The amplitude of the cross-covariance function of solar oscillations as a diagnostic tool for wave attenuation and geometrical spreading

Abstract

Context. In time-distance helioseismology, wave travel times are measured from the two-point cross-covariance function of solar oscillations and are used to image the solar convection zone in three dimensions. There is, however, also information in the amplitude of the cross-covariance function, for example about seismic wave attenuation. Aims. Here we develop a convenient procedure to measure the amplitude of the cross-covariance function of solar oscillations. Methods. In this procedure, the amplitude of the cross-covariance function is linearly related to the cross-covariance function and can be measured even for high levels of noise. Results. As an example application, we measure the amplitude perturbations of the seismic waves that propagate through the sunspot in active region NOAA 9787. We can recover the amplitude variations due to the scattering and attenuation of the waves by the sunspot and associated finite-wavelength effects. Conclusions. The proposed definition of cross-covariance amplitude is robust to noise, can be used to relate measured amplitudes to 3D perturbations in the solar interior under the Born approximation, and will provide independent information from the travel times.

arXiv commentaccepted for publication in A&A

References in corpus (6)

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• Sensitivity kernels for time-distance helioseismology: efficient computation for spherically-symmetric solar models
• Quantitative passive imaging by iterative holography: The example of helioseismic holography
• Comparison of Travel-Time and Amplitude Measurements for Deep-Focusing Time--Distance Helioseismology
• A general formulation for computing spherical helioseismic sensitivity kernels while incorporating systematical effects
• Helioseismic finite-frequency sensitivity kernels for flows in spherical geometry including systematic effects