全球岩石圈地磁梯度张量场椭球谐模型构建方法与评估

Construction method and evaluation of ellipsoidal harmonic model of global lithospheric geomagnetic gradient tensor field

岩石圈磁梯度张量场模型可以更好地保留短波长磁场信息,更准确地表示磁异常,在辅助导航、目标定位等领域成为新的研究热点.因地球表面更接近于旋转椭球体,采用传统的球谐函数建立全球岩石圈磁场模型时,布里渊球形内极区附近有计算不收敛现象.针对该问题,本文提出了椭球坐标系下的无奇异岩石圈梯度张量模型构建方法.重新推导了半归格化约束下,球谐系数至椭球谐系数的转换关系;基于最小二乘法和积分法计算了岩石圈磁梯度张量场模型的椭球谐系数,并建立了无奇异性岩石圈磁梯度张量模型.分别计算5 km海拔高度下和300 km海拔高度下,133阶的全球岩石圈磁梯度张量场分布,验证了椭球谐建模方法可以解决布里渊球形内的部分不收敛问题.最后,采用傅里叶变换,将磁矢量Bz分量转换为磁梯度张量对模型进行评估,验证了本文方法的准确性.全球岩石圈椭球谐模型构建方法将适用于高分辨率和高精度的模型建立.

The magnetic gradient tensor field model of the lithosphere effectively retains short-wavelength magnetic field information and accurately represents magnetic anomalies,making it a prominent area of research hotspot in the fields of auxiliary navigation and target positioning.Due to Earth's proximity to a rotating ellipsoid,constructing a global lithospheric magnetic field model using traditional spherical harmonics results in computational non-convergence near the inner polar regions of the Brillouin sphere.To address this issue,we propose a method for building a non-singular lithospheric gradient tensor model in an ellipsoidal coordinate system.We derive the transformation relationship between spherical and ellipsoidal harmonic coefficients under semi-normalization constraints.Using the least squares method and an integration technique,we calculate the ellipsoidal harmonic coefficients for the lithospheric magnetic gradient tensor field model and establish a non-singular model.We compute the global distribution of the lithospheric magnetic gradient tensor field up to degree 133 at altitudes of 5 km and 300 km.Our results confirm that the ellipsoidal harmonic modeling approach resolves the issue of partial non-convergence within the Brillouin sphere.Lastly,we use the Fourier transform to convert the magnetic vector Bz into a magnetic gradient tensor,validating the accuracy of our proposed method.This global lithospheric ellipsoidal harmonic modeling technique is suitable for establishing high-resolution and high-precision models.