### Abstract

For a given misfit function, a specified optimality measure of a model, its gradient describes the manner in which one may alter properties of the system to march toward a stationary point. The adjoint method, arising from partial-differential-equation-constrained optimization, describes a means of extracting derivatives of a misfit function with respect to model parameters through finite computation. It relies on the accurate calculation of wavefields that are driven by two types of sources, namely, the average wave-excitation spectrum, resulting in the forward wavefield, and differences between predictions and observations, resulting in an adjoint wavefield. All sensitivity kernels relevant to a given measurement emerge directly from the evaluation of an interaction integral involving these wavefields. The technique facilitates computation of sensitivity kernels (Fréchet derivatives) relative to three-dimensional heterogeneous background models, thereby paving the way for nonlinear iterative inversions. An algorithm to perform such inversions using as many observations as desired is discussed.

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

Article number | 100 |

Journal | Astrophysical Journal |

Volume | 738 |

Issue number | 1 |

DOIs | |

State | Published - Sep 1 2011 |

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### Keywords

- magnetohydrodynamics (MHD)
- Sun: dynamo
- Sun: helioseismology
- Sun: interior
- Sun: oscillations
- waves

### ASJC Scopus subject areas

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

### Cite this

*Astrophysical Journal*,

*738*(1), [100]. https://doi.org/10.1088/0004-637X/738/1/100

**The adjoint method applied to time-distance helioseismology.** / Hanasoge, Shravan; Birch, Aaron; Gizon, Laurent; Tromp, Jeroen.

Research output: Contribution to journal › Article

*Astrophysical Journal*, vol. 738, no. 1, 100. https://doi.org/10.1088/0004-637X/738/1/100

}

TY - JOUR

T1 - The adjoint method applied to time-distance helioseismology

AU - Hanasoge, Shravan

AU - Birch, Aaron

AU - Gizon, Laurent

AU - Tromp, Jeroen

PY - 2011/9/1

Y1 - 2011/9/1

N2 - For a given misfit function, a specified optimality measure of a model, its gradient describes the manner in which one may alter properties of the system to march toward a stationary point. The adjoint method, arising from partial-differential-equation-constrained optimization, describes a means of extracting derivatives of a misfit function with respect to model parameters through finite computation. It relies on the accurate calculation of wavefields that are driven by two types of sources, namely, the average wave-excitation spectrum, resulting in the forward wavefield, and differences between predictions and observations, resulting in an adjoint wavefield. All sensitivity kernels relevant to a given measurement emerge directly from the evaluation of an interaction integral involving these wavefields. The technique facilitates computation of sensitivity kernels (Fréchet derivatives) relative to three-dimensional heterogeneous background models, thereby paving the way for nonlinear iterative inversions. An algorithm to perform such inversions using as many observations as desired is discussed.

AB - For a given misfit function, a specified optimality measure of a model, its gradient describes the manner in which one may alter properties of the system to march toward a stationary point. The adjoint method, arising from partial-differential-equation-constrained optimization, describes a means of extracting derivatives of a misfit function with respect to model parameters through finite computation. It relies on the accurate calculation of wavefields that are driven by two types of sources, namely, the average wave-excitation spectrum, resulting in the forward wavefield, and differences between predictions and observations, resulting in an adjoint wavefield. All sensitivity kernels relevant to a given measurement emerge directly from the evaluation of an interaction integral involving these wavefields. The technique facilitates computation of sensitivity kernels (Fréchet derivatives) relative to three-dimensional heterogeneous background models, thereby paving the way for nonlinear iterative inversions. An algorithm to perform such inversions using as many observations as desired is discussed.

KW - magnetohydrodynamics (MHD)

KW - Sun: dynamo

KW - Sun: helioseismology

KW - Sun: interior

KW - Sun: oscillations

KW - waves

UR - http://www.scopus.com/inward/record.url?scp=80052783059&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=80052783059&partnerID=8YFLogxK

U2 - 10.1088/0004-637X/738/1/100

DO - 10.1088/0004-637X/738/1/100

M3 - Article

VL - 738

JO - Astrophysical Journal

JF - Astrophysical Journal

SN - 0004-637X

IS - 1

M1 - 100

ER -