Signal and noise in helioseismic holography

Abstract

Helioseismic holography is an imaging technique used to study heterogeneities and flows in the solar interior from observations of solar oscillations at the surface. Holograms contain noise due to the stochastic nature of solar oscillations. We provide a theoretical framework for modeling signal and noise in Porter-Bojarski helioseismic holography. The wave equation may be recast into a Helmholtz-like equation, so as to connect with the acoustics literature and define the holography Green's function in a meaningful way. Sources of wave excitation are assumed to be stationary, horizontally homogeneous, and spatially uncorrelated. Using the first Born approximation we calculate holograms in the presence of perturbations in sound-speed, density, flows, and source covariance, as well as the noise level as a function of position. This work is a direct extension of the methods used in time-distance helioseismology to model signal and noise. To illustrate the theory, we compute the hologram intensity numerically for a buried sound-speed perturbation at different depths in the solar interior. The reference Green's function is obtained for a spherically-symmetric solar model using a finite-element solver in the frequency domain. Below the pupil area on the surface, we find that the spatial resolution of the hologram intensity is very close to half the local wavelength. For a sound-speed perturbation of size comparable to the local spatial resolution, the signal-to-noise ratio is approximately constant with depth. Averaging the hologram intensity over a number $N$ of frequencies above 3 mHz increases the signal-to-noise ratio by a factor nearly equal to the square root of $N$. This may not be the case at lower frequencies, where large variations in the holographic signal are due to the individual contributions of the long-lived modes of oscillation.

arXiv commentSubmitted to Astronomy and Astrophysics

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Cited by in corpus (8)

• The Polarimetric and Helioseismic Imager on Solar Orbiter
• The Solar Orbiter Science Activity Plan: translating solar and heliospheric physics questions into action
• Imaging individual active regions on the Sun's far side with improved helioseismic holography
• Weighted Data Spaces for Correlation-Based Array Imaging in Experimental Aeroacoustics
• Uniqueness of an inverse source problem in experimental aeroacoustics
• Direct assessment of SDO/HMI helioseismology of active regions on the Sun's far side using SO/PHI magnetograms
• Analysis of Time-Distance Helioseismology for Detection of Emerging Active Regions
• Quantitative passive imaging by iterative holography: The example of helioseismic holography