3,092 research outputs found

    Travel Time Shifts due to Amplitude Modulation in Time-Distance Helioseismology

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    Correct interpretation of acoustic travel times measured by time-distance helioseismology is essential to get an accurate understanding of the solar properties that are inferred from them. It has long been observed that sunspots suppress p-mode amplitude, but its implications on travel times has not been fully investigated so far. It has been found in test measurements using a 'masking' procedure, in which the solar Doppler signal in a localized quiet region of the Sun is artificially suppressed by a spatial function, and using numerical simulations that the amplitude modulations in combination with the phase-speed filtering may cause systematic shifts of acoustic travel times. To understand the properties of this procedure, we derive an analytical expression for the cross-covariance of a signal that has been modulated locally by a spatial function that has azimuthal symmetry, and then filtered by a phase speed filter typically used in time-distance helioseismology. Comparing this expression to the Gabor wavelet fitting formula without this effect, we find that there is a shift in the travel times, that is introduced by the amplitude modulation. The analytical model presented in this paper can be useful also for interpretation of travel time measurements for non-uniform distribution of oscillation amplitude due to observational effects.Comment: 17 pages, 1 figure, accepted for publication in Ap

    Fast integral equation methods for the Laplace-Beltrami equation on the sphere

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    Integral equation methods for solving the Laplace-Beltrami equation on the unit sphere in the presence of multiple "islands" are presented. The surface of the sphere is first mapped to a multiply-connected region in the complex plane via a stereographic projection. After discretizing the integral equation, the resulting dense linear system is solved iteratively using the fast multipole method for the 2D Coulomb potential in order to calculate the matrix-vector products. This numerical scheme requires only O(N) operations, where NN is the number of nodes in the discretization of the boundary. The performance of the method is demonstrated on several examples
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