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Surface-Focused Seismic Holography of Sunspots: II. Expectations from Numerical Simulations Using Sound-Speed Perturbations

Abstract

Helioseismic observations of sunspots show that wave travel times, at fixed horizontal phase speed, depend on the temporal frequency of the waves employed in the data analysis. This frequency variation has been suggested to be consistent with near-surface (vertical length scales of order one Mm or smaller) changes in wave propagation properties relative to the quiet Sun. We investigate this suggestion by employing numerical simulations of acoustic-wave propagation through models with horizontally and vertically inhomogeneous structure. Standard methods of surface-focused helioseismic holography are applied to the resulting simulated wave fields. We find that the travel-time shifts measured using holography from the simulations with deep sound-speed perturbations (relative to a plane-parallel quiet-Sun model) do not show a systematic frequency dependence at phase speeds above about 20 km s−1. However, shallow sound-speed perturbations, similar to those proposed to model the acoustic scattering properties of sunspots observed with Hankel analysis, produce systematic frequency dependence at these phase speeds. In both cases, positive travel-time shifts can be caused by positive sound-speed perturbations. The details of the travel-time shifts are, however, model dependent.

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Correspondence to A. C. Birch.

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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.

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Birch, A.C., Braun, D.C., Hanasoge, S.M. et al. Surface-Focused Seismic Holography of Sunspots: II. Expectations from Numerical Simulations Using Sound-Speed Perturbations. Sol Phys 254, 17–27 (2009). https://doi.org/10.1007/s11207-008-9282-9

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Keywords

  • Helioseismology, forward modeling
  • Helioseismology, theory
  • Waves, propagation