1. Inversions from one of Konstantin’s Simulations Birch, Braun, & Crouch Data from Parchevsky & Kosovichev

2. Test of inversions for c 2 Start from simulated data “spot_model1” from Konstantin and Sasha Measure travel-time shifts using phase- speed filters and ridge filters Compute kernels in Born approx. Invert for change in c 2

3. Measure travel-time shifts Surface focusing holography Use phase-speed filters (first five from Couvidat et al. 2006) or ridge filters (n=1,2,3,4) Use one parameter fit (Gizon & Birch 2002) or phase method (phase of covariance in Fourier domain). Difference between methods is very small compared to noise level.

4. 2.5-3.0 mHz 3.0-3.5 mHz 3.5-4.0 mHz 4.0-4.5 mHz 4.5-5.0 mHz 5.0-5.5 mHz Phase-speed filters + Frequency filters 12.8 km/s14.9 km/s17.5 km/s24.8 km/s35.5 km/s

5. Ridge filters + frequency filters 2.5-3.0 mHz 3.0-3.5 mHz 3.5-4.0 mHz 4.0-4.5 mHz 4.5-5.0 mHz 5.0-5.5 mHz n=1n=2n=3n=4

6. Born approx. Horizontal integrals of sound-speed kernels for ridge-filtered measurements. Kernels are all one sign (like global modes) Kernels reflect mode structure.

7. Noise Correlation, TD5, 3.0-3.5 mHz Computed from ten noise realizations

8. Inversion method Look for fractional change in c 2 MCD 1D RLS at each k vector k-dependent regularization using norm of solution Use full noise covariance

9. Example inversion result: phase-speed filters Fractional change in c 2

10. Compare measurements with predictions of the model Units are seconds

11. Example inversion result, ridge filters. Fractional change in c 2

12. Compare measurements with predictions of the model, ridge filters Units are seconds

13. Example averaging kernels Ridge filters. Same regularization params as before.

14. Results depend on regularization parameter

15. So … did the inversions work ?

16. Can also regularize on second deriv. Change in c 2

17. Conclusions Ridge and phase-speed filters give qualitatively similar results. Details depend on choice of regularization params & regularization method. More physics !