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Forward Modeling for Time-Distance Helioseismology

Forward Modeling for Time-Distance Helioseismology. A C Birch CORA, NWRA. Outline . Introduction to time-distance Introduction to the forward problem Example calculations Open questions and future work. SOHO/MDI dopplergram, Ni I, colors range from +/- 2 km/s.

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Forward Modeling for Time-Distance Helioseismology

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  1. Forward Modeling for Time-Distance Helioseismology A C Birch CORA, NWRA

  2. Outline • Introduction to time-distance • Introduction to the forward problem • Example calculations • Open questions and future work

  3. SOHO/MDI dopplergram, Ni I, colors range from +/- 2 km/s

  4. The basic idea of t.d. helioseismology (Duvall et al., 93) • Measure the time for a wave packet to move from x1 to x2 and also the time from x2 to x1 • From the times infer subsurface conditions, e.g. sound speed, flows …

  5. Time-distance helioseismology

  6. Gizon (2003), f modes, hi-res SOHO/MDI

  7. Zhao, Kosovichev, & Duvall (2002) 13 hours hi-res SOHO/MDI Depth 0-3 Mm, red is down flow, longest arrow is 1 km/s

  8. Linear forward and inverse problems • Linear sensitivity to small changes in the solar model • In principle have to consider all possible types of perturbations: e.g. flows, sound speed, density, source properties, magnetic field, damping properties … • Could use other quantities in addition to the travel time, for example the amplitude or central frequency of the cross-correlation

  9. A recipe for computing kernels(Gizon & Birch, 2002 ApJ) Previous work was based on ray approximation or single-source approximation,need something more general: + Motivated by Woodard (1997, ApJ): wavefield, excited by stochastic sources (convection) + Compute the expectation value of the cross-covariance function + Linearize (Born Approximation) the dependence of the cross-covariance to changes in the solar interior (e.g. sound speed)

  10. Gizon, Birch (Apj,2002) Damping, source strength, f-mode kernels How big are these effects for reasonable sunspot models ?

  11. Example: mtf + phase speed(Birch, Kosovichev, & Duvall, ApJ 2004)

  12. Future work and open questions • Quiet Sun: have many of the pieces, need to put them together • Sunspots: need realistic forward modeling • Radiative transfer ? • Still some very hard questions: everything is correlated … wave excitation, damping, flows, sound speed etc.

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