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

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

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.

mHz mHz mHz mHz mHz mHz Phase-speed filters + Frequency filters 12.8 km/s14.9 km/s17.5 km/s24.8 km/s35.5 km/s

Ridge filters + frequency filters mHz mHz mHz mHz mHz mHz n=1n=2n=3n=4

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

Noise Correlation, TD5, mHz Computed from ten noise realizations

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

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

Compare measurements with predictions of the model Units are seconds

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

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

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

Results depend on regularization parameter

So … did the inversions work ?

Can also regularize on second deriv. Change in c 2

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