### 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. As 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 42ï¿½. The analytical travel-time difference agrees with the forward-modeled 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 42ï¿½. 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 ≲ l ≲ 170) are permitted, a noisy pattern of a spatial scale corresponding to l ≈ 260 appears near the surface. When mainly low-degree modes are used (l ≲ 70), 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.

Original language | English (US) |
---|---|

Article number | 49 |

Journal | Astrophysical Journal |

Volume | 824 |

Issue number | 1 |

DOIs | |

State | Published - Jun 10 2016 |

### Fingerprint

### Keywords

- scattering
- Sun: helioseismology
- Sun: interior
- Sun: oscillations
- waves

### ASJC Scopus subject areas

- Astronomy and Astrophysics
- Space and Planetary Science

### Cite this

*Astrophysical Journal*,

*824*(1), [49]. https://doi.org/10.3847/0004-637X/824/1/49

**SENSITIVITY KERNELS for FLOWS in TIME-DISTANCE HELIOSEISMOLOGY : EXTENSION to SPHERICAL GEOMETRY.** / Bï¿½ning, Vincent G.A.; Roth, Markus; Zima, Wolfgang; Birch, Aaron C.; Gizon, Laurent.

Research output: Contribution to journal › Article

*Astrophysical Journal*, vol. 824, no. 1, 49. https://doi.org/10.3847/0004-637X/824/1/49

}

TY - JOUR

T1 - SENSITIVITY KERNELS for FLOWS in TIME-DISTANCE HELIOSEISMOLOGY

T2 - EXTENSION to SPHERICAL GEOMETRY

AU - Bï¿½ning, Vincent G.A.

AU - Roth, Markus

AU - Zima, Wolfgang

AU - Birch, Aaron C.

AU - Gizon, Laurent

PY - 2016/6/10

Y1 - 2016/6/10

N2 - 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. As 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 42ï¿½. The analytical travel-time difference agrees with the forward-modeled 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 42ï¿½. 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 ≲ l ≲ 170) are permitted, a noisy pattern of a spatial scale corresponding to l ≈ 260 appears near the surface. When mainly low-degree modes are used (l ≲ 70), 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.

AB - 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. As 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 42ï¿½. The analytical travel-time difference agrees with the forward-modeled 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 42ï¿½. 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 ≲ l ≲ 170) are permitted, a noisy pattern of a spatial scale corresponding to l ≈ 260 appears near the surface. When mainly low-degree modes are used (l ≲ 70), 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.

KW - scattering

KW - Sun: helioseismology

KW - Sun: interior

KW - Sun: oscillations

KW - waves

UR - http://www.scopus.com/inward/record.url?scp=84976382138&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84976382138&partnerID=8YFLogxK

U2 - 10.3847/0004-637X/824/1/49

DO - 10.3847/0004-637X/824/1/49

M3 - Article

VL - 824

JO - Astrophysical Journal

JF - Astrophysical Journal

SN - 0004-637X

IS - 1

M1 - 49

ER -