Shue et al.在1997年提出了一個數學函數，r =r0 [ 2 / ( 1 + cos(theta))]^(alpha)，r 和theta是表示磁層頂的位置，而大小與形狀藉由式中的r0 和alpha來描述。theta是天頂角；r 是在某特定theta角下由地球中心到磁層頂之長度；r0是在theta角等於零時由地球中心到磁層頂之長度，亦即the standoff distance；alpha為the level of tail flaring，用於描述磁層頂側邊磁尾的開放程度。由Shue et al. [1997]的模式可知，太陽風上游地區的行星際磁場南北分量(Bz)和動壓(Dp)與r0 和alpha有關。以Shue et al. [1997]的模式做基礎，研究三維情況下磁層頂的位置，由於原模式為二維，所以在這次的研究中加入另一變數phi，用於表示另一維度。1997年Shue et al.的研究中，使用ISEE 1 and 2, AMPTE/IRM, ISEE 3 and IMP 8等五顆衛星的資料；於此次研究，除了使用上述的資料外，亦新增Hawkeye衛星提供的資料。新資料不同於舊資料，其資料點分佈為高緯區域。結果發現磁層頂的大小與形狀，於黃昏和黎明兩側有不對稱的現象，而在夜側的不對稱現象較日側明顯。 Shue et al. [1997] proposed a new function form, r =r0 [2/( 1 + cos(theta))]^(alpha), to determine the size and shape of the magnetopause, where r0 and alpha represent the standoff distance and the level of tail flaring, respectively; r is the radial distance from the center of the Earth to a point on the magnetopause and theta is the angle between the sun-earth line and the direction of r. Both the values of r0 and alpha vary with the z component of the interplanetary magnetic field and the dynamic pressure of the upstream solar wind. Shue et al. [1997] magnetopause model is constructed in 2-D under an assumption of axis-symmetry on the sun-earth line. In our study, we remove the assumption and extend the model to 3-D with an additional variable phi, which is the angle between the z axis and the projection of r on the y-z plane in GSM. We use the low-latitude magnetopause crossing data obtained from ISEE 1 and 2, AMPTE/IRM, ISEE 3 and IMP-8, with an additional set of highlatitude Hawkeye magnetopause crossing data. We are able to study relationships between phi and alpha; it is found that the magnetopause location has a dawn-dusk asymmetry. The asymmetry level is higher on the nightside than on the dayside.
