The cross-phase spectrum provides a powerful tool to identify the eigenfrequencies of the magnetospheric field lines. At the eigenfrequency of a field line centered between two neighboring stations in a north-south chain the phase difference maximizes[Best et al., 1986; Waters et al., 1991; Green et al., 1993]. Waters et al.  showed that the patterns of the maximum phase differences in the cross-phase spectrograms were observed consistently from day to day in the dayside region over baselines of about 100 km in the magnetic meridian. They found that this technique is superior to other eigenfrequency identifiers, such as the amplitude-difference method proposed by Baransky et al. . Green et al.  also reported that, among the several methods that determine the resonant frequency, the phase shift is least affected by geologic inhomogeneity and consistently defines the resonant frequencies. As a tool for "observing" the eigenfrequencies of field lines, the cross-phase method has shown its potential in remotely sensing the plasma mass density in the plasmasphere [Waters et al., 1996] and comparing different ionosphere models [Waters et al., 1994].
Many authors have contributed to the study of standing waves on magnetospheric field lines [Chen and Hasegawa, 1974; Southwood, 1974; Hughes and Southwood, 1976]. In particular, Southwood  has shown that the phase of the H component changes across the resonant point. This theory predicts the scale length for this phase change and the phase change in the other components. The model proposed by Waters et al.  does not derive from this theory. Rather it uses a model of two simple harmonic oscillators to describe the oscillations of field lines at the latitudes of the two stations, both driven by a pump wave. The results depend on the Q of the resonators and the relationship between the driving frequency and the resonant frequencies. In this study, we show that the original field line resonance theory and the ionospheric effects on pulsation signals [Hughes and Southwood, 1976] can explain the properties of the cross-phase spectrum of pulsations. We also show why the simplified oscillators model has limited capability in interpreting these observations.
We use the data from a comparatively longer chain of stations than the ones that have been used by previous observers on this topic. In addition, we extend the cross-phase technique by considering all three components and overlapping station pairs.