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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 A C Birch CORA, NWRA
Outline • Introduction to time-distance • Introduction to the forward problem • Example calculations • Open questions and future work
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 …
Zhao, Kosovichev, & Duvall (2002) 13 hours hi-res SOHO/MDI Depth 0-3 Mm, red is down flow, longest arrow is 1 km/s
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
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)
Gizon, Birch (Apj,2002) Damping, source strength, f-mode kernels How big are these effects for reasonable sunspot models ?
Example: mtf + phase speed(Birch, Kosovichev, & Duvall, ApJ 2004)
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.