Acoustic Imaging and Its Inverse Problem MingTsung Sun

Acoustic Imaging and Its Inverse Problem Ming-Tsung Sun Chang-Gung University

Acoustic Waves in the Sun • Wave propagator

Collecting Acoustic Signals on the Solar Surface • Acoustic signals on the solar surface are collected coherently to form wave packets traveling through a target point in the Sun. a dj g k h eb m p i f c

Collecting Acoustic Signals on the Solar Surface • Before and after traveling through a target point, the wave packets can be collected according the time-distance relation.

Results of Acoustic Imaging

The Inversion Problem In ray approximation: In Cartesian coordinate: In Fourier domain:

The Inversion Method With piecewise constant approximation: In the discrete form: Phase travel time perturbation can be expressed as:

Regularized Least Square Fit Minimizing 2 to solve for S: Solve for estimated S:

Averaging Kernel and Error Magnification Solution of estimated S: Phase travel time perturbation: Estimated solution and real solution: Averaging kernel Error Magnification Variance

Averaging Kernel Averaging kernel

Error Magnification

Results Using TON Mark Model

Results Using Real 2 -D Configuration Hrizontal view Vertical view

Results Using Real 2 -D Configuration Quantitative Comparison

Results Using 3 -D Configuration

Results Using 3 -D Configuration

Results Using Data of Active Region NOAA 7981

Estimated S in Active Region NOAA 7981 Vertical View Horizontal View of at Solar Surface = 2. 67 = 267

Further Investigation • Can the tool be improved? • How to interpret the noisy inversion results? • What is the tool for? • What is the one-to-one relation between sound speed perturbation and magnetic fields, temperature perturbation, or flow velocity? • Can we apply the technique to invert the absorption map?