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.
维普
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