1. the need for physics-based inversions of sunspot structure and flows D. Braun, A. Birch, A. Crouch NWRA/CoRA M. Rempel NCAR/HAO

2. 12/5/2015 2GONG 2010-SOHO 24 main points goal of sunspot seismology is to determine subsurface structure, dynamics & evolution of sunspots after 3 decades this goal remains challenging & elusive forward, numerical, sunspot models are now reproducing helioseismic observations & suggest need to include acoustic to slow-mode conversion effects HMI/SDO provides incentive for inverse procedures demonstration of inversions around magneto-hydro-static (MHS) model faster

3. 12/5/2015 3GONG 2010-SOHO 24 issues in sunspot seismology strong & unexplained sensitivities to methodology strong & unexplained sensitivities to methodology measurements of travel-times depend on type of filtering used measurements of travel-times depend on type of filtering used frequency content of cross-correlations can vary considerably between spot and quiet-Sun frequency content of cross-correlations can vary considerably between spot and quiet-Sun kernels may not contain essential physics kernels may not contain essential physics forward models w/ mode conversion explain both absorption & phase/travel-time shifts, but disagree with pure wave-speed inversions forward models w/ mode conversion explain both absorption & phase/travel-time shifts, but disagree with pure wave-speed inversions no inversion method exists which includes mode conversion no inversion method exists which includes mode conversion faster slower

4. phase-speed filters yield near-surface inflows yield near-surface inflows ridge filters yield near-surface outflows yield near-surface outflows J. Zhao & HMI team A. Birch & D. Braun

5. 12/5/2015 5GONG 2010-SOHO 24 filter sensitivities travel-times, and their inversion results, depend strongly on filtering methods & parameters travel-times, and their inversion results, depend strongly on filtering methods & parameters  Braun & Birch, 2008; Thompson & Zharkov 2008; Moradi, et al. 2009; Jackiewicz et al. 2009) positive (slower) travel-time shifts using phase-speed filters observed in simulations with only positive (faster) wave-speed perturbations positive (slower) travel-time shifts using phase-speed filters observed in simulations with only positive (faster) wave-speed perturbations  sound-speed models (Birch et al. 2008)  magnetic models (Moradi, Hanasoge, Cally 2009) faster slower

6. 12/5/2015 6GONG 2010-SOHO 24 postive mean (sunspot-like) travel-times in Rempel simulation AR 10615 Rempel simulation ω /k phase speed frequency

7. 7 discrepancies between sunspot models fundamental differences between 2- layer TD inversion and strong near- surface perturbations suggested by other models fundamental differences between 2- layer TD inversion and strong near- surface perturbations suggested by other models recent near-surface models include effects of mode conversion recent near-surface models include effects of mode conversion figure from Gizon, Birch & Spruit (ARAA, in press) faster slower

8. a nested-magnetic-cylinder sunspot model concentric cylinders (each w/ uniform B) genetic algorithm to determine field strength & inclination within each cylinder Crouch, et al. (2005) matches both phase-shifts & absorption observed in Hankel analyses (e.g. Braun 1995)

9. 12/5/2015 9GONG 2010-SOHO 24 semi-empirical sunspot model slower Cameron, Gizon, Schunker & Pietarila 2010 existing umbral & penumbral thermodynamic models Maltby et al. 1996; Ding & Fang 1989 parameterization of magnetic field numerically propagation (SLiM) of planar wave packets (f, p 1, p 2 ) matches both phase-shifts & absorption of AR9286

10. 12/5/2015 10GONG 2010-SOHO 24 towards inversions including magnetic effects construct magnetohydrostatic (MHS) AR model construct magnetohydrostatic (MHS) AR model surface field measurements (?) surface field measurements (?) provides reference for linearization of both measurements and kernels provides reference for linearization of both measurements and kernels measure travel-time differences between active region and MHS model measure travel-time differences between active region and MHS model MHS travel-times determined by numerical wave propagation MHS travel-times determined by numerical wave propagation derive and apply relevant kernels derive and apply relevant kernels horizontally variant – numerically derived horizontally variant – numerically derived sound speed, magnetic field, flows, etc. sound speed, magnetic field, flows, etc.

11. 12/5/2015 11GONG 2010-SOHO 24 demonstration: inverting for sound-speed in uniform vertical field assume reference MHS model is uniform vertical field assume reference MHS model is uniform vertical field use TIMs (Crouch & Birch) to compute eigenfunctions, power spectra and synthetic wavefields use TIMs (Crouch & Birch) to compute eigenfunctions, power spectra and synthetic wavefields use B-spline representations of sound-speed perturbation use B-spline representations of sound-speed perturbation resulting travel-time maps are used to numerically solve for the kernels resulting travel-time maps are used to numerically solve for the kernels TD1, 3.75mHz

12. 12/5/2015 12GONG 2010-SOHO 24 demonstration: inverting for sound-speed with synthetic data (TIMs) in uniform vertical field Case 0: sound-speed perturbation, B=0 travel times referenced to model S (B=0) sound-speed kernels are referenced to model S (B=0) Case 1: sound-speed perturbation, B=3kG travel times referenced to model S w/ B=3kG sound-speed kernels are referenced to model S (B=0)

13. 12/5/2015 13GONG 2010-SOHO 24 demonstration: inverting for sound-speed with synthetic data (TIMs) in uniform vertical field Case 2: sound-speed perturbation, B=3kG travel times referenced to model S w/ B=3kG sound-speed kernels are referenced to model S w/ B=3kG

14. 12/5/2015 14GONG 2010-SOHO 24 main points goal of sunspot seismology is to determine subsurface structure, dynamics & evolution of sunspots after 3 decades, this goal remains challenging & elusive forward, numerical, sunspot models are now reproducing helioseismic observations & suggest need to include acoustic to slow-mode conversion HMI/SDO provides incentive for inverse procedures demonstration of inversions around magneto-hydro-static (MHS) model faster slower supported by: NASA SDO Science Center NNH09CE41C