Inversions from one of Konstantin’s Simulations

Birch, Braun, & Crouch

Data from Parchevsky & Kosovichev

Test of inversions for c2

• 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 c2

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.

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/s 14.9 km/s 17.5 km/s 24.8 km/s 35.5 km/s

Ridge filters + frequencyfilters

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=1 n=2 n=3 n=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, 3.0-3.5 mHzComputed from ten noise realizations

Inversion method

• Look for fractional change in c2

• MCD

• 1D RLS at each k vector

• k-dependent regularization using norm of solution

• Use full noise covariance

Example inversion result: phase-speed filters

Fractionalchange in c2

Compare measurements with predictions of the model

Units are seconds

Example inversion result, ridge filters.

Fractionalchange in c2

Compare measurements with predictions of the model, ridge filters

Units are seconds

Example averaging kernelsRidge filters. Same regularization params as before.

Results depend on regularization parameter

So … did the inversions work ?

Can also regularize on second deriv.

Changein c2

Conclusions

• Ridge and phase-speed filters give qualitatively similar results.

• Details depend on choice of regularization params & regularization method.

• More physics !