Sensitivity Kernels for Flows in Time-Distance Helioseismology: Extension to Spherical Geometry

TL;DR

This paper extends the Born approximation method for helioseismic travel-time sensitivity kernels from Cartesian to spherical geometry, enabling better inference of large-scale solar interior flows.

Contribution

It develops a spherical geometry extension of the Born approximation for helioseismic kernels and validates it through comparisons and consistency tests.

Findings

Spherical kernels agree with Cartesian kernels within 0.3%.

Travel-time differences match analytical and modeled results within 2%.

Kernel sensitivity depends on filter choice and mode degree.

Abstract

We extend an existing Born approximation method for calculating the linear sensitivity of helioseismic travel times to flows from Cartesian to spherical geometry. This development is necessary for using the Born approximation for inferring large-scale flows in the deep solar interior. In a first sanity check, we compare two $f-$mode kernels from our spherical method and from an existing Cartesian method. The horizontal and total integrals agree to within 0.3 %. As a second consistency test, we consider a uniformly rotating Sun and a travel distance of 42 degrees. The analytical travel-time difference agrees with the forward-modelled travel-time difference to within 2 %. In addition, we evaluate the impact of different choices of filter functions on the kernels for a meridional travel distance of 42 degrees. For all filters, the sensitivity is found to be distributed over a large fraction of the convection zone. We show that the kernels depend on the filter function employed in the data analysis process. If modes of higher harmonic degree ($90\lesssim l \lesssim 170$) are permitted, a noisy pattern of a spatial scale corresponding to $l\approx 260$ appears near the surface. When mainly low-degree modes are used ($l\lesssim70$), the sensitivity is concentrated in the deepest regions and it visually resembles a ray-path-like structure. Among the different low-degree filters used, we find the kernel for phase-speed filtered measurements to be best localized in depth.