Comparison of Travel-Time and Amplitude Measurements for Deep-Focusing Time–Distance Helioseismology

Abstract

The purpose of deep-focusing time-distance helioseismology is to construct seismic measurements that have a high sensitivity to the physical conditions at a desired target point in the solar interior. With this technique, pairs of points on the solar surface are chosen such that acoustic ray paths intersect at this target (focus) point. Considering acoustic waves in a homogeneous medium, we compare travel-time and amplitude measurements extracted from the deepfocusing cross-covariance functions. Using a single-scattering approximation, we find that the spatial sensitivity of deep-focusing travel times to sound-speed perturbations is zero at the target location and maximum in a surrounding shell. This is unlike the deep-focusing amplitude measurements, which have maximum sensitivity at the target point. We compare the signal-to-noise ratio for traveltime and amplitude measurements for different types of sound-speed perturbations, under the assumption that noise is solely due to the random excitation of the waves. We find that, for highly localized perturbations in sound speed, the signal-to-noise ratio is higher for amplitude measurements than for traveltime measurements. We conclude that amplitude measurements are a useful complement to travel-time measurements in time-distance helioseismology.

Quantitative passive imaging by iterative holography: the example of helioseismic holography

“…In all three cases, we have achieved reconstructions with a resolution of slightly less than half of the local wave-length by the iteratively regularized Gauss-Newton method, even for strong realization noise. This is well below the spatial resolution of traditional time-distance helioseismology (see [15]).…”

“…In traditional approaches, like time-distance helioseismology, the cross-correlations are reduced to a smaller number of observable quantities, such as travel times [1] or cross-correlation amplitudes (e.g. [13][14][15]). Since the reduction to these quantities leads to a loss in information, we are interested in using the whole cross-correlation data throughout the inversion procedure, stepping forward to full waveform inversions.…”

Signal and noise in helioseismic holography

“…This confirms the claim by Lindsey & Braun (1997, 2000a) that helioseismic holography is diffraction-limited. In that sense, helioseismic holography is superior to deep-focusing time-distance helioseismology, which gives lower spatial resolution (Munk 2001;Pourabdian et al 2018).…”