摘要：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.
