The Accuracy of the Born and Ray Approximations in Time-Distance Helioseismology

Birch, A. C.; Kosovichev, A. G.; Price, Gary H.; Schlottmann, R. B.

doi:10.1086/324766

Cited by 47 publications

(38 citation statements)

References 19 publications

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“…The kernels are mostly sensitive to perturbations within the first Fresnel zone. Figure 39 shows the test results for both the ray and Born approximations for a simple model of a smooth sphere in an uniform medium by comparing with precise numerical results [160]. These results show that for typical perturbations in the solar interior the Born approximation is sufficiently accurate, while the ray approximation significantly overestimates the travel times for perturbations smaller than the size of the first Fresnel zone.…”

Section: Born Approximationmentioning

confidence: 96%

See 1 more Smart Citation

Advances in Global and Local Helioseismology: An Introductory Review

Kosovichev

2011

The Pulsations of the Sun and the Stars

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Abstract. Helioseismology studies the structure and dynamics of the Sun's interior by observing oscillations on the surface. These studies provide information about the physical processes that control the evolution and magnetic activity of the Sun. In recent years, helioseismology has made substantial progress towards the understanding of the physics of solar oscillations and the physical processes inside the Sun, thanks to observational, theoretical and modeling efforts. In addition to the global seismology of the Sun based on measurements of global oscillation modes, a new field of local helioseismology, which studies oscillation travel times and local frequency shifts, has been developed. It is capable of providing 3D images of the subsurface structures and flows. The basic principles, recent advances and perspectives of global and local helioseismology are reviewed in this article.

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Section: Born Approximationmentioning

confidence: 96%

“…The development of a more accurate theory for the travel times, based on the Born approximation is currently under way [156,160,161,157,158]. One unexpected feature of the single-source travel-time kernels calculated in the Born approximation is that these kernels have zero value along the ray path (called 'banana-doughnut kernels').…”

Section: Born Approximationmentioning

confidence: 99%

Advances in Global and Local Helioseismology: An Introductory Review

Kosovichev

2011

The Pulsations of the Sun and the Stars

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“…Although an acousticwave theory for time-distance helioseismology is under development (Birch & Kosovichev 2000;, it was argued that ray approximation could give credible inversion results with fewer computations (Birch et al 2001;Jensen et al 2001). Because of a cross-talk effect between the horizontal divergence and the vertical flows in time-distance measurement (Kosovichev & Duvall 1997), the weak vertical flows in the quiet solar regions derived from our inversions are considered less reliable than the stronger vertical velocity in active regions (Zhao & Kosovichev 2003).…”

Section: Data Reductionmentioning

confidence: 99%

Torsional Oscillation, Meridional Flows, and Vorticity Inferred in the Upper Convection Zone of the Sun by Time‐Distance Helioseismology

Zhao

Kosovichev

2004

ApJ

314

241

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By applying time-distance helioseismology measurements and inversions to Solar and Heliospheric Observatory (SOHO) Michelson Doppler Imager (MDI) dynamics campaign data, we obtain synoptic maps of subsurface plasma-flow fields at a depth of 0-12 Mm for seven solar Carrington rotations, covering the years 1996-2002, from solar-activity minimum to maximum. Vorticity distribution and both zonal and meridional flows are derived from such synoptic flow maps, which contain an enormous amount of information about solar dynamics. The results for the zonal flows agree well with previous results. The meridional flows of an order of 20 m s À1 are found to remain poleward during the whole period of observations. In addition to the poleward meridional flows observed at the solar minimum, extra meridional circulation cells of flow converging toward the activity belts are found in both hemispheres, which may imply plasma downdrafts in the activity belts. These converging flow cells migrate toward the solar equator together with the activity belts as the solar cycle evolves. The vorticity distributions are largely linear with latitude, and the deviations from the vorticity caused by the mean differential rotation are presented. Patterns of large-scale flows are investigated for a large active region at different depths. Converging flows toward the center of the active region are found near the solar surface, and divergent flows in this large active region are found to be rooted much deeper than similar flows observed in individual sunspots. We conclude that the extremely rich and complicated dynamics of the upper convection zone reveal remarkable organization on the large scale, which can be correlated with the magnetic activity zones.

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“…In these models, the Born approximation is typically seen to be valid when travel-time shifts are a small fraction of the wave period. The validity of the Born approximation for scattering from steady soundspeed inhomogeneities has been studied extensively in the context of earth seismology and helioseismology (e.g., Fan et al 1995;Hung et al 2000;Birch et al 2001;Baig et al 2003). In these studies, it is again typical that the Born approximation is valid when travel-time shifts are small compared to the mean wave period (although it can sometimes be valid well past this limit).…”

Section: Forward Modelsmentioning

confidence: 99%

Helioseismic Holography of Simulated Solar Convection and Prospects for the Detection of Small‐Scale Subsurface Flows

Braun

Birch

Benson

et al. 2007

ApJ

Self Cite

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We perform helioseismic holography on realistic solar convection simulations and compare the observed traveltime perturbations with the expected travel times from the horizontal flows in the simulations computed from forward models under the assumption of the Born approximation. We demonstrate reasonable agreement between the observed and model travel times, which reinforces the validity of helioseismic holography in the detection of subsurface horizontal flows. An assessment is made of the uncertainty of the measured p-mode travel times from the rms of the residuals. From the variation of the signal-to-noise ratio with depth we conclude that the helioseismic detection of individual flow structures with spatial scales of supergranulation or smaller is not possible for depths below about 5 Mm below the surface over timescales of less than a day. The travel-time noise estimated from these simulations appears to be similar to noise in measurements made using solar observations. We therefore suggest that similar limitations exist regarding the detection of analogous subsurface flows in the Sun. A study of the depth dependence of the contribution to the travel-time perturbations for focus depths between 3 and 7 Mm is made, showing that approximately half of the observed signal originates within the first 2 Mm below the surface. A consequence of this is a rapid decrease (and reversal in some cases) of the travel-time perturbations with depth due to the contribution to the measurements of oppositely directed surface flows in neighboring convective cells. This confirms an earlier interpretation of similar effects reported from observations of supergranulation. Subject headingg s: Sun: helioseismology -Sun: interior

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The Accuracy of the Born and Ray Approximations in Time-Distance Helioseismology

Cited by 47 publications

References 19 publications

Advances in Global and Local Helioseismology: An Introductory Review

Advances in Global and Local Helioseismology: An Introductory Review

Torsional Oscillation, Meridional Flows, and Vorticity Inferred in the Upper Convection Zone of the Sun by Time‐Distance Helioseismology

Helioseismic Holography of Simulated Solar Convection and Prospects for the Detection of Small‐Scale Subsurface Flows

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