Finite-Frequency Resolution Finite-Frequency Resolution Limits Limits of Traveltime Tomography of Traveltime Tomography for Smoothly Varying for Smoothly Varying Velocity Models Velocity Models Jianming Sheng and Gerard T. Jianming Sheng and Gerard T. Schuster Schuster University of Utah University of Utah
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Jianming Sheng and Gerard T. Schuster University of Utah
Finite-Frequency Resolution Limits of Traveltime Tomography for Smoothly Varying Velocity Models. Jianming Sheng and Gerard T. Schuster University of Utah. Outline. Objective Inverse GRT and Resolution Limits Numerical Examples Summary. Objective. Develop a resolution method that. - PowerPoint PPT Presentation
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Finite-Frequency Resolution Limits Finite-Frequency Resolution Limits of Traveltime Tomography of Traveltime Tomography
for Smoothly Varying for Smoothly Varying Velocity ModelsVelocity Models
Jianming Sheng and Gerard T. SchusterJianming Sheng and Gerard T. Schuster
University of UtahUniversity of Utah
OutlineOutline• ObjectiveObjective
• InverseInverse GRT and Resolution Limits GRT and Resolution Limits
• Numerical ExamplesNumerical Examples
• SummarySummary
ObjectiveObjective
• Estimates spatial resolution of traveltime Estimates spatial resolution of traveltime
tomogramstomograms
• Accounts for finite-frequency effectsAccounts for finite-frequency effects
• Is applicable for arbitrary velocity Is applicable for arbitrary velocity
modelsmodels
Develop a resolution method thatDevelop a resolution method that
OutlineOutline• ObjectiveObjective
• InverseInverse GRT and Resolution Limits GRT and Resolution Limits
• Numerical ExamplesNumerical Examples
• SummarySummary
Traveltime LinearizationTraveltime Linearization
• Under Rytov approximationUnder Rytov approximation
B. Transmission TomographyB. Transmission Tomography
x4 12
3 X Xz
The results are similar to SchusterThe results are similar to Schuster (1996) for (1996) for
traveltime tomography in far-field traveltime tomography in far-field approximationapproximation
Key IdeaKey Idea
• The velocity anomalies within the The velocity anomalies within the first-first-Fresnel zone or wavepathFresnel zone or wavepath affect the affect the traveltime traveltime
• The intersection area of the wavepathsThe intersection area of the wavepaths at the at the
scatterer scatterer defines the spatial resolution limitsdefines the spatial resolution limits
Wavepath IntersectionWavepath Intersection
Transmission ExampleTransmission Example
rrs1s1
rrg1g1
Fresnel ZoneFresnel Zone
Wavepath IntersectionWavepath Intersection
Transmission ExampleTransmission Example
rrs1s1
rrg1g1
rrg2g2rrs2s2
rrs1s1
rrg1g1
rrs2s2 rrg2g2
rrs3s3
rrg3g3
Wavepath IntersectionWavepath IntersectionTransmission ExampleTransmission Example
• InverseInverse GRT and Resolution Limits GRT and Resolution Limits
• Numerical ExamplesNumerical Examples
• SummarySummary
SummarySummary
• Used the Used the inverseinverse GRT to get the spatial GRT to get the spatial traveltime resolution formulastraveltime resolution formulas
We haveWe have
• Developed a practical means of estimating Developed a practical means of estimating
traveltime resolution limits for arbitrary velocity traveltime resolution limits for arbitrary velocity
models and finite-frequency source datamodels and finite-frequency source data
• Obtained resolution limits of global tomo.Obtained resolution limits of global tomo.
AcknowledgmentAcknowledgment
We thank the sponsors of the University of We thank the sponsors of the University of Utah Tomography and Modeling Utah Tomography and Modeling /Migration (UTAM) Consortium for their /Migration (UTAM) Consortium for their financial support .financial support .