1. Advanced Seismic Imaging GG 6770 Tomography Inversion Project By Travis Crosby

2. 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 Jackson’s Principle determination of lambda

3. 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

4. Unregularized Tomography Experiment 1 Rays Left to Right Rays

5. Unregularized Tomography Experiment 2 Rays Top to Bottom Rays

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

7. Unregularized Tomography Experiment 4 10% change stopping criteria Rays

8. Unregularized Tomography Experiment 5 1% change stopping criteria Rays

9. Unregularized Tomography Experiment 6 0.1% change stopping criteria Rays

10. Unregularized Tomography Experiment 7 0.01% change stopping criteria Rays

11. Unregularized Tomography Experiment 8 0.05% Noise Added - 0.1% change stopping criteria Rays

12. Regularized Tomography Experiment 9 0.1 Lambda Rays Unregularized

13. Regularized Tomography Experiment 10 0.01 Lambda Rays Unregularized

14. Jackson’s Principle – Determination of Lambda 0.05% Noise Added Original Data

15. Jackson’s Principle – Determination of Lambda Original Data Residual 1.35e-8 Optimal lambda = 0.201 or 0.05*max(LtL) = 0.005

16. Acknowledgements Much Thanks to Ruiqing He