Fig. 8

a For the 10 substorm events listed in Table 1, the phase velocity of Pi2 disturbance of δB _x , δB _y , and δB _z observed by Th D and Th E spacecraft versus the velocity of the wave-like arc brightening structure. The positive (negative) moving velocity of wave-like arc brightening structure indicates westward (eastward) variation. The positive (negative) phase velocity of Pi2 δB _y disturbance means propagation from Th D to Th E (from Th E to Th D). b The phase velocity of Pi2 disturbance versus the velocity of the wave-like arc brightness structure movement mapped to the equatorial position using the T96 model. We also mark the standard deviation of the data points with respect to the perfect match line (dashed line)