Interferometric Traveltime Tomography M. Zhou & G.T. Schuster Geology and Geophysics Department University of Utah
Interferometry In Phase Out of Phase oil Film
Interferometry
Outline Objective Objective Interferometry Methodology Interferometry Methodology Numerical Results Numerical Results Refraction Data Refraction Data Crosswell Data Crosswell Data Conclusions Conclusions
Objective Eliminate Shot / Receiver Eliminate Shot / Receiver Static Errors in Seismic Data Static Errors in Seismic Data
Outline Objective Objective Interferometry Methodology Interferometry Methodology Numerical Results Numerical Results Conclusions Conclusions
Methodology t ij = (t i - t j ) obs - (t i - t j ) cal - (t i - t j ) cal Standard Tomography Interferometric Tomography Smear residual t i along raypath t i obs t i = t i obs - t i cal Smear residual t ij along raypaths t j obs t i obs
Why Interferometry? t ij = (t i - t j ) obs - (t i - t j ) cal t i ’ =t i+ t t j ’ =t j+ t tttt Source timing error Eliminate the source timing error
t ij = (t i - t j ) obs - (t i - t j ) cal t j ’ =t j+ t tttt Receiver-timing error t i ’ =t i+ t Eliminate the receiver timing error
t = t 1 + t 2 + t 3 = t 11 - t 12 + t 23 - t 21 + t 32 - t 33 t 11 ’ =t 11+ t s1+ t r1 t s1 t r1 t s2 t r3 t r2 t s3 t 1 = t 11 - t 12 + t r1 - t r2 t 11 t 12 ’ =t 12+ t s1+ t r2 t 2 = t 23 - t 21 + t r3 - t r1 t 3 = t 32 - t 33 + t r2 - t r3 “Phase closure“ Theorem Eliminate both the source and receiver timing errors
ITT Can Eliminate source and receiver static errors
Problem with ITT Smear residual t ij along raypaths t ij = (t i - t j ) - (t i - t j ) cal tjtjtjtj titititi Lose Resolution
Outline Objective Objective Methodology Methodology Numerical Results Numerical Results Synthetic Refraction Data Synthetic Refraction Data Synthetic Crosswell Data Synthetic Crosswell Data Little Cottonwood Field Data Little Cottonwood Field Data Kidd Creek Crosswell Data Kidd Creek Crosswell Data Conclusions Conclusions
Surface-refraction Experiment Synthetic Model Depth (m) km/sec Offset (m) Shot/receiver interval 2 m No. of shots/receivers 251 Master trace
Inversion Results (Refraction Data) b) Standard Method km/sec Offset (m) d) ITT + timing shifts km/sec a) Synthetic model Depth (m) c) Standard + timing shifts Depth (m) Offset (m)
Outline Objective Objective Methodology Methodology Numerical Results Numerical Results Synthetic Refraction Data Synthetic Refraction Data Synthetic Crosswell Data Synthetic Crosswell Data Little Cottonwood Field Data Little Cottonwood Field Data Kidd Creek Crosswell Data Kidd Creek Crosswell Data ConclusionsConclusions
Crosswell Experiment Shot/receiver interval 4 m No. of shots/receivers 301 Synthetic Model Depth (m) km/sec Offset (m) Master trace
Inversion Results (Crosswell Data) a) Synthetic model Depth (m) c) Standard + shifts Depth (m) Offset (m) b) Standard Method km/sec d) ITT + shifts Offset (m) 0500km/sec
Outline Objective Objective Methodology Methodology Numerical Results Numerical Results Synthetic Refraction Data Synthetic Refraction Data Synthetic Crosswell Data Synthetic Crosswell Data Little Cottonwood Field Data Little Cottonwood Field Data Kidd Creek Crosswell Data Kidd Creek Crosswell Data Conclusions Conclusions
Recording Geometry Shot / geophone Ground Surface feet feet Shot / geophone interval 1.5 feet No. of shots / geophones 144
Inversion Results a) Standard method Depth (ft) c) Standard + timing shifts Depth (ft) Offset (ft) b) ITT kft/sec 0 d) ITT + timing shifts Offset (ft) kft/sec
Outline Objective Objective Methodology Methodology Numerical Results Numerical Results Synthetic Refraction Data Synthetic Refraction Data Synthetic Crosswell Data Synthetic Crosswell Data Little Cottonwood Field Data Little Cottonwood Field Data Kidd Creek Crosswell Data Kidd Creek Crosswell Data Conclusions Conclusions
Recording Geometry Y (km) Source Hole Receiver Hole X (km) Z (km)
Inversion Results Offset (m) b) Standard km/sec Ore body km/sec a) ITT Depth (m) Offset (m) Source hole receiver hole 6.0 Ore body
Inversion Results a) Standard ms Depth (m) Offset (m) Source hole receiver hole Ore body b) ITT Offset (m) km/sec
Outline Objective Objective Methodology Methodology Numerical Results Numerical Results Conclusions Conclusions
Conclusions ITT is effective and stable in eliminating ITT is effective and stable in eliminating shot-timing shifts, shot-timing shifts, At the cost of reduced model resolution At the cost of reduced model resolution
Future Work Improve slowness resolutionImprove slowness resolution Recover the DC componentRecover the DC component Regularization Methods Regularization Methods Develop ‘Phase Closure’ for CDP Data Eliminate source- and receiver-Eliminate source- and receiver- static errors simultaneously static errors simultaneously
Acknowledgements I am grateful for the financial I am grateful for the financial support from the members of support from the members of the 1999 UTAM consortium. the 1999 UTAM consortium.