### Abstract

The hodograph method enables estimating the latitudinal profile of the field-line resonance (FLR) frequency (f_{R}) using the data from two ground magnetometers. This paper provides the full details of this method for the first time,and uses a latitudinal chain of ground magnetometers to examine its validity and usefulness. The hodograph method merges the widely-used amplitude-ratio and cross-phase methods in a sense that the hodograph method uses both the amplitude ratio and the phase difference in a unified manner; further than that,the hodograph method provides f_{R} at any latitude near those of the two ground magnetometers. It is accomplished by (1) making a complex number by using the amplitude ratio (phase difference) as its real (imaginary) part; (2) drawing thus obtained complex numbers (one number for one frequency) in the complex plane to make a hodograph; and (3) fitting to thus obtained hodograph a model satisfying the FLR condition,which is a circle with the assumption that the resonance width is independent of the latitude. To examine the validity and usefulness of the hodograph method,we apply it to a Pc 4 event observed by the Scandinavian BEAR array. We also apply the amplitude-phase gradient method (Pilipenko and Fedorov, 1994; Kawano et al., 2002) to the same event,and compare the results; this is the first article applying the both methods to the same dataset.

Original language | English |
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Pages (from-to) | 435-446 |

Number of pages | 12 |

Journal | earth, planets and space |

Volume | 65 |

Issue number | 5 |

DOIs | |

Publication status | Published - 2013 |

### All Science Journal Classification (ASJC) codes

- Geology
- Space and Planetary Science

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## Cite this

*earth, planets and space*,

*65*(5), 435-446. https://doi.org/10.5047/eps.2013.02.007