### Abstract

Inferring interior properties of the Sun from photospheric measurements of the seismic wavefield constitutes the helioseismic inverse problem. Deviations in seismic measurements (such as wave travel times) from their fiducial values estimated for a given model of the solar interior imply that the model is inaccurate. Contemporary inversions in local helioseismology assume that properties of the solar interior are linearly related to measured travel-time deviations. It is widely known, however, that this assumption is invalid for sunspots and active regions and is likely for supergranular flows. Here, we introduce nonlinear optimization, executed iteratively, as a means of inverting for the subsurface structure of large-amplitude perturbations. Defining the penalty functional as the L _{2} norm of wave travel-time deviations, we compute the total misfit gradient of this functional with respect to the relevant model parameters at each iteration around the corresponding model. The model is successively improved using either steepest descent, conjugate gradient, or the quasi-Newton limited-memory Broyden-Fletcher-Goldfarb-Shanno algorithm. Performing nonlinear iterations requires privileging pixels (such as those in the near field of the scatterer), a practice that is not compliant with the standard assumption of translational invariance. Measurements for these inversions, although similar in principle to those used in time-distance helioseismology, require some retooling. For the sake of simplicity in illustrating the method, we consider a two-dimensional inverse problem with only a sound-speed perturbation.

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

Article number | 69 |

Journal | Astrophysical Journal |

Volume | 784 |

Issue number | 1 |

DOIs | |

State | Published - Mar 20 2014 |

### Fingerprint

### Keywords

- helioseismology - waves
- Sun

### ASJC Scopus subject areas

- Space and Planetary Science
- Astronomy and Astrophysics
- Nuclear and High Energy Physics

### Cite this

*Astrophysical Journal*,

*784*(1), [69]. https://doi.org/10.1088/0004-637X/784/1/69

**Full waveform inversion for time-distance helioseismology.** / Hanasoge, Shravan; Tromp, Jeroen.

Research output: Contribution to journal › Article

*Astrophysical Journal*, vol. 784, no. 1, 69. https://doi.org/10.1088/0004-637X/784/1/69

}

TY - JOUR

T1 - Full waveform inversion for time-distance helioseismology

AU - Hanasoge, Shravan

AU - Tromp, Jeroen

PY - 2014/3/20

Y1 - 2014/3/20

N2 - Inferring interior properties of the Sun from photospheric measurements of the seismic wavefield constitutes the helioseismic inverse problem. Deviations in seismic measurements (such as wave travel times) from their fiducial values estimated for a given model of the solar interior imply that the model is inaccurate. Contemporary inversions in local helioseismology assume that properties of the solar interior are linearly related to measured travel-time deviations. It is widely known, however, that this assumption is invalid for sunspots and active regions and is likely for supergranular flows. Here, we introduce nonlinear optimization, executed iteratively, as a means of inverting for the subsurface structure of large-amplitude perturbations. Defining the penalty functional as the L 2 norm of wave travel-time deviations, we compute the total misfit gradient of this functional with respect to the relevant model parameters at each iteration around the corresponding model. The model is successively improved using either steepest descent, conjugate gradient, or the quasi-Newton limited-memory Broyden-Fletcher-Goldfarb-Shanno algorithm. Performing nonlinear iterations requires privileging pixels (such as those in the near field of the scatterer), a practice that is not compliant with the standard assumption of translational invariance. Measurements for these inversions, although similar in principle to those used in time-distance helioseismology, require some retooling. For the sake of simplicity in illustrating the method, we consider a two-dimensional inverse problem with only a sound-speed perturbation.

AB - Inferring interior properties of the Sun from photospheric measurements of the seismic wavefield constitutes the helioseismic inverse problem. Deviations in seismic measurements (such as wave travel times) from their fiducial values estimated for a given model of the solar interior imply that the model is inaccurate. Contemporary inversions in local helioseismology assume that properties of the solar interior are linearly related to measured travel-time deviations. It is widely known, however, that this assumption is invalid for sunspots and active regions and is likely for supergranular flows. Here, we introduce nonlinear optimization, executed iteratively, as a means of inverting for the subsurface structure of large-amplitude perturbations. Defining the penalty functional as the L 2 norm of wave travel-time deviations, we compute the total misfit gradient of this functional with respect to the relevant model parameters at each iteration around the corresponding model. The model is successively improved using either steepest descent, conjugate gradient, or the quasi-Newton limited-memory Broyden-Fletcher-Goldfarb-Shanno algorithm. Performing nonlinear iterations requires privileging pixels (such as those in the near field of the scatterer), a practice that is not compliant with the standard assumption of translational invariance. Measurements for these inversions, although similar in principle to those used in time-distance helioseismology, require some retooling. For the sake of simplicity in illustrating the method, we consider a two-dimensional inverse problem with only a sound-speed perturbation.

KW - helioseismology - waves

KW - Sun

UR - http://www.scopus.com/inward/record.url?scp=84896756823&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84896756823&partnerID=8YFLogxK

U2 - 10.1088/0004-637X/784/1/69

DO - 10.1088/0004-637X/784/1/69

M3 - Article

AN - SCOPUS:84896756823

VL - 784

JO - Astrophysical Journal

JF - Astrophysical Journal

SN - 0004-637X

IS - 1

M1 - 69

ER -