Results Field Data ResultField Data Result Conclusions & Future WorkConclusions & Future Work

Conventional Migration m(r) = S(z g,  sr +  rg )   sr  rg s r g

PS Transmission Migration m(r) = S(z g, d sr /V p + d rg /V s )  d sr /V p d rg /V s s g r

km/sec Problem Well Receiver Well Source Depth (m) Offset (m)

Reduced-Time Migration Data time shiftData time shift S’(g, t) = S(z g, t +  sg   sg  Observed direct-P time obs obs

Depth (m) Time (ms) Original Data Depth (m) Time (s) Shifted Muted Data SP PSPPS S SP Data Shift

Reduced-Time Migration Data time shiftData time shift S’(z g, t) = S(z g, t +  sg   sg  Observed direct-P time obs obs Modify the migration equation Modify the migration equation m(r) = S(z g,  sr +  rg -  sg +  sg ) obs calc  calc m(r) = S’(z g,  sr +  rg –  sg ) 

Outline MotivationMotivation Migration TheoryMigration Theory Error AnalysisError Analysis Synthetic Data ResultsSynthetic Data Results Field Data ResultField Data Result Conclusions & Future WorkConclusions & Future Work

Error Analysis -- CWM Single traceSingle trace Homogeneous mediaHomogeneous media True velocity = cTrue velocity = c Migration velocityMigration velocity c’ = c +  c c’ = c +  c V p /V s = psrV p /V s = psr Assumptions: m(r) = S(z g,  sr +  rg psr )  l m(r) = S(z g, (d sr + d rg psr )/c’ )  l

Error Analysis Conventional Migration (d sr + d rg psr )/c’ l (d sr + d rg psr )/(c +  c) l = ~ (d sr + d rg psr )(s – s  c) l 2~  (d sr + d rg psr ) s  c 2 l cm

m(r) = S(g,  Error Analysis Reduced-Time Migration ) obscalc  sr +  rg -  sg +  sg

Error Analysis Reduced-Time Migration obscalc  sr +  rg -  sg +  sg =l (d sr + d rg psr - d sg )(s – s  c) + d sg s l 2  (d sr + d rg psr - d sg ) s  c rtm 2 l

Error Functions CWM vs. RTM rtm  (d sr + d rg psr - d sg ) s  c 2 l cm  (d sr + d rg psr ) s  c 2 l

rtm cm Depth (m) Offset (m) Depth (m) Offset (m) Imaging-Time Error Imaging Error Error (ms) (ms)

Outline MotivationMotivation Migration TheoryMigration Theory Error AnalysisError Analysis Synthetic Data ResultsSynthetic Data Results Field Data ResultField Data Result Conclusions & Future WorkConclusions & Future Work

Crosswell Model Depth (m) Offset (m) V2 V1 V = 5500 m/s 2 V = 5000 m/s 1 V p /V s = 1.5 Well Separation = 100 m = 100 m Source = 1500 Hz ds = 2 m dg = 2 m

Synthetic Data Depth (m) Time (ms) Original Data Depth (m) Time (s) Shifted Muted Data SPPS PPS S SP

PS Transmission Migration True Velocity Depth (m) Offset (m)

Conventional PS Migration + 10 % Velocity Depth (m) Offset (m)

Reduced-Time PS Migration + 10% Velocity Depth (m) Offset (m)

Outline MotivationMotivation Migration TheoryMigration Theory Error AnalysisError Analysis Synthetic Data ResultsSynthetic Data Results Field Data ResultField Data Result Conclusions & Future WorkConclusions & Future Work

Time Delay = 3 ms ?Time Delay = 3 ms ? Well locationWell location Velocity ModelVelocity Model Data Problems

km/sec Kidd Creek Well Receiver Well Source Depth (m) Offset (m)

6 Time (ms) Depth (m) 0 Time Shifted CRG

Conventional PS Migration Depth (m) Offset (m)

Reduced-Time PS Migration Depth (m) Offset (m)

RTM-PS CRG # Depth (m) Offset (m)

Kidd Creek Offset (m) 50 0

Outline MotivationMotivation Migration TheoryMigration Theory Error AnalysisError Analysis Synthetic Data ResultsSynthetic Data Results Field Data ResultField Data Result Conclusions & Future WorkConclusions & Future Work

Discussion & Conclusions PS migration can image structure invisible to reflection migration.PS migration can image structure invisible to reflection migration. Reduced-time migraton decreases the error of an incorrect velocity model.Reduced-time migraton decreases the error of an incorrect velocity model. Converted wave reduced-time migration can successfully image a transmitting boundary.Converted wave reduced-time migration can successfully image a transmitting boundary.

Future Work Model and migrate salt proximity VSP data with converted wave RTM.Model and migrate salt proximity VSP data with converted wave RTM. Model and test PP RTM.Model and test PP RTM. Search for other applications of RTM.Search for other applications of RTM. Graduate.Graduate.