Advanced Seismic ImagingAdvanced Seismic ImagingGG 6770GG 6770

Tomography Inversion ProjectTomography Inversion Project

ByByTravis CrosbyTravis Crosby

Outline

• Experiment parametersExperiment parameters

• Results of unregularized tomography experimentResults of unregularized tomography experiment - Various Ray orientations - Various stopping criteria

- Noise added (±0.05% max traveltime)

• Results of regularized tomography experimentResults of regularized tomography experiment- Different lambdas

• Jackson’s Principle determination of lambdaJackson’s Principle determination of lambda

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 = [L’L] –1 L’d ), 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

Unregularized Tomography Experiment 1Rays Left to Right

Rays

Unregularized Tomography Experiment 2Rays Top to Bottom

Rays

Unregularized Tomography Experiment 3Rays Left to Right & Top to Bottom

Rays

Unregularized Tomography Experiment 410% change stopping criteria

Rays

Unregularized Tomography Experiment 51% change stopping criteria

Rays

Unregularized Tomography Experiment 60.1% change stopping criteria

Rays

Unregularized Tomography Experiment 70.01% change stopping criteria

Rays

Unregularized Tomography Experiment 80.05% Noise Added - 0.1% change stopping criteria

Rays

Regularized Tomography Experiment 90.1 Lambda

Rays

Unregularized

Regularized Tomography Experiment 100.01 Lambda

Rays

Unregularized

Jackson’s Principle – Determination of Lambda

0.05% Noise Added

Original Data

Jackson’s Principle – Determination of Lambda

Original Data

Residual 1.35e-8

Optimal lambda = 0.201

or 0.05*max(LtL) = 0.005

Acknowledgements

Much Thanks to Ruiqing He