Acoustic Imaging and Its Inverse Problem

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Acoustic Imaging and Its Inverse Problem

• Ming-Tsung Sun
• Chang-Gung University

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Acoustic Waves in the Sun

• Wave propagator

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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.

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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.

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Results of Acoustic Imaging
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The Inversion Problem
In ray approximation
In Cartesian coordinate
In Fourier domain
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The Inversion Method
With piecewise constant approximation
In the discrete form
Phase travel time perturbation can be expressed
as
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Regularized Least Square Fit
Minimizing ?2 to solve for S
Minimizing ?2 to solve for S
Solve for estimated S
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Averaging Kernel and Error Magnification
Solution of estimated S
Phase travel time perturbation
Estimated solution and real solution
Variance
Averaging kernel
Error Magnification
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Averaging Kernel
Averaging kernel
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Error Magnification
Error Magnification
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Results Using TON Mark Model
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Results Using Real 2-D Configuration
Hrizontal view
Vertical view
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Results Using Real 2-D Configuration
Quantitative Comparison
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Results Using 3-D Configuration
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Results Using 3-D Configuration
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Results Using Data of Active Region NOAA 7981
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Estimated S in Active Region NOAA 7981
Vertical View
Horizontal View of ?? at Solar Surface
? 2.67
? 26.7
? 267
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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?