Combined helioseismic inversions for 3D vector flows and sound-speed perturbations

Context. Time–distance helioseismology is the method of the study of the propagation of waves through the solar interior via the travel times of those waves. The travel times of wave packets contain information about the conditions in the interior integrated along the propagation path of the wave. The travel times are sensitive to perturbations of a variety of quantities. The usual task is to invert for the vector of plasma flows or the sound–speed perturbations separately. The separate inversions may be polluted by systematic bias, for instance, originating in the leakage of vector flows into the sound–speed perturbations and vice versa (called a cross-talk). Information about the cross-talk is necessary for a proper interpretation of results. Aims. We introduce an improved methodology of the time-distance helioseismology which allows us to invert for a full 3D vector of plasma flows and the sound–speed perturbations at once. Using this methodology one can also derive the mean value of the vertical component of plasma flows and the cross-talk between the plasma flows and the sound–speed perturbations. Methods. We used the Subtractive Optimally Localised Averaging method with a minimisation of the cross-talk as a tool for inverse modelling. In the forward model, we use Born approximation travel-time sensitivity kernels with the Model S as a background. The methodology was validated using forward-modelled travel times with both mean and difference point-to-annulus averaging geometries applied to a snapshot of fully self-consistent simulation of the convection. Results. We tested the methodology on synthetic data. We demonstrate that we are able to recover flows and sound–speed perturbations in the near-surface layers. We have taken the advantage of the sensitivity of our methodology to entire vertical velocity, and not only to its variations as in other available methodologies. The cross-talk from both the vertical flow component and the sound–speed perturbation has only a negligible effect for inversions for the horizontal flow components. Furthermore, this cross-talk can be minimised if needed. The inversions for the vertical component of the vector flows or for the sound–speed perturbations are affected by the cross-talk from the horizontal components, which needs to be minimised in order to provide valid results. It seems that there is a nearly constant cross-talk between the vertical component of the vector flows and the sound–speed perturbations.

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Time-distance helioseismology of solar Rossby waves

Astronomy and Astrophysics ◽

10.1051/0004-6361/201834849 ◽

2019 ◽

Vol 626 ◽

pp. A3 ◽

Cited By ~ 14

Author(s):

Zhi-Chao Liang ◽

Laurent Gizon ◽

Aaron C. Birch ◽

Thomas L. Duvall

Keyword(s):

Rossby Waves ◽

Power Spectra ◽

Solar Interior ◽

Data Sets ◽

Travel Times ◽

Solar Cycles ◽

Near Surface ◽

Ring Diagram ◽

Time Distance ◽

One Year

Context. Solar Rossby waves (r modes) have recently been discovered in the near-surface horizontal flow field using the techniques of granulation-tracking and ring-diagram analysis applied to six years of SDO/HMI data. Aims. Here we apply time-distance helioseismology to the combined SOHO/MDI and SDO/HMI data sets, which cover 21 years of observations from May 1996 to April 2017. The goal of this study is to provide an independent confirmation over two solar cycles and in deeper layers of the Sun. Methods. We have measured south-north helioseismic travel times along the equator, which are sensitive to subsurface north-south flows. To reduce noise, the travel times were averaged over travel distances from 6° to 30°; the mean distance corresponds to a p-mode lower turning point of 0.91 R⊙. The 21-year time series of travel-time measurements was split into three seven-year subsets and transformed to obtain power spectra in a corotating frame. Results. The power spectra all show peaks near the frequencies of the classical sectoral Rossby waves for azimuthal wavenumbers in the range 3 ≤ m ≤ 15. The mode frequencies and linewidths of the modes with m ≤ 9 are consistent with a previous study whereas modes with m ≥ 10 are shifted toward less negative frequencies by 10–20 nHz. While most of these modes have e-folding lifetimes on the order of a few months, the longest lived mode, m = 3, has an e-folding lifetime of more than one year. For each mode, the rms velocity at the equator is in the range of 1–3 m s−1, with the largest values for m ∼ 10. No evidence for the m = 2 sectoral mode is found in the power spectrum, implying that the rms velocity of this mode is below ∼0.5 m s−1. Conclusions. This work confirms the existence of equatorial global Rossby waves in the solar interior over the past two solar cycles and shows that time-distance helioseismology is a promising technique to study them deep in the convection zone.

