1. High Altitude Observatory (HAO) – National Center for Atmospheric Research (NCAR) The National Center for Atmospheric Research is operated by the University Corporation for Atmospheric Research under sponsorship of the National Science Foundation. An Equal Opportunity/Affirmative Action Employer. Inversion code for HMI vector polarimetric mode J.M. Borrero, S.Tomczyk, T. Darnell, H. Socas-Navarro, A. Norton, B. Lites, D. Elmore High Altitude Observatory National Center for Atmospheric Research Jan 2005

2. How it works ? J.M.Borrero Jan 2005

3. MELANIE by Socas-Navarro Milne-Eddington model Non-linear Squares fitting (Levenberg-Marquardt) Modified SVD by Ruiz Cobo & del Todo Iniesta Numerical derivatives Speed performance of 30 pixels/min Under ideal conditions With limited spectral sampling (5-6 wv.positions) -number of tuning positions With non-simultaneous wv. sampling (oscillations) - tuning sequence With limited exposure time(noise) With two-beam polarimetric acquisition -combination of polarization states What's the plan ? Take any IC and make sure it gives a numerical correct solution. The IC must be independent of the initial guess model. J.M.Borrero Jan 2005 MELANIE by Socas-Navarro Milne-Eddington model Non-linear Squares fitting (Levenberg-Marquardt) Modified SVD by Ruiz Cobo & del Todo Iniesta Numerical derivatives Speed performance of 30 pixels/min Under ideal conditions With limited spectral sampling (5-6 wv.positions) -number of tuning positions With non-simultaneous wv. sampling (oscillations) - tuning sequence With limited exposure time(noise) With two-beam polarimetric acquisition -combination of polarization states

4. Inversion Speed J.M.Borrero Jan 2005 Iterative algorithms (Current) Current speed: 30 pix/min + analytical derivatives + initial parameters optimization + thermodynamics neglected + improved CPU speed Estimated speed: 200-500 pix/min Non-Iterative algorithms (PCA,ANN) Current speed: 4x10e4 pix/min + thermodynamics neglected + improved CPU speed Estimated speed: 10e5 pix/min Adding 100 CPUs for parallel computing Estimated speed: 2-5x10e4 pix/min Estimated speed: 10e6 pix/min

5. J.M.Borrero Jan 2005 Other products More complex inversions might be possible if : - we manage to get rid of the p-modes (tuning sequence, temporal average) - we improve the spectral resolution ( 6 wavelength positions) - we improve the S/R (spatial temporal average) Would require Iterative algorithms Would be only suitable for small ROI (e.g:sunspots) Policy: inversions done systematically or upon request ? Horizonal features - 2 component inversion: using filling factor - can allow to retrieve field strength rather than flux even in the weak field regime Vertical features - inversion including gradients along the LOS