Reduced-Time Migration of Converted Waves David Sheley and Gerard T. Schuster University of Utah

Outline MotivationMotivation Reduced-Time Migration TheoryReduced-Time Migration Theory Error AnalysisError Analysis ResultsResults –Synthetic Data –Field Data ConclusionsConclusions

Outline MotivationMotivation Reduced-Time Migration TheoryReduced-Time Migration Theory Error AnalysisError Analysis ResultsResults –Synthetic Data –Field Data ConclusionsConclusions

Problem: Dark Flanks Depth Offset 0 Z Receiver Well Source Well X 0 ? ? P P ? ? ? ? m(r) = d(z g,  sr +  rg )

P Solution: PS Transmission Migration Depth Offset 0 Z Receiver Well Source Well X 0PSP PS m(r) = d(z g,  sr +  rg )

Motivation Solutions: Solutions: 1. PS Transmission Migration Problems: Problems: 1. Dark Flanks

Motivation Solutions: Solutions: PS Transmission Migration Problems: Problems: Dark Flanks 2. Velocity Errors (Vp, Vs)

Motivation Solutions: Solutions: PS Transmission Migration 2. Reduced-Time Migration Problems: Problems: Dark Flanks 2. Velocity Errors (Vp, Vs)

Outline MotivationMotivation Reduced-Time Migration TheoryReduced-Time Migration Theory Error AnalysisError Analysis ResultsResults –Synthetic Data –Field Data ConclusionsConclusions

Reduced-Time Migration 1. Data time shift Depth (m) Time (ms) P PS S d(z g, t  d(z g, t 

Reduced-Time Migration 1. Data time shift Time (ms) P PS S Depth (m) obs d’(g, t) = d(z g, t +  sg 

Reduced-Time Migration 1. Data time shift d’(z g, t) = d(z g, t    sg  Observed direct-P traveltime obs 2. Modify the migration equation m(r) = d’(z g,  sr +  rg ) obs  sg calc –  sg

Outline MotivationMotivation Reduced-Time Migration TheoryReduced-Time Migration Theory Error AnalysisError Analysis ResultsResults –Synthetic Data –Field Data ConclusionsConclusions

Focusing-Time Error Conventional vs. Reduced-Time Reduced-Time  (d sr + d rg psr - d sg)  c/c l Conventional  (d sr + d rg psr )  c/c l 2 2

Depth (m) Offset (m) Depth (m) Offset (m) Focusing-Time Error Imaging Error Error (ms) (ms) Conventional Trans. PS Migration Reduced-TimeMigration

Outline MotivationMotivation Reduced-Time Migration TheoryReduced-Time Migration Theory Error AnalysisError Analysis ResultsResults –Synthetic Data –Field Data ConclusionsConclusions

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

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

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

Conventional PS Transmission Migration Depth (m) Offset (m) True Velocity + 10 % Velocity Offset (m) 0100

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

Depth (m) Offset (m) True Velocity Reduced-Time PS Migration + 10 % Velocity Offset (m) 0100

Depth (m) Offset (m) Conventional PS Comparison +10% Velocity Recuced-Time Offset (m) 0100

Outline MotivationMotivation Reduced-Time Migration TheoryReduced-Time Migration Theory Error AnalysisError Analysis ResultsResults –Synthetic Data –Field Data ConclusionsConclusions

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

Time Delay = 3 ms ?Time Delay = 3 ms ? Well LocationWell Location Velocity ModelVelocity Model Data Problems

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

Conventional Offset (m) Depth (m)

Conventional Offset (m) 50 0Reduced-Time Depth (m)

Outline MotivationMotivation Reduced-Time Migration TheoryReduced-Time Migration Theory Error AnalysisError Analysis ResultsResults –Synthetic Data –Field Data ConclusionsConclusions

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

Acknowledgements I sincerely thank the 1999 sponsors of the UTAM consortium for their financial support. I sincerely thank the 1999 sponsors of the UTAM consortium for their financial support.