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Comparison of time–distance inversion methods applied to SDO/HMI Dopplergrams

Astronomy and Astrophysics ◽

10.1051/0004-6361/201936268 ◽

2019 ◽

Vol 629 ◽

pp. A55 ◽

Cited By ~ 2

Author(s):

David Korda ◽

Michal Švanda ◽

Junwei Zhao

Keyword(s):

Cross Talk ◽

Sound Speed ◽

Target Function ◽

Horizontal Flow ◽

The Sun ◽

Data Products ◽

Time Distance ◽

The Cross ◽

Flow Components ◽

Target Depth

Context. The Helioseismic and Magnetic Imager (HMI) onboard the Solar Dynamics Observatory (SDO) satellite has been observing the Sun since 2010. The uninterrupted series of Dopplergrams are ideal for studying the dynamics of the upper solar convection zone. Within the Joint Science Operations Center (JSOC) the time–distance inversions for flows and sound-speed perturbations were introduced. The automatic pipeline has produced flow and sound-speed maps every 8 h. We verify the results of JSOC inversions by comparing the data products to equivalent results from inverse modelling obtained by an independent inversion pipeline. Aims. We compared the results from the JSOC pipeline for horizontal flow components and the perturbations of the speed of sound at set of depths with equivalent results from an independently implemented pipeline using a different time–distance inversion scheme. Our inversion pipeline allows inversion for all quantities at once while allowing minimisation of the crosstalk between them. This gives us an opportunity to discuss the possible biases present in the JSOC data products. Methods. For the tests we used the subtractive optimally localised averaging (SOLA) method with a minimisation of the cross-talk. We compared three test inversions for each quantity at each target depth. At first, we used the JSOC setup to reproduce the JSOC results. Subsequently, we used the extended pipeline to improve these results by incorporating more independent travel-time measurements but keeping the JSOC-indicated localisation in the Sun. Finally, we inverted for flow components and sound-speed perturbations using a localisation kernel with properties advertised in the JSOC metadata. Results. We successfully reproduced the horizontal flow components. The sound-speed perturbations are strongly affected by the high level of the cross-talk in JSOC products. This leads to larger amplitudes in the inversions for the sound-speed perturbations. Different results were obtained when a target function localised around the target depth was used. This is a consequence of non-localised JSOC averaging kernels. We add that our methodology also allows inversion for the vertical flow.

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Plasma flows and sound-speed perturbations in the average supergranule

Astronomy and Astrophysics ◽

10.1051/0004-6361/202039928 ◽

2021 ◽

Vol 646 ◽

pp. A184

Author(s):

David Korda ◽

Michal Švanda

Keyword(s):

Travel Time ◽

Sound Speed ◽

Deep Structure ◽

Solar Rotation ◽

Vertical Component ◽

Inversion Method ◽

Time Averaging ◽

Vertical Flow ◽

Near Surface ◽

Time Distance

Context. Supergranules create a peak in the spatial spectrum of photospheric velocity features. Even though they have some properties of convection cells, their origin is still being debated in the literature. The time–distance helioseismology constitutes a method that is suitable for investigating the deep structure of supergranules. Aims. Our aim is to construct the model of the flows in the average supergranular cell using fully consistent time–distance inverse methodology. Methods. We used the Multi-Channel Subtractive Optimally Localised Averaging inversion method with regularisation of the cross-talk. We combined the difference and the mean travel-time averaging geometries. We applied this methodology to travel-time maps averaged over more than 104 individual supergranular cells. These cells were detected automatically in travel-time maps computed for 64 quiet days around the disc centre. The ensemble averaging method allows us to significantly improve the signal-to-noise ratio and to obtain a clear picture of the flows in the average supergranule. Results. We found near-surface divergent horizontal flows which quickly and monotonously weakened with depth; they became particularly weak at the depth of about 7 Mm, where they even apparently switched sign. The amplitude of the ‘reversed’ flow was comparable to the background flows. The inverted vertical flows and sound-speed perturbations were spoiled by unknown systematic errors. To learn about the vertical component, we integrated the continuity equation from the surface. The derived estimates of the vertical flow depicted a sub-surface increase from about 5 m s−1 at the surface to about 35 m s−1 at the depth of about 3 Mm followed by a monotonous decrease to greater depths. The vertical flow remained positive (an upflow) and became indistinguishable from the background at the depth of about 15 Mm. We further detected a systematic flow in the longitudinal direction. The course of this systematic flow with depth agrees well with the model of the solar rotation in the sub-surface layers.

