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

TL;DR

This paper compares travel-time and amplitude measurements in deep-focusing helioseismology, revealing that amplitude measurements have higher sensitivity at the target point and better signal-to-noise ratios for localized sound-speed perturbations.

Contribution

It demonstrates that amplitude measurements can complement travel-time measurements by providing higher sensitivity at the target location in deep-focusing helioseismology.

Findings

Amplitude measurements have maximum sensitivity at the target point.

Travel-time sensitivity is zero at the target and peaks in a surrounding shell.

Amplitude measurements show higher signal-to-noise ratio for localized perturbations.

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 deep-focusing 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 travel-time 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 travel-time measurements. We conclude that amplitude measurements are a useful complement to travel-time measurements in time--distance helioseismology.