Time‐Distance Helioseismology: The Forward Problem for Random Distributed Sources

Gizon, Laurent; Birch, A. C.

doi:10.1086/340015

Cited by 197 publications

(272 citation statements)

References 41 publications

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“…A positive time delay corresponds to a flow to the north in the case of meridional flows or a flow to the west for east-west flows. The measurement of the traveltime shifts due to flows follows closely the method discussed by Gizon & Birch (2002). At each distance, a mean reference cross-correlation symmetric for the two senses of time lag was derived.…”

Section: Analysis and Resultsmentioning

confidence: 99%

A New Component of Solar Dynamics: North-South Diverging Flows Migrating toward the Equator with an 11 Year Period

Beck

Gizon

Duvall

2002

The Astrophysical Journal

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Section: Analysis and Resultsmentioning

confidence: 99%

A New Component of Solar Dynamics: North-South Diverging Flows Migrating toward the Equator with an 11 Year Period

Beck

Gizon

Duvall

2002

The Astrophysical Journal

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“…Although the Fresnel-zone, Born, and Rytov approximations implemented to simulate wave effects in previous helioseismic studies (e.g., Gizon & Birch 2002;Jensen & Pijpers 2003) involve less computational effort than full wavefield inversion, this is mainly because their sensitivity kernels were fixed throughout the inversion. Moreover, computational cost with these approximations is relatively low only if sensitivity kernels are based on the initial one-dimensional (depth-dependent-only) models.…”

Section: Discussionmentioning

confidence: 99%

Inversion of Full Acoustic Wavefield in Local Helioseismology: A Study With Synthetic Data

Cobden¹,

Tong²,

Warner³

2011

ApJ

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We present the first results from the inversion of full acoustic wavefield in the helioseismic context. In contrast to time-distance helioseismology, which involves analyzing the travel times of seismic waves propagating into the solar interior, wavefield tomography models both the travel times and amplitude variations present in the entire seismic record. Unlike the use of ray-based, Fresnel-zone, Born, or Rytov approximations in previous time-distance studies, this method does not require any simplifications to be made to the sensitivity kernel in the inversion. In this study, the acoustic wavefield is simulated for all iterations in the inversion. The sensitivity kernel is therefore updated while lateral variations in sound-speed structure in the model emerge during the course of the inversion. Our results demonstrate that the amplitude-based inversion approach is capable of resolving sound-speed structures defined by relatively sharp vertical and horizontal boundaries. This study therefore provides the foundation for a new type of subsurface imaging in local helioseismology that is based on the inversion of the entire seismic wavefield.

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“…The statement that a number of scatterers acts on the wave field to create small shifts in travel times [δτ a (r)] may be expressed as follows (e.g. Gizon and Birch, 2002):…”

Section: Setup Of the Inverse Problemmentioning

confidence: 99%

“…Note that in Equation (2) we have explicitly assumed that the background solar model and the sensitivity kernels are invariant under horizontal translations. Sensitivity kernels result from forward modeling under the single-scattering Born approximation (Gizon and Birch, 2002 …”

Section: Setup Of the Inverse Problemmentioning

confidence: 99%

Multichannel Three-Dimensional SOLA Inversion for Local Helioseismology

et al. 2011

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Inversions for local helioseismology are an important and necessary step for obtaining three-dimensional maps of various physical quantities in the solar interior. Frequently, the full inverse problems that one would like to solve prove intractable because of computational constraints. Due to the enormous seismic data sets that already exist and those forthcoming, this is a problem that needs to be addressed. To this end, we present a very efficient linear inversion algorithm for local helioseismology. It is based on a subtractive optimally localized averaging (SOLA) scheme in the Fourier domain, utilizing the horizontal-translation invariance of the sensitivity kernels. In Fourier space the problem de- couples into many small problems, one for each horizontal wave vector. This multichannel SOLA method is demonstrated for an example problem in time-distance helioseismology that is small enough to be solved both in real and Fourier space. We find that both approaches are successful in solving the inverse problem. However, the multichannel SOLA algorithm is much faster and can easily be parallelized.

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Time‐Distance Helioseismology: The Forward Problem for Random Distributed Sources

Cited by 197 publications

References 41 publications

A New Component of Solar Dynamics: North-South Diverging Flows Migrating toward the Equator with an 11 Year Period

A New Component of Solar Dynamics: North-South Diverging Flows Migrating toward the Equator with an 11 Year Period

Inversion of Full Acoustic Wavefield in Local Helioseismology: A Study With Synthetic Data

Multichannel Three-Dimensional SOLA Inversion for Local Helioseismology

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