Issue 
A&A
Volume 530, June 2011



Article Number  A148  
Number of page(s)  23  
Section  The Sun  
DOI  https://doi.org/10.1051/00046361/201016426  
Published online  27 May 2011 
Online material
Fig. 16
Slices through the x and z components of the simulated flow v at depths 1 Mm, 3.5 Mm, and 5.5 Mm. 

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Fig. 17
The pointtoannulus sensitivity kernels for three flow components computed for the fmode, distance 28 Mm and outwardinward geometry. The white circle represents the location of the averaging annulus. 

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Fig. 18
Horizontal averages of sensitivity kernels may serve useful when estimating which depths are easier to target. The trend for each mode/ridge was obtained by taking and averaging over all as within the given mode. 

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Fig. 19
An example noisecovariance matrix for fmode travel times averaged over 6 h. In this plot, a stands for the combination of the fmode, oi geometry, and annulus radius of 7.3 Mm, b stands for the combination of fmode, we geometry, and annulus radius of 8.8 Mm. 

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Fig. 20
All components of the averaging kernel for v_{x} inversion at 1 Mm depth with a FWHM of s_{z} = 1.1 Mm and s_{h} = 15 Mm. Bottom row: with crosstalk minimised, top row: crosstalk is ignored. Random error of the results is 14 m s^{1} when assuming data averaged over 4 days. Overplotted contours, which are also marked on the colour bar for reference, denote the following: halfmaximum of the kernel (white), halfmaximum of the target function (red), and ± 5% of the maximum value of the kernel (blue and green, respectively). 

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Fig. 21
All components of the averaging kernel for v_{x} inversion at 3.5 Mm depth with a FWHM of s_{z} = 2.2 Mm and s_{h} = 15 Mm. Random error of the results is 20 m s^{1} when assuming data averaged over 4 days. For details see Fig. 20. 

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Fig. 22
All components of the averaging kernel for v_{x} inversion at 5.5 Mm depth with a FWHM of s_{z} = 3.5 Mm and s_{h} = 15 Mm. Random error of the results is 28 m s^{1} when assuming data averaged over 4 days. For details see Fig. 20. 

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Fig. 23
The contributions of particular modes to the horizontally averaged averaging kernel for v_{x} inversions using travel times averaged over 4 days for depths 1 and 3.5 Mm. We do not display the inversion for the depth of 5.5 Mm, because it is heavily dominated by noise. 

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Fig. 24
To solve the peculiarity of the v_{z} inversion, we introduced two formalisms in Sect. 5.1. Here we plot performance of those. In black, the magnified section a y = 0 and z = z_{0} of different target functions are displayed, one with removed mean (1) and one constructed with negative sidelobes (2). The resulting averaging kernels are also plotted. It is evident that the resulting averaging kernels are qualitatively very similar even when different formalisms were used to compute them. 

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Fig. 25
All components of the averaging kernel for v_{z} inversion at 3.5 Mm depth with a FWHM of s_{z} = 2.2 Mm and s_{h} = 15 Mm. Random error of the results is 13 m s^{1} when assuming data averaged over 4 days. For details see Fig. 20. 

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Fig. 26
All components of the averaging kernel for v_{z} inversion at 5.5 Mm depth with a FWHM of s_{z} = 3.5 Mm and s_{h} = 15 Mm. Random error of the results is 133 m s^{1} when assuming data averaged over 4 days. For details see Fig. 20. 

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Fig. 27
The cut through the x = y = 0 point of the averaging kernel (solid) and the respective target function (dashed) for the v_{x} (left) and v_{z} (right) inversions using averaging over many flow realisations plotted along with the corresponding target functions at three discussed depths (1 Mm in blue, 3.5 Mm in green, and 5.5 Mm in red). Compare to Figs. 4 and 9 where the resemblance of the target functions is worse. The random error of the results is given in Table 2. 

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Fig. 28
The azimuthallyaveraged power spectra of the v_{z} inversion components at depths of 1, 3.5 and 5.5 Mm for averaging over many flow representations. For reference, we plot the power spectrum of using the black solid line. Then we plot the power spectrum of (solid line) and power spectrum of the noise (i.e., the power spectrum of ; dashed line) for the inversion where the crosstalk is minimised (blue) and ignored (red). Compare to Fig. 14. 

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© ESO, 2011
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