### 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) |
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Article number | 100 |

Journal | Astrophysical Journal |

Volume | 738 |

Issue number | 1 |

DOIs | |

State | Published - Sep 1 2011 |

### All Science Journal Classification (ASJC) codes

- Astronomy and Astrophysics
- Space and Planetary Science

### Keywords

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

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## Cite this

*Astrophysical Journal*,

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