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Phase Inversion: Inferring Solar Subphotospheric Flow and Other Asphericity from the Distortion of Acoustic WavesA method is proposed for analyzing an almost monochromatic train of waves propagating in a single direction in an inhomogeneous medium that is not otherwise changing in time. An effective phase is defined in terms of the Hilbert transform of the wave function, which is related, via the JWKB approximation, to the spatial variation of the background state against which the wave is propagating. The contaminating effect of interference between the truly monochromatic components of the train is eliminated using its propagation properties. Measurement errors, provided they are uncorrelated, are manifest as rapidly varying noise; although that noise can dominate the raw phase-processed signal, it can largely be removed by low-pass filtering. The intended purpose of the analysis is to determine the distortion of solar oscillations induced by horizontal structural variation and material flow. It should be possible to apply the method directly to sectoral modes. The horizontal phase distortion provides a measure of longitudinally averaged properties of the Sun in the vicinity of the equator, averaged also in radius down to the depth to which the modes penetrate. By combining such averages from different modes, the two-dimensional variation can be inferred by standard inversion techniques. After taking due account of horizontal refraction, it should be possible to apply the technique also to locally sectoral modes that propagate obliquely to the equator and thereby build a network of lateral averages at each radius, from which the full three-dimensional structure of the Sun can, in principle, be determined as an inverse Radon transform.
Document ID
Document Type
Reprint (Version printed in journal)
External Source(s)
Gough, Douglas (Institute of Astronomy Cambridge, United Kingdom)
Merryfield, William J. (Institute of Ocean Sciences Sidney, British Columbia Canada)
Toomre, Juri (Colorado Univ. Boulder, CO United States)
Date Acquired
August 19, 2013
Publication Date
July 10, 1998
Publication Information
Publication: Astrophysical Journal
Volume: 501
Subject Category
Solar Physics
Funding Number(s)
Distribution Limits