Advanced Seismic Imaging GG 6770

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Advanced Seismic ImagingGG 6770

• Tomography Inversion Project

By Travis Crosby
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Outline

• Experiment parameters
• Results of unregularized tomography experiment
• - Various Ray orientations
• - Various stopping criteria
• - Noise added (0.05 max traveltime)
• Results of regularized tomography experiment
• - Different lambdas
• Jacksons Principle determination of lambda

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Tomography Experiment Parameters

• Real velocity model
• shown to the left.
• 3000 units/s homogeneous
• starting model.
• Straight rays from left to right
• and top to bottom.
• Solve by least square steepest
• descent (s LL 1 Ld ),
• regularized and unregularized.
• Ratio of knowns (441 rays) to unknowns (400 grid
  units)
• is 1.1025.
• Noise added was random and 0.05 of maximum
  traveltime.
• No preconditioning used.

Real Velocity Model
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Unregularized Tomography Experiment 1Rays Left
to Right
Rays
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Unregularized Tomography Experiment 2Rays Top to
Bottom
Rays
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Unregularized Tomography Experiment 3Rays Left
to Right Top to Bottom
Rays
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Unregularized Tomography Experiment 410 change
stopping criteria
Rays
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Unregularized Tomography Experiment 51 change
stopping criteria
Rays
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Unregularized Tomography Experiment 60.1 change
stopping criteria
Rays
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Unregularized Tomography Experiment 70.01
change stopping criteria
Rays
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Unregularized Tomography Experiment 80.05 Noise
Added - 0.1 change stopping criteria
Rays
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Regularized Tomography Experiment 90.1 Lambda
Rays
Unregularized
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Regularized Tomography Experiment 100.01 Lambda
Rays
Unregularized
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Jacksons Principle Determination of Lambda
0.05 Noise Added
Original Data
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Jacksons Principle Determination of Lambda
Residual 1.35e-8
Original Data
Optimal lambda 0.201
or 0.05max(LtL) 0.005
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Acknowledgements
Much Thanks to Ruiqing He