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Inversion for ring diagram analysis in GONG++ Pipeline

Inversion for ring diagram analysis in GONG++ Pipeline. What are we currently doing ? RLS inversion and its details What could be done? Tests with OLA. Data Statistic. Kernel Interpolation. Choice of functional form. Mode Selection. The Inverse problem in Ring Diagram Analysis.

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Inversion for ring diagram analysis in GONG++ Pipeline

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  1. Inversion for ring diagram analysis in GONG++ Pipeline • What are we currently doing ? RLS inversion and its details • What could be done? Tests with OLA Thierry Corbard, LoHCo Tucson Feb 10 2004

  2. Data Statistic Kernel Interpolation Choice of functional form Mode Selection The Inverse problem in Ring Diagram Analysis Ring Fitting => (n,ע) ≡ i {ux, σx, uy, σy } i=1…N Thierry Corbard, LoHCo Tucson Feb 10 2004

  3. =1000µHz Mode Selection • n-≤ n ≤ n+n-=0 n+=6 • |ux| < umax & |uy|< umax umax= 500m/s • There exists 2 modes in kernel file such that • => we exclude the extreme frequencies for each n • ℓ- > ℓmin & ℓ+ > ℓminℓmin=175 Thierry Corbard, LoHCo Tucson Feb 10 2004

  4. Kernel Interpolation We use: C, b Thierry Corbard, LoHCo Tucson Feb 10 2004

  5. r1=0.9 m=50 RLS Inversion • Choice of regularization: second derivative • Choice of functional form for v(r): step function Thierry Corbard, LoHCo Tucson Feb 10 2004

  6. Central differences for second derivatives Thierry Corbard, LoHCo Tucson Feb 10 2004

  7. Chi-square value Covariance Matrix Resolution Kernel Diagnostic Tools Thierry Corbard, LoHCo Tucson Feb 10 2004

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  14. What could be done? • Exploring the choice (automatic?) of the regularization parameter for different CMD • Use other functional forms: spline, related to theories … • Use GSVD for RLS • Fast and more robust than solving normal equations • Solve quasi-simultaneously for a set of regularization parameters => automatic choices (L-curve, GCV) easier to implement • Use OLA type of method • Allow different regularization for different depths • Easier to interpret in terms of resolution Thierry Corbard, LoHCo Tucson Feb 10 2004

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  24. Correlation Matrix Thierry Corbard, LoHCo Tucson Feb 10 2004

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