Slices through the x and z components of the simulated flow v at depths 1 Mm, 3.5 Mm, and 5.5 Mm.

The point-to-annulus sensitivity kernels for three flow components computed for the f-mode, distance 28 Mm and outward-inward geometry. The white circle represents the location of the averaging annulus.

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.

An example noise-covariance matrix for f-mode travel times averaged over 6 h. In this plot, a stands for the combination of the f-mode, oi geometry, and annulus radius of 7.3 Mm, b stands for the combination of f-mode, we geometry, and annulus radius of 8.8 Mm.

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 cross-talk minimised, top row: cross-talk is ignored. Random error of the results is 14 m s^-1 when assuming data averaged over 4 days. Over-plotted contours, which are also marked on the colour bar for reference, denote the following: half-maximum of the kernel (white), half-maximum of the target function (red), and  ± 5% of the maximum value of the kernel (blue and green, respectively).

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.

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.

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.

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 = z₀ of different target functions are displayed, one with removed mean (1) and one constructed with negative side-lobes (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.

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.

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.

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.

The azimuthally-averaged 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 cross-talk is minimised (blue) and ignored (red). Compare to Fig. 14.