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Towards a Wave Theory Interpretation of Time-Distance Helioseismology Data

Symposium - International Astronomical Union ◽

10.1017/s0074180900219025 ◽

2001 ◽

Vol 203 ◽

pp. 180-182

Author(s):

A. C. Birch ◽

A. G. Kosovichev

Keyword(s):

Spatial Scale ◽

Born Approximation ◽

Acoustic Waves ◽

Sound Speed ◽

Large Scale ◽

Small Scale ◽

Ray Theory ◽

Travel Times ◽

Large Spatial Scale ◽

Time Distance

Time-distance helioseismology, which measures the time for acoustic waves to travel between points on the solar surface, has been used to study small-scale three-dimensional features in the sun, for example active regions, as well as large-scale features, such as meridional flow, that are not accessible by standard global helioseismology. Traditionally, travel times have been interpreted using geometrical ray theory, which is not always a good approximation. In order to develop a wave interpretation of time-distance data we employ the first Born approximation, which takes into account finite-wavelength effects and is expected to provide more accurate inversion results. In the Born approximation, in contrast with ray theory, travel times are sensitive to perturbations to sound speed which are located off the ray path. In an example calculation of travel time perturbations due to sound speed perturbations that are functions only of depth, we see that that the Born and ray approximations agree when applied to perturbations with large spatial scale and that the ray approximation fails when applied to perturbations with small spatial scale.

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Investigation of a sunspot complex by time-distance helioseismology

Proceedings of the International Astronomical Union ◽

10.1017/s1743921311015456 ◽

2010 ◽

Vol 6 (S273) ◽

pp. 320-324 ◽

Cited By ~ 1

Author(s):

A. G. Kosovichev ◽

T. L. Duvall

Keyword(s):

Acoustic Waves ◽

Sound Speed ◽

Active Regions ◽

Magnetic Activity ◽

Depth Range ◽

Travel Times ◽

Magnetic Structures ◽

Flow Maps ◽

Time Distance ◽

Deep Focus

AbstractSunspot regions often form complexes of activity that may live for several solar rotations, and represent a major component of the Sun's magnetic activity. It had been suggested that the close appearance of active regions in space and time might be related to common subsurface roots, or “nests” of activity. EUV images show that the active regions are magnetically connected in the corona, but subsurface connections have not been established. We investigate the subsurface structure and dynamics of a large complex of activity, NOAA 10987-10989, observed during the SOHO/MDI Dynamics run in March-April 2008, which was a part of the Whole Heliospheric Interval (WHI) campaign. The active regions in this complex appeared in a narrow latitudinal range, probably representing a subsurface toroidal flux tube. We use the MDI full-disk Dopplergrams to measure perturbations of travel times of acoustic waves traveling to various depths by using time-distance helioseismology, and obtain sound-speed and flow maps by inversion of the travel times. The subsurface flow maps show an interesting dynamics of decaying active regions with persistent shearing flows, which may be important for driving the flaring and CME activity, observed during the WHI campaign. Our analyses, including the seismic sound-speed inversion results and the distribution of deep-focus travel-time anomalies, gave indications of diverging roots of the magnetic structures, as could be expected from Ω-loop structures. However, no clear connection in the depth range of 0-48 Mm among the three active regions in this complex of activity was detected.

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