*Earth Planets Space,* Vol. 65 (No. 5), pp. 435-446, 2013

doi:10.5047/eps.2013.02.007

##
Hodograph method to estimate the latitudinal profile of the field-line resonance frequency using the data from two ground magnetometers

V. A. Pilipenko^{1,2}, H. Kawano^{3,4}, and I. R. Mann^{5}

^{1}Institute of the Earth Physics, Moscow 123995, Russia

^{2}Solar-Terrestrial Environment Laboratory, Nagoya University, Nagoya 464-8601, Japan

^{3}Department of Earth and Planetary Sciences, Kyushu University, Fukuoka 812-8581, Japan

^{4}International Center for Space Weather Science and Education, Kyushu University, Fukuoka 812-8581, Japan

^{5}Department of Physics, University of Alberta, Alberta T6G 2E1, Canada

(Received July 4, 2012; Revised January 12, 2013; Accepted February 27, 2013; Online published June 10, 2013)

**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.

**Key words: **
Hodograph method, field-line resonance, ground magnetometers, amplitude-phase gradient method.

Corresponding author E-mail: hkawano@geo.kyushu-u.ac.jp

[Full text] (PDF 644 KB)